Exploring_Correlation_10_14_21.ipynb

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  "metadata": {
    "colab": {
      "name": "Exploring_Correlation_10-14-21.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true,
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/hussain0048/Machine-Learning/blob/master/Exploring_Correlation_10_14_21.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ejk9e9yNn0Vi"
      },
      "source": [
        "# **Agenda**\n",
        "\n",
        "\n",
        "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
        "    <ul>\n",
        "        <li><a href=\"https:\">Import libaray</a></li>\n",
        "        <li><a href=\"#downloading_data\">Introduction</a></li>\n",
        "        <li><a href=\"#pre-processing\">Data Loading</a></li>\n",
        "         <li><a href=\"#pre-processing\">Preprocessing</a></li>\n",
        "         <li><a href=\"#pre-processing\">Descriptiv Statistics</a></li>\n",
        "         <li><a href=\"#evaluation\">Bivariate Analysis</a></li>\n",
        "        <li><a href=\"#evaluation\">Correlation\n",
        "        <ul>\n",
        "        <li><a href=\"#evaluation\">Pearson Correlation linear Correlation </a></li>\n",
        "    </ul>\n",
        "</div>\n",
        "<br>\n",
        "<hr>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BiE4HQuXA1jb"
      },
      "source": [
        "# **Import libaray**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CYcSX5ofA8Yz"
      },
      "source": [
        "import numpy as np \n",
        "import pandas as pd \n",
        "import seaborn as sns \n",
        "import matplotlib.pyplot as plt\n",
        "from prettytable import PrettyTable\n",
        "from sklearn.metrics import roc_curve, auc\n",
        "from mlxtend.plotting import plot_confusion_matrix \n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import classification_report, confusion_matrix\n",
        "from sklearn.tree import DecisionTreeClassifier\n",
        "from sklearn.ensemble import RandomForestClassifier\n",
        "from sklearn.svm import LinearSVC\n",
        "from sklearn.linear_model import LogisticRegression\n",
        "from sklearn.neighbors import KNeighborsClassifier\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-dEH-aOwYdNx"
      },
      "source": [
        "# **Introduction**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "69-GFSEUYpQA"
      },
      "source": [
        "# **Data Loading**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ucwJyax-cZmZ"
      },
      "source": [
        "**Load data from google drive** "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fYNNsGgxmxyQ",
        "outputId": "4711ad3a-b72a-4cfe-9b47-42c77a13a378"
      },
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/drive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bkoAdyxInLR4"
      },
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "data = pd.read_csv(\"/content/drive/MyDrive/Datasets/Student field Recommendation /Placement_Data_Full_Class.csv\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OE_f4-bToHWA"
      },
      "source": [
        "data.head()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y7r4GCZ_r578"
      },
      "source": [
        "# **Preprocessing**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JL1FYrIa5kv8"
      },
      "source": [
        "**Check Missing Value**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_6sqt75_5o9y"
      },
      "source": [
        "total = data.isnull().sum().sort_values(ascending=False)\n",
        "percent = (data.isnull().sum()/data.isnull().count()).sort_values(ascending=False)\n",
        "missing = pd.concat([total, percent], axis=1, keys=['Total', 'Percent'])\n",
        "missing.head(4)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y_DhzYPtFlrL"
      },
      "source": [
        "missing_v = [col for col in data.columns if (data[col].isnull().sum()/data.shape[0]) * 100 > 0.001]\n",
        "print(len(missing_v))\n",
        "for cols in missing_v:\n",
        "    del data[cols]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "21xYr0iDF-wc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "400a2441-cda2-4a72-d4ef-33ac65abdd8e"
      },
      "source": [
        "np.sum(data.isnull().any(axis=1))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tnvVuWKg6vj1"
      },
      "source": [
        "**Hot Encoding**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2Fa0DkFL6yEq",
        "outputId": "35ec4251-e05d-42c3-f924-d592ccb55a3b"
      },
      "source": [
        "data.select_dtypes(include=['object']).columns"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Index(['gender', 'ssc_b', 'hsc_b', 'hsc_s', 'degree_t', 'workex',\n",
              "       'specialisation', 'status'],\n",
              "      dtype='object')"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7g24nkqr7Qx8"
      },
      "source": [
        "data['gender'] = data['gender'].fillna(data['gender'].mode()[0])\n",
        "data['ssc_b'] = data['ssc_b'].fillna(data['ssc_b'].mode()[0])\n",
        "data['hsc_b'] = data['hsc_b'].fillna(data['hsc_b'].mode()[0])\n",
        "data['hsc_s'] = data['hsc_s'].fillna(data['hsc_s'].mode()[0])\n",
        "data['degree_t'] = data['degree_t'].fillna(data['degree_t'].mode()[0])\n",
        "data['workex'] = data['workex'].fillna(data['workex'].mode()[0])\n",
        "data['specialisation'] = data['specialisation'].fillna(data['specialisation'].mode()[0])\n",
        "data['status'] = data['status'].fillna(data['status'].mode()[0])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fLaZar8T-YkY"
      },
      "source": [
        "from sklearn.preprocessing import LabelEncoder\n",
        "lencoders = {}\n",
        "for col in data.select_dtypes(include=['object']).columns:\n",
        "    lencoders[col] = LabelEncoder()\n",
        "    data[col] = lencoders[col].fit_transform(data[col])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w5GR2wIi-k--"
      },
      "source": [
        "data"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1X3_s7X8_hEc"
      },
      "source": [
        "**Feature Scaling**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iQgnWr7Q_jey"
      },
      "source": [
        "# Standardizing data\n",
        "from sklearn import preprocessing\n",
        "r_scaler = preprocessing.MinMaxScaler()\n",
        "r_scaler.fit(data)\n",
        "data = pd.DataFrame(r_scaler.transform(data), index=data.index, columns=data.columns)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2m6tWQEIAQfb"
      },
      "source": [
        "**Data spliting**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j9t6Ik9SAUPX"
      },
      "source": [
        "X=data.drop('specialisation',axis=1)\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f52X64tDAYXY"
      },
      "source": [
        "y=data[['specialisation']]\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5-S8fYFyApQB"
      },
      "source": [
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.30, random_state=100)\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "agw3C1c4ql5A"
      },
      "source": [
        "# **Statistical Summary**[3]"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5z3gLJtvqvew"
      },
      "source": [
        "!pip install skimpy"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ep7WoA2YrbUY"
      },
      "source": [
        "from skimpy import skim, generate_test_data\n",
        "import seaborn as sns"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nCx2Z7EqsG_P"
      },
      "source": [
        "df = sns.load_dataset(\"tips\")\n",
        "skim(df)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ItaksFxesxeP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 559
        },
        "outputId": "f843e09d-6e0d-4ea2-d70e-6bed8476172e"
      },
      "source": [
        "skim(data)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">╭───────────────────────────────────── skimpy summary ──────────────────────────────────────╮\n",
              "│ <span style=\"font-style: italic\">         Data Summary         </span> <span style=\"font-style: italic\">      Data Types       </span>                                    │\n",
              "│ ┏━━━━━━━━━━━━━━━━━━━┳━━━━━━━━┓ ┏━━━━━━━━━━━━━┳━━━━━━━┓                                    │\n",
              "│ ┃<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\"> dataframe         </span>┃<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\"> Values </span>┃ ┃<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\"> Column Type </span>┃<span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\"> Count </span>┃                                    │\n",
              "│ ┡━━━━━━━━━━━━━━━━━━━╇━━━━━━━━┩ ┡━━━━━━━━━━━━━╇━━━━━━━┩                                    │\n",
              "│ │ Number of rows    │ 215    │ │ float64     │ 14    │                                    │\n",
              "│ │ Number of columns │ 14     │ └─────────────┴───────┘                                    │\n",
              "│ └───────────────────┴────────┘                                                            │\n",
              "│ <span style=\"font-style: italic\">                                         number                                         </span>  │\n",
              "│ ┏━━━━━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━┳━━━━━━┳━━━━━┳━━━━━━┳━━━━━━┳━━━━━━┳━━━━━━━━┓  │\n",
              "│ ┃<span style=\"font-weight: bold\">             </span>┃<span style=\"font-weight: bold\"> missing </span>┃<span style=\"font-weight: bold\"> complete   </span>┃<span style=\"font-weight: bold\"> mean </span>┃<span style=\"font-weight: bold\"> sd   </span>┃<span style=\"font-weight: bold\"> p0  </span>┃<span style=\"font-weight: bold\"> p25  </span>┃<span style=\"font-weight: bold\"> p75  </span>┃<span style=\"font-weight: bold\"> p100 </span>┃<span style=\"font-weight: bold\"> hist   </span>┃  │\n",
              "│ ┃             ┃         ┃<span style=\"font-weight: bold\"> rate       </span>┃      ┃      ┃     ┃      ┃      ┃      ┃        ┃  │\n",
              "│ ┡━━━━━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━╇━━━━━━╇━━━━━╇━━━━━━╇━━━━━━╇━━━━━━╇━━━━━━━━┩  │\n",
              "│ │ <span style=\"color: #af87ff; text-decoration-color: #af87ff\">sl_no      </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0    </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0       </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.5 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.29</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.25</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.75</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008000; text-decoration-color: #008000\">██████</span> │  │\n",
              "│ │ <span style=\"color: #af87ff; text-decoration-color: #af87ff\">gender     </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0    </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0       </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.65</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.48</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008000; text-decoration-color: #008000\">▄    █</span> │  │\n",
              "│ │ <span style=\"color: #af87ff; text-decoration-color: #af87ff\">ssc_p      </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0    </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0       </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.54</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.22</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.41</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.72</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008000; text-decoration-color: #008000\">▁▄█▇▆▄</span> │  │\n",
              "│ │ <span style=\"color: #af87ff; text-decoration-color: #af87ff\">ssc_b      </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0    </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0       </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.46</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.5 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008000; text-decoration-color: #008000\">█    ▇</span> │  │\n",
              "│ │ <span style=\"color: #af87ff; text-decoration-color: #af87ff\">hsc_p      </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0    </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0       </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.48</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.18</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.39</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.59</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008000; text-decoration-color: #008000\">▁▂█▄▂▁</span> │  │\n",
              "│ │ <span style=\"color: #af87ff; text-decoration-color: #af87ff\">hsc_b      </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0    </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0       </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.61</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.49</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008000; text-decoration-color: #008000\">▅    █</span> │  │\n",
              "│ │ <span style=\"color: #af87ff; text-decoration-color: #af87ff\">hsc_s      </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0    </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0       </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.69</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.29</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.5 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008000; text-decoration-color: #008000\">▁  █ ▆</span> │  │\n",
              "│ │ <span style=\"color: #af87ff; text-decoration-color: #af87ff\">degree_p   </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0    </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0       </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.4 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.18</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.27</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.54</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008000; text-decoration-color: #008000\">▂▄█▄▂ </span> │  │\n",
              "│ │ <span style=\"color: #af87ff; text-decoration-color: #af87ff\">degree_t   </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0    </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0       </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.3 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.45</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008000; text-decoration-color: #008000\">█  ▁ ▃</span> │  │\n",
              "│ │ <span style=\"color: #af87ff; text-decoration-color: #af87ff\">workex     </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0    </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0       </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.34</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.48</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008000; text-decoration-color: #008000\">█    ▄</span> │  │\n",
              "│ │ <span style=\"color: #af87ff; text-decoration-color: #af87ff\">etest_p    </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0    </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0       </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.46</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.28</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.21</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.7 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008000; text-decoration-color: #008000\">▆█▆▆▆▄</span> │  │\n",
              "│ │ <span style=\"color: #af87ff; text-decoration-color: #af87ff\">specialisat</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0    </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0       </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.44</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.5 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008000; text-decoration-color: #008000\">█    ▆</span> │  │\n",
              "│ │ <span style=\"color: #af87ff; text-decoration-color: #af87ff\">ion        </span> │         │            │      │      │     │      │      │      │        │  │\n",
              "│ │ <span style=\"color: #af87ff; text-decoration-color: #af87ff\">mba_p      </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0    </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0       </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.41</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.22</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.25</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.56</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008000; text-decoration-color: #008000\">▄▇█▆▃▁</span> │  │\n",
              "│ │ <span style=\"color: #af87ff; text-decoration-color: #af87ff\">status     </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0    </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0       </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.69</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.46</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0</span> │ <span style=\"color: #008080; text-decoration-color: #008080\">0.0 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008080; text-decoration-color: #008080\">1.0 </span> │ <span style=\"color: #008000; text-decoration-color: #008000\">▄    █</span> │  │\n",
              "│ └─────────────┴─────────┴────────────┴──────┴──────┴─────┴──────┴──────┴──────┴────────┘  │\n",
              "╰─────────────────────────────────────────── End ───────────────────────────────────────────╯\n",
              "</pre>\n"
            ],
            "text/plain": [
              "╭───────────────────────────────────── skimpy summary ──────────────────────────────────────╮\n",
              "│ \u001b[3m         Data Summary         \u001b[0m \u001b[3m      Data Types       \u001b[0m                                    │\n",
              "│ ┏━━━━━━━━━━━━━━━━━━━┳━━━━━━━━┓ ┏━━━━━━━━━━━━━┳━━━━━━━┓                                    │\n",
              "│ ┃\u001b[1;36m \u001b[0m\u001b[1;36mdataframe        \u001b[0m\u001b[1;36m \u001b[0m┃\u001b[1;36m \u001b[0m\u001b[1;36mValues\u001b[0m\u001b[1;36m \u001b[0m┃ ┃\u001b[1;36m \u001b[0m\u001b[1;36mColumn Type\u001b[0m\u001b[1;36m \u001b[0m┃\u001b[1;36m \u001b[0m\u001b[1;36mCount\u001b[0m\u001b[1;36m \u001b[0m┃                                    │\n",
              "│ ┡━━━━━━━━━━━━━━━━━━━╇━━━━━━━━┩ ┡━━━━━━━━━━━━━╇━━━━━━━┩                                    │\n",
              "│ │ Number of rows    │ 215    │ │ float64     │ 14    │                                    │\n",
              "│ │ Number of columns │ 14     │ └─────────────┴───────┘                                    │\n",
              "│ └───────────────────┴────────┘                                                            │\n",
              "│ \u001b[3m                                         number                                         \u001b[0m  │\n",
              "│ ┏━━━━━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━┳━━━━━━┳━━━━━┳━━━━━━┳━━━━━━┳━━━━━━┳━━━━━━━━┓  │\n",
              "│ ┃\u001b[1m \u001b[0m\u001b[1m           \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mmissing\u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mcomplete  \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mmean\u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1msd  \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mp0 \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mp25 \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mp75 \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mp100\u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mhist  \u001b[0m\u001b[1m \u001b[0m┃  │\n",
              "│ ┃             ┃         ┃\u001b[1m \u001b[0m\u001b[1mrate      \u001b[0m\u001b[1m \u001b[0m┃      ┃      ┃     ┃      ┃      ┃      ┃        ┃  │\n",
              "│ ┡━━━━━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━╇━━━━━━╇━━━━━╇━━━━━━╇━━━━━━╇━━━━━━╇━━━━━━━━┩  │\n",
              "│ │ \u001b[38;5;141msl_no      \u001b[0m │ \u001b[36m0.0    \u001b[0m │ \u001b[36m1.0       \u001b[0m │ \u001b[36m0.5 \u001b[0m │ \u001b[36m0.29\u001b[0m │ \u001b[36m0.0\u001b[0m │ \u001b[36m0.25\u001b[0m │ \u001b[36m0.75\u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[32m██████\u001b[0m │  │\n",
              "│ │ \u001b[38;5;141mgender     \u001b[0m │ \u001b[36m0.0    \u001b[0m │ \u001b[36m1.0       \u001b[0m │ \u001b[36m0.65\u001b[0m │ \u001b[36m0.48\u001b[0m │ \u001b[36m0.0\u001b[0m │ \u001b[36m0.0 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[32m▄    █\u001b[0m │  │\n",
              "│ │ \u001b[38;5;141mssc_p      \u001b[0m │ \u001b[36m0.0    \u001b[0m │ \u001b[36m1.0       \u001b[0m │ \u001b[36m0.54\u001b[0m │ \u001b[36m0.22\u001b[0m │ \u001b[36m0.0\u001b[0m │ \u001b[36m0.41\u001b[0m │ \u001b[36m0.72\u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[32m▁▄█▇▆▄\u001b[0m │  │\n",
              "│ │ \u001b[38;5;141mssc_b      \u001b[0m │ \u001b[36m0.0    \u001b[0m │ \u001b[36m1.0       \u001b[0m │ \u001b[36m0.46\u001b[0m │ \u001b[36m0.5 \u001b[0m │ \u001b[36m0.0\u001b[0m │ \u001b[36m0.0 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[32m█    ▇\u001b[0m │  │\n",
              "│ │ \u001b[38;5;141mhsc_p      \u001b[0m │ \u001b[36m0.0    \u001b[0m │ \u001b[36m1.0       \u001b[0m │ \u001b[36m0.48\u001b[0m │ \u001b[36m0.18\u001b[0m │ \u001b[36m0.0\u001b[0m │ \u001b[36m0.39\u001b[0m │ \u001b[36m0.59\u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[32m▁▂█▄▂▁\u001b[0m │  │\n",
              "│ │ \u001b[38;5;141mhsc_b      \u001b[0m │ \u001b[36m0.0    \u001b[0m │ \u001b[36m1.0       \u001b[0m │ \u001b[36m0.61\u001b[0m │ \u001b[36m0.49\u001b[0m │ \u001b[36m0.0\u001b[0m │ \u001b[36m0.0 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[32m▅    █\u001b[0m │  │\n",
              "│ │ \u001b[38;5;141mhsc_s      \u001b[0m │ \u001b[36m0.0    \u001b[0m │ \u001b[36m1.0       \u001b[0m │ \u001b[36m0.69\u001b[0m │ \u001b[36m0.29\u001b[0m │ \u001b[36m0.0\u001b[0m │ \u001b[36m0.5 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[32m▁  █ ▆\u001b[0m │  │\n",
              "│ │ \u001b[38;5;141mdegree_p   \u001b[0m │ \u001b[36m0.0    \u001b[0m │ \u001b[36m1.0       \u001b[0m │ \u001b[36m0.4 \u001b[0m │ \u001b[36m0.18\u001b[0m │ \u001b[36m0.0\u001b[0m │ \u001b[36m0.27\u001b[0m │ \u001b[36m0.54\u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[32m▂▄█▄▂ \u001b[0m │  │\n",
              "│ │ \u001b[38;5;141mdegree_t   \u001b[0m │ \u001b[36m0.0    \u001b[0m │ \u001b[36m1.0       \u001b[0m │ \u001b[36m0.3 \u001b[0m │ \u001b[36m0.45\u001b[0m │ \u001b[36m0.0\u001b[0m │ \u001b[36m0.0 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[32m█  ▁ ▃\u001b[0m │  │\n",
              "│ │ \u001b[38;5;141mworkex     \u001b[0m │ \u001b[36m0.0    \u001b[0m │ \u001b[36m1.0       \u001b[0m │ \u001b[36m0.34\u001b[0m │ \u001b[36m0.48\u001b[0m │ \u001b[36m0.0\u001b[0m │ \u001b[36m0.0 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[32m█    ▄\u001b[0m │  │\n",
              "│ │ \u001b[38;5;141metest_p    \u001b[0m │ \u001b[36m0.0    \u001b[0m │ \u001b[36m1.0       \u001b[0m │ \u001b[36m0.46\u001b[0m │ \u001b[36m0.28\u001b[0m │ \u001b[36m0.0\u001b[0m │ \u001b[36m0.21\u001b[0m │ \u001b[36m0.7 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[32m▆█▆▆▆▄\u001b[0m │  │\n",
              "│ │ \u001b[38;5;141mspecialisat\u001b[0m │ \u001b[36m0.0    \u001b[0m │ \u001b[36m1.0       \u001b[0m │ \u001b[36m0.44\u001b[0m │ \u001b[36m0.5 \u001b[0m │ \u001b[36m0.0\u001b[0m │ \u001b[36m0.0 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[32m█    ▆\u001b[0m │  │\n",
              "│ │ \u001b[38;5;141mion        \u001b[0m │         │            │      │      │     │      │      │      │        │  │\n",
              "│ │ \u001b[38;5;141mmba_p      \u001b[0m │ \u001b[36m0.0    \u001b[0m │ \u001b[36m1.0       \u001b[0m │ \u001b[36m0.41\u001b[0m │ \u001b[36m0.22\u001b[0m │ \u001b[36m0.0\u001b[0m │ \u001b[36m0.25\u001b[0m │ \u001b[36m0.56\u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[32m▄▇█▆▃▁\u001b[0m │  │\n",
              "│ │ \u001b[38;5;141mstatus     \u001b[0m │ \u001b[36m0.0    \u001b[0m │ \u001b[36m1.0       \u001b[0m │ \u001b[36m0.69\u001b[0m │ \u001b[36m0.46\u001b[0m │ \u001b[36m0.0\u001b[0m │ \u001b[36m0.0 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[36m1.0 \u001b[0m │ \u001b[32m▄    █\u001b[0m │  │\n",
              "│ └─────────────┴─────────┴────────────┴──────┴──────┴─────┴──────┴──────┴──────┴────────┘  │\n",
              "╰─────────────────────────────────────────── End ───────────────────────────────────────────╯\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "veVGTXVWmwvl"
      },
      "source": [
        "# **Correlation**\n",
        "\n",
        "One of the most fundamental questions in statistical learning is the relationship between variables. Estimating a measure of association between two variables can help make the right decisions in everyday data science-related problems for different reasons:[6]\n",
        "\n",
        "- Reduce model complexity — by implementing correlation-based feature selection.\n",
        "- Reduce multicollinearity — by manipulating highly correlated variables.\n",
        "- Reduce model uncertainty and infer insights."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hjilCSB-wTIV"
      },
      "source": [
        "**Correlation** **is a statistical technique that can show whether and how strongly pairs of variables are related/interdependent**. When we look at two variables over time if one variable changes how does this affect change in another variable.This post deals with correlation coefficients. **Correlation** is the statistical phrase describing the degree of relationship between any two variables. Since\n",
        "relying on the wrong correlation coefficient might lead to critical mistakes, it is essential to choose the correct correlation coefficient for our problem.[6].We will examine different correlations coefficients, considering different variable types (i.e., numerical, ordinal, and categorical) and types of relationships (linear/nonlinear).[6]"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Correlation** is a statistical relationship, whether causal or not, between any two random variables.\n",
        "A correlation coefficient should quantify the strength of the relationship and answer the following questions:\n",
        "\n",
        "- Is there a statistically significant relationship between the two variables?\n",
        "- What is the direction of the relationship (if it exists)?**[6]**"
      ],
      "metadata": {
        "id": "OettLprkBSkA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Common mistakes:**\n",
        "\n",
        "Measuring correlation is tricky since there are many correlation coefficients. Furthermore, each coefficient suits different setups and assumptions.**[6]**\n",
        "\n",
        "Many people fail in this since they tend to use the **Pearson coefficient** in every setup. It’s important to emphasize that using the Pearson correlation coefficient in a non-linear relationship of two variables is fundamentally wrong.\n",
        "\n",
        "For example, In the plot below, we can obtain a strong non-linear relationship between x and y. However, the Pearson coefficient of x and y is only -0.01, which is very low considering the clear non-linear relationship. Therefore, we should use a different and correct coefficient for this setup to identify this relationship.**[9]**"
      ],
      "metadata": {
        "id": "BOKUVdqSBrOI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1khq9qZYCy7-yL1wbamRghuSN4mxn8LpB)"
      ],
      "metadata": {
        "id": "wuIsLGTGDFnW"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "This section is divided into combinations of variable types, such as\n",
        "numerical-numerical, numerical-ordinal, etc.\n",
        "Possible types of variables are numerical, categorical, and ordinal. We provide at least one appropriate correlation coefficient for each\n",
        "setup, describe it and provide its code implantation.**[6]**"
      ],
      "metadata": {
        "id": "6mptfJ9tDa-u"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Kb6MkqEhnEau"
      },
      "source": [
        "**Correlation measures to what extend different variables are interdependent.**\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xaRrTKZEwjR4"
      },
      "source": [
        "For example, lung cancer and smoking are related; smokers tend to develop lung cancer more than non-smokers. The relationship isn't perfect. You can easily think of two people you know who smoke but don't have lung cancer. Nonetheless, the average cancer development in smokers is higher than in non-smokers. Correlation can tell you just how much of the variation in chances of getting cancer is related to their cigarette consumption.\n",
        "\n",
        "Although this correlation is fairly obvious, your data may contain unsuspected correlations. You may also suspect there are correlations but don't know which are the strongest. Intelligent correlation analysis can lead to a greater understanding of your data.\n",
        "\n",
        "The long and short of correlation is the following: Correlation is a number between –1.0 and +1.0. A correlation could be positive, meaning both variables move in the same direction, or negative, meaning that when one variable’s value increases, the other variables values decrease. Correlation can also be neural or zero, meaning that the variables are unrelated."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "675uBwhfxE6U"
      },
      "source": [
        "- **Positive Correlation:** both variables change in the same direction.\n",
        "- **Neutral Correlation**: No relationship in the change of the variables.\n",
        "- **Negative Correlation:** variables change in opposite directions."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IAOVFF4XxXX4"
      },
      "source": [
        "It is important to note that correlation doesn't imply causation. Correlation quantifies the strength of the relationship between the features of a dataset. In some cases, the association is caused by a factor common to several features of interest. (For example, umbrellas are used during the rain, but they don't cause rain).\n",
        "\n",
        "There are several statistics that you can use to quantify correlation. In this article, you’ll learn about three correlation coefficients:\n",
        "\n",
        "- **Pearson’s r**\n",
        "- **Spearman’s ρ (rho)**\n",
        "- **Kendall’s τ (tau)**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vCJZ8p5B4weG"
      },
      "source": [
        "**Pearson’s** coefficient measures linear correlation, while the S**pearman and Kendall** coefficients compare the ranks of data."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QEZc1xnz5AkB"
      },
      "source": [
        "Correlation can be useful in data analysis and modelling to better understand the relationships between variables. So it is important that you have a good understanding of it before you attempt a data analysis or modelling"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Type of Correlations**"
      ],
      "metadata": {
        "id": "UpmiVeE_xWCh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "  - Pearson correlation - Linear correlation\n",
        "  - Spearman Correlation - Rank correlation\n",
        "  - Distance correlation\n",
        "  - Goodman-Kruskal’s lambda\n",
        "  - Cramér’s v\n",
        "  - Point-biserial correlation coefficient\n",
        "  - Rank-biserial correlation coefficient:\n",
        "  - Kendall correlation - Rank correlation\n",
        "  - All in one solution — Phik (𝜙k)\n"
      ],
      "metadata": {
        "id": "iuHt1Fsuy_l6"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OS2jKFB3-tKZ"
      },
      "source": [
        "### **- Pearson correlation - Linear correlation**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u4K88TEq5PXI"
      },
      "source": [
        "One way to measoure the strenth of corelation between continuose numerical variables is to use Pearson correlation. Pearson correlation method will give you two values:\n",
        "\n",
        "- **correlation coefficient**\n",
        "- **p-value**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vlv6hgUD5hdJ"
      },
      "source": [
        "The Pearson correlation coefficient (named for Karl Pearson) can be used to summarize the strength of the linear relationship between two data samples.\n",
        "\n",
        "Several conditions have to be met for Pearson correlation:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HicOMJ3L5vwI"
      },
      "source": [
        "- The variables x and y must have a linear relationship.\n",
        "- Both variables x and y must be numerical (or quantitative). That is, they must represent measurements with no restriction on their level of precision. For example, numbers with many places after the decimal point (such as 11.332 or 0.229) must be possible.\n",
        "- The y values must have a normal distribution for each x, with the same variance at each x."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OeyCBx3b6Fj_"
      },
      "source": [
        "The Pearson’s correlation coefficient is calculated as the covariance of the two variables divided by the product of the standard deviation of each data sample. It is the normalization of the covariance between the two variables to give an interpretable score.\n",
        "\n",
        "Correlation coefficient and p-value will tell you the following:\n",
        "\n",
        "Correlation coefficient"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Pearson’s r is the ratio between the covariance of two variables and the product of their\n",
        "\n",
        "standard deviations. The result ranges between −1 and 1; 1/-1 indicates a perfect linear positive/negative relationship, 0 means no linear relationship.[6]"
      ],
      "metadata": {
        "id": "R9lVJv6aJts3"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cxxPuD6j6Raq"
      },
      "source": [
        "- close to +1: Large Positive relationship\n",
        "- close to -1: Large Negative relationship\n",
        "- close to 0: No relationship"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wx_WkV8M6aCa"
      },
      "source": [
        "P-value\n",
        "\n",
        "- P-value <0.001: Strong certainty in the result\n",
        "- P-value <0.05:  Moderate certainty in the result\n",
        "- P-value <0.1: Weak certainty in the result\n",
        "- P-value > 0.1: No certainty in the result"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZBJOy_QB6flI"
      },
      "source": [
        "The Pearson’s correlation coefficient can be used to evaluate the relationship between more than two variables.\n",
        "\n",
        "This can be done by calculating a matrix of the relationships between each pair of variables in the dataset. The result is a symmetric matrix called a correlation matrix with a value of 1.0 along the diagonal as each column always perfectly correlates with itself."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We use a simplified version of the PetFinder dataset for examples. Each row in the PetFinder dataset describes a pet, and each column represents a variable.[6]"
      ],
      "metadata": {
        "id": "X8V199SjDywe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "df = pd.read_csv('petfinder-mimi.csv')"
      ],
      "metadata": {
        "id": "0eXbAuUJEA5V"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Following is a description of this dataset.\n"
      ],
      "metadata": {
        "id": "yg7BJ1jGEEBW"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1LNP-XJv7B0gzvbqeDkzTC5k-4etRGucP)"
      ],
      "metadata": {
        "id": "Ushc8KGQE7t1"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Numerical vs Numerical:\n",
        "\n",
        "Setup: X, Y — represents a numerical variable."
      ],
      "metadata": {
        "id": "aynEQtC7FKdU"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Assumptions:**\n",
        "\n",
        "The primary assumption of the model is “linear relationship”. We can scatter plot the\n",
        "data (on two dimensions) and visually test if it has a linear relationship.[6]"
      ],
      "metadata": {
        "id": "tf5fiTJYJ9qi"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Pros and cons:**\n",
        "\n",
        "The main drawback is that it ignores nonlinear relationship forms (e.g., a quadratic form of\n",
        "correlation, etc.).\n",
        "\n",
        " On the other hand, the advantages are low time complexity and model simplicity.[6]"
      ],
      "metadata": {
        "id": "044LTtffKInA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Pearson’s r Equation:**"
      ],
      "metadata": {
        "id": "U9k0oCOlKhEE"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=14oAaogUu6Eppws8AV93I-v2fy4laJ3LX)"
      ],
      "metadata": {
        "id": "kCsxuOJxKjfE"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Python implementation:**[6]\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "sNaxStZiMZii"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df['PhotoAmt'].corr(df['Fee'], method='pearson')"
      ],
      "metadata": {
        "id": "k14y4f4PMhCo"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Using Pandas Dataframe**\n"
      ],
      "metadata": {
        "id": "FJKRBsEoi6o9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import pandas as pd# initialise random data points\n",
        "data_1 = np.random.randn(1, 20)\n",
        "data_2 = np.random.randn(1, 20)\n",
        "data_3 = np.random.randn(1, 20)\n",
        "data_4 = np.random.randn(1, 20)\n",
        "data = {\"Column 1\":data_1[0], \"Column 2\":data_2[0], \"Column 3\":data_3[0], \"Column 4\":data_4[0]}\n",
        "# Initialise a dataframe with all the columns\n",
        "df = pd.DataFrame(data)\n",
        "# .corr() can calculate 'pearson', 'kendall', 'spearman' correlations.\n",
        "print(df.corr(method='pearson'))"
      ],
      "metadata": {
        "id": "JVixx-Zui9Nc"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Calculating the correlation between series in a Data Frame using the default Pearson**\n",
        " "
      ],
      "metadata": {
        "id": "8iki4H7EikBo"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd \n",
        "import numpy as np\n",
        "df = pd.DataFrame(np.random.randn(200,4), columns = [\"a\",\"b\",\"c\",\"d\"])\n",
        "df[\"a\"]. corr(df[\"b\"])"
      ],
      "metadata": {
        "id": "BWpnxTb-h-kk",
        "outputId": "b1aff283-bc43-4976-f4ab-81a46a561e01",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-0.08049580000458638"
            ]
          },
          "metadata": {},
          "execution_count": 1
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Using SciPy:**\n"
      ],
      "metadata": {
        "id": "89BCAyLmiwJI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import scipy.stats as stats\n",
        "import numpy as np# initialise random data points\n",
        "data_1 = np.random.randn(1, 20)\n",
        "data_2 = np.random.randn(1, 20)# The stats.pearsonr() returns 2 values the correlation coefficient and the p-value\n",
        "r, p_value = stats.pearsonr(data_1[0], data_2[0])\n",
        "print(f\"Correlation coefficient of data_1 and data_2 = {r}\")"
      ],
      "metadata": {
        "id": "W7RkGQURivIO",
        "outputId": "59091b87-fcb2-49d0-cd46-5699e551d66c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Correlation coefficient of data_1 and data_2 = -0.20791615980798292\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Calculating the pairwise correlation between Data Frame columns**\n"
      ],
      "metadata": {
        "id": "n87Lo9NjNivN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df.corr()\n"
      ],
      "metadata": {
        "id": "wUtpALhbNU7v"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "corrwith ()"
      ],
      "metadata": {
        "id": "CsA0SDXGOpWz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "index = [\"a\",\"b\",\"c\",\"d\",\"e\"]\n",
        "\n",
        "columns = [\"one\",\"two\",\"three\",\"four\"]\n",
        "\n",
        "df1 = pd.DataFrame(np.random.randn(5,4), index = index, columns = columns )\n",
        "\n",
        "df2 = pd.DataFrame(np.random.randn(4,4), index = index[:4], columns = columns)\n",
        "\n",
        "df1.corrwith(df2)"
      ],
      "metadata": {
        "id": "61S4JuZ1OuCK",
        "outputId": "df3f6ff7-a442-4b16-f0ad-f6aa62d337db",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "one      0.081163\n",
              "two      0.758367\n",
              "three   -0.296436\n",
              "four    -0.122699\n",
              "dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df2.corrwith(df1, axis=1)"
      ],
      "metadata": {
        "id": "9fFP-rKMO-NM"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**visualize this correlation using Heatmaps**"
      ],
      "metadata": {
        "id": "5bdl-YNNQUW9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import seaborn as sns\n",
        "import matplotlib.pyplot as pltfig = plt.figure(figsize=(15,10))\n",
        "sns.heatmap(df.corr(method='pearson'), annot = True, cmap=\"Blues\")\n",
        "plt.title(\"Correlation Heatmap\")"
      ],
      "metadata": {
        "id": "8sNRXpSDQXDp"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**make a correlation matrix much more readable**"
      ],
      "metadata": {
        "id": "fIIewE-yQj9F"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.datasets import load_boston\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "# Import data\n",
        "boston = load_boston()\n",
        "housing = pd.DataFrame(boston.data, columns=boston.feature_names)\n",
        "housing['MEDV'] = boston.target\n",
        "corr = housing.corr()\n",
        "fig, ax = plt.subplots(figsize=(9,7))\n",
        "\n",
        "# To make this look nicer slice off half of this since it duplicates information unecessarily otherwise\n",
        "mask = np.zeros_like(corr, dtype=np.bool)  # returns an array of False values with same shape as corr dataframe\n",
        "mask[np.triu_indices_from(mask)] = True  # creates a boolean mask by making half the zero values == True\n",
        "ax = sns.heatmap(corr.round(2), mask=mask, ax=ax, annot=True, annot_kws={'fontsize':10}, cmap=\"RdYlGn\")\n",
        "ax.set_xticklabels(ax.xaxis.get_ticklabels(), fontsize=14)\n",
        "ax.set_yticklabels(ax.yaxis.get_ticklabels(), fontsize=14);"
      ],
      "metadata": {
        "id": "Gs7xQv5AQm5r"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JMOFGpMS-5t3"
      },
      "source": [
        "### **- Spearman Correlation - Rank correlation**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jsn6ukJr9sPk"
      },
      "source": [
        "Pearson’s correlation coefficient is the most common correlation measure out there, but it is not the only one out there. Pearson’s correlation can't be used in all cases. It can be used only when certain conditions are met (those are listed above). If those conditions are not met, the rank correlation can be used (Spearman and Kendall correlation).\n",
        "\n",
        "Pearson correlation assumes that the data we are comparing is normally distributed. When that assumption is not true, the correlation value is reflecting the true association. Spearman correlation does not assume that data is from a specific distribution, so it is a non-parametric correlation measure."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WOwfhdxb98ML"
      },
      "source": [
        "Spearman’s rank correlation doesn’t require the relationship between the variables x and y to be linear, nor does it require the variables to be numerical. You use Spearman’s rank when the variables are ordinal or/and quantitative. Rather than examining a linear relationship between x and y, Spearman’s rank correlation tests whether two ordinal or/and quantitative variables are dependent.\n",
        "\n",
        "Note that Spearman’s rank applies to ordinal data only.\n",
        "\n",
        "Spearman's correlation coefficient, (ρ, also signified by rs) measures the strength and direction of the association between two ranked variables. You interpret the value of Spearman’s rank correlation, ρ the same way you interpret Pearson’s correlation, r. The values of ρ can go between –1 and +1. The higher the magnitude of ρ (in the positive or negative directions), the stronger the relationship."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Spearman’s rank correlation** coefficient determines the strength and direction of the monotonic relationship between two variables. This coefficient can be calculated between any mixture of **numerical and ordinal variables**. The result ranges between −1 and 1, similar to Pearson’s r.[6]"
      ],
      "metadata": {
        "id": "K-FMMZMQMpoZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Assumptions:**\n",
        "\n",
        "The primary assumption of the model is “monotonic relationship”. We can\n",
        "scatter plot the data and visually test if it has a monotonic relationship. A function is called monotonic if and only if it is either entirely non-increasing or entirely non-decreasing.[6]"
      ],
      "metadata": {
        "id": "forc5FTHM0YP"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Pros and cons:**\n",
        "\n",
        "The main drawback of Spearman rank correlation is that it ignores non-monotonic relationship forms. Its advantages are low time complexity, model simplicity, and the ability to be calculated on ordinal or nominal variables.[6]"
      ],
      "metadata": {
        "id": "Fhm-SPhoNCnn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Equation:**"
      ],
      "metadata": {
        "id": "L3OGiduRZBPi"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=18oFA4iKwLqb-7idY0X5Wi3CKi8Cvt62j)"
      ],
      "metadata": {
        "id": "RpO12OgYZDdg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Python implementation:\n",
        "df['PhotoAmt'].corr(df['Fee'], method='spearman')"
      ],
      "metadata": {
        "id": "LrM8vG3JZ6z5"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Distance correlation**\n"
      ],
      "metadata": {
        "id": "_HzgGwDcaEln"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Distance correlation is a fairly new correlation measurement introduced in 2005 by Gábor J. Székely. It measures the dependency between any two paired random vectors of arbitrary, not necessarily equal dimension. The distance correlation coefficient is zero if and only if the random vectors are independent and measures both linear and nonlinear association between\n",
        "two random variables or random vectors[6]"
      ],
      "metadata": {
        "id": "rC0ZPqicaOma"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Assumptions:**\n",
        "\n",
        "Distance correlation assumes data is i.i.d, and both X and Y have finite first moments."
      ],
      "metadata": {
        "id": "yQ3fWxTobFw4"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**The most significant drawbacks of distance correlation:**[6]\n",
        "\n",
        "The distance correlation is always positive and does not indicate the direction of the relationship.\n",
        "2. Computational time.\n",
        "\n",
        "The advantages:\n",
        "\n",
        "Handling various types of relationships between variables.\n",
        "Distance correlation of zero implies independence, unlike other correlation coefficients.\n",
        "\n",
        "It can be calculated on non-equal dimension variables."
      ],
      "metadata": {
        "id": "OibNV1YWbsIl"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Equation:**"
      ],
      "metadata": {
        "id": "tqKv0J_zb5dF"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1U2I80eSHAVf3C-K2j0xQAMgyumVwzDe3)"
      ],
      "metadata": {
        "id": "utAW5XG3cQr7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Python implementation:**"
      ],
      "metadata": {
        "id": "W2bc4X-Jca8L"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import dcor\n",
        "dcor.distance_correlation(df['PhotoAmt'], df['Fee'])"
      ],
      "metadata": {
        "id": "rzl-D3qkcc9V"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Goodman-Kruskal’s lambda**"
      ],
      "metadata": {
        "id": "NIeuBmAFcmk5"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Goodman - Kruskal’s lambda is an asymmetric measure of proportional reduction in error contingency table analysis. It is based on measuring relationships by asking how much knowledge about one variable will help us predict the dependent variable better than the naive prediction. The lambda value ranges from 0 to 1, where 0 indicates no association and 1 indicates perfect association[6]"
      ],
      "metadata": {
        "id": "lR1ffeoOcsFh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Categorical vs Categorical:**\n",
        "\n",
        "Setup: X, Y - represents a categorical variable with two or more categories."
      ],
      "metadata": {
        "id": "7yl2WgrUdV3O"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Assumptions:**\n",
        "\n",
        "Categorical vs categorical setup"
      ],
      "metadata": {
        "id": "bxeZzWrDdb8v"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Pros and cons:**[6]\n",
        "\n",
        "A very intuitive measure that tells us the strength of association without making strong assumptions. However, this measure fails when the dependent variable has the same dominant class in each independent variable level."
      ],
      "metadata": {
        "id": "hv5jh5nOdmp1"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Equation:**\n",
        "\n",
        "We will use the following Wikipedia example:"
      ],
      "metadata": {
        "id": "QV59HJJ6rCqj"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1xhM-sP4N--XrjeUC0duau8GeQaBEDs2N)"
      ],
      "metadata": {
        "id": "yClYTNIxr5zJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Since this measure is asymmetric, we will get different results for different directions of calculations. Let’s consider “Relationship Status” to be Y (dependent variable) and “Blood Pressure” to be X. We first naively predict all Y values to be the most frequent category in the given sample. Therefore, we will predict y_i to be “Married” for each i =1…n, and refer to the number of mistakes as E1.\n",
        "\n",
        "Then, given the value of x_i, we’ll predict y_i to be the most frequent category inside the population of\n",
        "the corresponding xi level (“Married” when Blood Pressure is “High” and “Unmarried” otherwise), and we will do that for every i=1…n. We will refer to the number of mistakes as E2.\n",
        "The lambda value is defined to be the percent of error redaction.[6]"
      ],
      "metadata": {
        "id": "4s1J_GXisFC3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](\n",
        "https://drive.google.com/uc?export=view&id=1e4nU_zJYjpYAhLYlcxPlx1Ucpp5ItoWZ)"
      ],
      "metadata": {
        "id": "DykSJhWRsoUl"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "So, in our example, we get:\n"
      ],
      "metadata": {
        "id": "0fA_LDxctOf3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1v8IXh0nI6C0WfplUM0ANauLZ5xTb6lPr)"
      ],
      "metadata": {
        "id": "9GiLZK66suBt"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Suppose we consider “Blood Pressure” as the dependent variable. In that case, we will get lambda equals zero due to the dominance of “Normal” in every level of “Relationship Status”, which will result in no error reduction in our calculation."
      ],
      "metadata": {
        "id": "-sWdNssotSSm"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Python implementation:**"
      ],
      "metadata": {
        "id": "AZpE6O9BtWKu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from pypair.association import categorical_categorical\n",
        "categorical_categorical(df['Type'], df['Color2'], 'gk_lambda')"
      ],
      "metadata": {
        "id": "qmFBoGbQtYaZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Cramér’s v**"
      ],
      "metadata": {
        "id": "dXL0mepbtdXf"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Cramér’s v is a symmetrical measure of association for categorical variables. Cramér’s v is based on Pearson’s chi-squared statistic, and its value ranges from 0 to 1, where 0 indicates no association and 1 indicates perfect association.[6]"
      ],
      "metadata": {
        "id": "VaUcePcdtqL-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Assumptions:**\n",
        "\n",
        "Categorical vs. categorical setup. The observations are independent inside and outside the group."
      ],
      "metadata": {
        "id": "bjq73u6wuT6Y"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Pros and cons:**\n",
        "\n",
        "Cramér’s v is a common choice to measure the association of two categorical variables. Since it is based on a chi-squared statistic, it makes no assumptions about the distribution of the population. However, it is not appropriate for dependent data.[6]"
      ],
      "metadata": {
        "id": "1DLBMTC-uihA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](\n",
        "https://drive.google.com/uc?export=view&id=1Pd-ijtXc5DXEqSniKIghE4uAyqZX0s8v)"
      ],
      "metadata": {
        "id": "84sQMh6svErg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Python implementation:**\n"
      ],
      "metadata": {
        "id": "R25mjM97vQUY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import scipy.stats as stats\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "\n",
        "def cramers_v(var1, var2):\n",
        "    data = pd.crosstab(var1, var2).values\n",
        "    chi_2 = stats.chi2_contingency(data)[0]\n",
        "    n = data.sum()\n",
        "    phi_2 = chi_2 / n\n",
        "    r, k = data.shape\n",
        "    return np.sqrt(phi_2 / min((k-1), (r-1)))\n",
        "cramers_v(df['Type'], df['Color2'])"
      ],
      "metadata": {
        "id": "-jE97G_QvSoJ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Point-biserial correlation coefficient**"
      ],
      "metadata": {
        "id": "NSaHrMl2x-Pr"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Numerical vs. categorical**\n",
        "\n",
        "Setup: Y - numerical variable, X - categorical variable with two or more categories."
      ],
      "metadata": {
        "id": "cLkez4XOzQwo"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Point- biserial correlation coefficient ranges between –1 and +1. Values close to ±1 indicate a strong positive/negative relationship, and values close to zero indicate no relationship between the two variables.\n",
        "Calculation of the point-biserial correlation coefficient is accomplished by coding the two levels of the binary variable “0” and “1” and obtaining the coefficient between the continuous variable (Y) and this coded binary variable.[6]"
      ],
      "metadata": {
        "id": "lA5KOyT_yIFw"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Assumptions:**\n",
        "\n",
        "Numerical and binary variable (categorical variable with two categories only). However, suppose the categorical variable has more than two categories. In that case, we can overcome it by creating a series of dummy variables for the categorical variable (e.g., one-hot encoding) and calculating the point-biserial correlation between the numerical variable and the dummies variables. Of course, this trick will provide many correlation scores, so we might want to use the max value or any other calculation of those scores as our final measure of the relationship."
      ],
      "metadata": {
        "id": "DYXJ5t6syNRJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Equation:**"
      ],
      "metadata": {
        "id": "nT3ZHPAvySgg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1MMVvEwJGOEcv0LlSYShSZitzG8bsqpLD)"
      ],
      "metadata": {
        "id": "FdMQVap3y771"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](\n",
        "https://drive.google.com/uc?export=view&id=1cHM_hJCpg7f71u_rFOLQj4oWakNGEkSb)"
      ],
      "metadata": {
        "id": "DZ9KWLYiyiXl"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Python implementation:**\n"
      ],
      "metadata": {
        "id": "cOwZBlcQzGst"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import scipy.stats as stats\n",
        "point_biserial, p_value = stats.pointbiserialr((df['Type'] == 'Cat'), df['PhotoAmt'])"
      ],
      "metadata": {
        "id": "ngVJIdfUzMZF"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Rank-biserial correlation coefficient**\n",
        "\n"
      ],
      "metadata": {
        "id": "VRzKLDItuOVm"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The rank-biserial correlation is similar to the point-biserial correlation coefficient, but it aims to measure the correlation between a binary and an ordinal variable.\n",
        "The calculation of the rank-biserial correlation coefficient is accomplished by coding the two levels of the binary variable “0” and “1” and obtaining the coefficient between the ranked variable (Y) and this coded binary variable[6]"
      ],
      "metadata": {
        "id": "y8Dx1zMCufti"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Categorical vs. Ordinal** [6]\n",
        "\n",
        "Setup: Y - represents a categorical variable with two or more categories. X -represents an ordinal variable."
      ],
      "metadata": {
        "id": "iS0jj-YeubrB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Assumptions:**\n",
        "\n",
        "Binary vs ordinal setup.\n",
        "However, we can use the same one-hot encoding trick used in point-biserial to make this coefficient relevant also for cases of a categorical variable with more than two categories."
      ],
      "metadata": {
        "id": "Y_npO4ISup1U"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Equation:**"
      ],
      "metadata": {
        "id": "IG6xOhMMuwsX"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1n1V3CvDZdtbwQm2EC2ZWLkbduOtaiH8E)"
      ],
      "metadata": {
        "id": "cpfUz-tMuz6u"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Python implementation:**\n"
      ],
      "metadata": {
        "id": "RvLbK4LevULK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from pypair.association import binary_continuous\n",
        "binary_continuous((df['Type'] == 'Cat'), df['AdoptionSpeed'], 'rank_biserial')"
      ],
      "metadata": {
        "id": "NRQVpuyCvbth"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c9k2A14Y_FIF"
      },
      "source": [
        "### **- Kendall correlation - Rank correlation**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PP3IflHn-LZB"
      },
      "source": [
        "The Kendall correlation coefficient compares the number of concordant and discordant pairs of data. This coefficient is based on the difference in the counts of concordant and discordant pairs relative to the number of x-y pairs. It’s often denoted with τ called Kendall’s tau. It is considered an alternative to the nonparametric Spearman correlation coefficient (especially when you have a small sample size with many tied ranks)."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "When the sample size is small and has many tied ranks, the Kendall rank correlation coefficient (tau) is a better choice for a correlation coefficient. There are three types of Kendall rank correlation: We refer to Kendall rank correlation tau-b. Similar to Spearman, it ranges between 1 and -1. [6]"
      ],
      "metadata": {
        "id": "5reSiYyavz6K"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XnUpBepE-ZKK"
      },
      "source": [
        "Important facts about the Kendall correlation coefficient are:\n",
        "\n",
        "- It can take a real value in the range −1 ≤ τ ≤ 1.\n",
        "- Its maximum value τ = 1 corresponds to the case when the ranks of the corresponding values in x and y are the same. In other words, all pairs are concordant.\n",
        "- Its minimum value τ = −1 corresponds to the case when the rankings in x are the reverse of the rankings in y. In other words, all pairs are discordant."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Assumptions:**\n",
        "\n",
        "Ordinal or numerical data. Monotonic relationships between the two variables.[6]"
      ],
      "metadata": {
        "id": "1wXO1-18v9rK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Pros and cons:**\n",
        "\n",
        "Better to use on small data with many tied ranks.[6]"
      ],
      "metadata": {
        "id": "WedPRrLiwEQa"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Equation:**\n"
      ],
      "metadata": {
        "id": "D6rkYNUhwv3S"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1qUQoaZainuRXCCzj3EU-rkm4e04MOA9o)"
      ],
      "metadata": {
        "id": "cKRBRt21wnwS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Python implementation:**\n"
      ],
      "metadata": {
        "id": "MnxpNohNwzH6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import scipy.stats as stats\n",
        "tau, p_value = stats.kendalltau(df['FurLength'], df['MaturitySize'])"
      ],
      "metadata": {
        "id": "V62i01w-w556"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **All in one solution — Phik (𝜙k)**"
      ],
      "metadata": {
        "id": "3riqxdUdxDxq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We have seen many different correlation coefficients so far. However, none of the coefficients above can be used for all setups and types of relationships.\n",
        "We recently encountered the Phik(𝜙k) method, which is based on several refinements of Pearson’s\n",
        "χ2 (chi-squared) contingency test and can capture non-linear relationships between all variable types.[6]"
      ],
      "metadata": {
        "id": "sT5leFBnxKry"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Pros and cons:**\n",
        "\n",
        "The calculation of 𝜙k is computationally expensive. Furthermore, it has no closed-form formula, and it does not indicate the direction of the relationship.\n",
        "Also, other appropriate correlation coefficients will be more precise when used in their proper setup.\n",
        "However, Phik(𝜙k) gives us a global and generic solution for all types of variables and relationships between variables [6]"
      ],
      "metadata": {
        "id": "YvlKv9qM6rqi"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Python implementation:**\n"
      ],
      "metadata": {
        "id": "8nfACf8s600N"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import phik\n",
        "from phik.report import plot_correlation_matrix\n",
        "\n",
        "phik_overview = df.phik_matrix()"
      ],
      "metadata": {
        "id": "_Vt_rVqD63Ld"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Decision table:**\n"
      ],
      "metadata": {
        "id": "lWP-WV8-74ut"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](\n",
        "https://drive.google.com/uc?export=view&id=1SpPkI2d5WdLd07WyG8Cs4p3pPP7tiSth)"
      ],
      "metadata": {
        "id": "gSBHB2pk7Lo7"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1qFAXK9i_Nf-"
      },
      "source": [
        "## **Correlation Calculation in Pandas**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M1FLafx6-nuy"
      },
      "source": [
        "Pandas offers **.corr()** function that we can use to calculate correlation coefficient.\n",
        "\n",
        "Pandas **dataframe.corr()**is used to find the pairwise correlation of all columns in the dataframe. Any NA values are automatically excluded. For any non-numeric data type columns in the dataframe it is ignored."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 266
        },
        "id": "VPY44tER6QoO",
        "outputId": "a74bd582-7d5c-452d-bdb2-ebb2ff0ab329"
      },
      "source": [
        "data.corr(method='pearson', min_periods=1)\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>sl_no</th>\n",
              "      <th>ssc_p</th>\n",
              "      <th>hsc_p</th>\n",
              "      <th>degree_p</th>\n",
              "      <th>etest_p</th>\n",
              "      <th>mba_p</th>\n",
              "      <th>salary</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>sl_no</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.078155</td>\n",
              "      <td>-0.085711</td>\n",
              "      <td>-0.088281</td>\n",
              "      <td>0.063636</td>\n",
              "      <td>0.022327</td>\n",
              "      <td>0.063764</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>ssc_p</th>\n",
              "      <td>-0.078155</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.511472</td>\n",
              "      <td>0.538404</td>\n",
              "      <td>0.261993</td>\n",
              "      <td>0.388478</td>\n",
              "      <td>0.035330</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>hsc_p</th>\n",
              "      <td>-0.085711</td>\n",
              "      <td>0.511472</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.434206</td>\n",
              "      <td>0.245113</td>\n",
              "      <td>0.354823</td>\n",
              "      <td>0.076819</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>degree_p</th>\n",
              "      <td>-0.088281</td>\n",
              "      <td>0.538404</td>\n",
              "      <td>0.434206</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.224470</td>\n",
              "      <td>0.402364</td>\n",
              "      <td>-0.019272</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>etest_p</th>\n",
              "      <td>0.063636</td>\n",
              "      <td>0.261993</td>\n",
              "      <td>0.245113</td>\n",
              "      <td>0.224470</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.218055</td>\n",
              "      <td>0.178307</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mba_p</th>\n",
              "      <td>0.022327</td>\n",
              "      <td>0.388478</td>\n",
              "      <td>0.354823</td>\n",
              "      <td>0.402364</td>\n",
              "      <td>0.218055</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.175013</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>salary</th>\n",
              "      <td>0.063764</td>\n",
              "      <td>0.035330</td>\n",
              "      <td>0.076819</td>\n",
              "      <td>-0.019272</td>\n",
              "      <td>0.178307</td>\n",
              "      <td>0.175013</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "             sl_no     ssc_p     hsc_p  degree_p   etest_p     mba_p    salary\n",
              "sl_no     1.000000 -0.078155 -0.085711 -0.088281  0.063636  0.022327  0.063764\n",
              "ssc_p    -0.078155  1.000000  0.511472  0.538404  0.261993  0.388478  0.035330\n",
              "hsc_p    -0.085711  0.511472  1.000000  0.434206  0.245113  0.354823  0.076819\n",
              "degree_p -0.088281  0.538404  0.434206  1.000000  0.224470  0.402364 -0.019272\n",
              "etest_p   0.063636  0.261993  0.245113  0.224470  1.000000  0.218055  0.178307\n",
              "mba_p     0.022327  0.388478  0.354823  0.402364  0.218055  1.000000  0.175013\n",
              "salary    0.063764  0.035330  0.076819 -0.019272  0.178307  0.175013  1.000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qz3TRxFz_ga0"
      },
      "source": [
        "**Parameters:**\n",
        "\n",
        "**methods :**\n",
        "\n",
        "- pearson : Standard correlation coefficient\n",
        "- kendall : Kendall Tau correlation coefficient\n",
        "- spearman : Spearman rank correlation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G4h7TZMIB-tH"
      },
      "source": [
        "**min_periods :** Minimum number of observations required per pair of columns to have a valid result. Currently only available for Pearson and Spearman correlation.\n",
        "\n",
        "- It returns a dataframe (Correlation matrix).\n",
        "\n",
        "- Let's create a datasets to illustare how the function works.\n",
        "\n",
        "- Here we are creating a dataframe with two columns that have positive correlation."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "id": "u9tOCs3QCLX3",
        "outputId": "379b30d3-6f1a-42f1-9538-b4a1eded8d7c"
      },
      "source": [
        "# creating a datasets to illustrate positive correlation.\n",
        "\n",
        "# importing libraries\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "\n",
        "from numpy import mean\n",
        "from numpy import std\n",
        "from numpy.random import randn\n",
        "from numpy.random import seed\n",
        "from matplotlib import pyplot\n",
        "\n",
        "# seed random number generator\n",
        "seed(1)\n",
        "\n",
        "# creating data for columns\n",
        "d1 = 30 * randn(1500) + 100\n",
        "d2 = d1 + (20 * randn(1500) + 50)\n",
        "\n",
        "# let's convert to a dataframe\n",
        "df = pd.DataFrame({'Column1': d1, 'Column2': d2})\n",
        "\n",
        "# summarize\n",
        "print('d1: mean=%.3f stdv=%.3f' % (mean(d1), std(d1)))\n",
        "print('d2: mean=%.3f stdv=%.3f' % (mean(d2), std(d2)))\n",
        "\n",
        "# plot\n",
        "pyplot.scatter(d1, d2)\n",
        "pyplot.show()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "d1: mean=101.554 stdv=29.851\n",
            "d2: mean=151.104 stdv=35.806\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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HYmkulry7IvrADqCmKZlb5VFpTnFqulQtM73nyUORLjaj1jG4UyoNb1wZe947TZy9dYJUHhVLs7hzx2TkK4qpeQzulFoLe/nr3Sxnb50wn4I4ik8OTqhSooXZpNp+/L1PHZ7XpYhRC9P7PSOCdX/Uj6dfPIHLRnY31Q7ZXlHs9nMK+/Ok5jG4UySi+Efr12Pd3uJu/LWTrpUcnx871NZ+Lu22aEEGZ85F30/+/ltW464dk4Guy/23rG7o7fPI/qNYtCCDXNbC6WIJF2UtnDk347mxtlsqJ8q+QeSPn1upZW59XMJ+NHd7jUddesEoyuWG9a89NlGY14EdQFsCe08ldR4ktSIo7/XqNkI/c24WZ87O4IEtazC59Tps/9hqz/4xbu8XVd8gCobBnVoWxT9at9cwBWoFcPfjB2taAm/fc2ReB/Z2mVNg+ImDuPbKJb4TzPaG3yalOcW2XeWNvocG8tg3sgFf3rKm4XVNK4qj6htEwTAtQy0L84/WLX0DIPRiHzuHXJgq4s4dkz6P7m6lOcX3Dx6PZGFV/UIpO50SJCUXVd8gCobBnVoW9B+tW851+DsHk927NiWmiiUMDeQx/tpJz/RVLmvh7MxcqE6QQVcUR9U3iIJhWoZa5lZT7vaP1nUxzKyiFHQDUWqJ37xE1spg242rcN/NV8G0hWx/C33uo+obRMFw5E4tC/rRnLnVzlm0IOM7L7F5be0IfPg7B2sqYqyMYOsNq1o6jyj6BlEwDO4UiSD/aDvVhpcAK9Pje3N1NlsLk0unZGJwp9i45VytjAAKpmYCEpRvkqfOnMV0iA1FThdLvjfX+uDPUfb8xpw7xcYt57r9Y6ux/eOrkcs2n8vtFusvX4wHtqwBAEyX5kL1cLdH3l7lkKxaSReO3LtQM6tJm12B6va8fSMbGh7zh3dmWvp/6gY//81J/Pzlk9UukM7POvlcFmfOzrj2dBeg5udlas/QqQ1OqD0Y3LtMM0vAm102bnre+Gsn8fSLJ1CYKqJHygttyJ/pOuWyFvaNbHDtuy4APrluefXnZP/5Xx6fbHi9Hc8ew+Cli5mKSQmmZbpMmNWkYxMFrB/dizt3TDa1AtX0Xo/uP1rN/TKwt84erbulvR7YsqahD8/2PUdcr3tpVtkKIEU4cu8yQVeTuo0Cg76W3/cZz9snyCSo18+N5arpweDeZYKuJnUbdfs9B6jNsfeEaDVLzVu0IIP1o3tRmCpW2/vmm2gDYH+P0oFpmS4TdDWp3wjO7Tn1nR0Z2ONx5txsNVg7e+6YOnMOb1wJq6ex1sbKCFsBpAiDe5dxy8tuXpvH9j1Haroseo3gMiINqxkB82jf3rItTOketc40LzI0kG8oP+3vs7D9Y6s5mZoiogkYXQ0ODur4+HinT6MrueXWs1YGVy+/CD97+aRnH5L6viArRna7PtZeeOO1gEYEyPb2oFiaQ9bqCbVAh8wEwCujmzp9GtQmInJAVQfdvseRe5czVbR4BXb7Mc5R4dhEwTgyvySX9U3zqJYX5iiABb0ZWPzNjMRFWQvrR/fWfCqj7sB/Ql2ulYoW53O9mlJNn5tBLkQ3waliCRy4t87qEZw5N1Ozu9VdOybx+bFDnT41igGDe5drpTrC+Vyvkfmp6RI3rI5IPpfF+ssX+85f5HNZXHhBb8M+p6ZtCil9GNy7nFv1TJCJz/pqGZbQxePM2Rn84tVTrp+S8rksvrxlDV4d3YR9IxswZbihKsDFSl2Ade5dzq2167VXLsGOZ48Zd7fv77Ow9YZVGBrIV+va2co3Hm69Y4ByYK/v2eM1ic3FSunH4E6uqxq/f/C4MZC8U0mIB1nFSvFwC9bDG1firh2TrqN8ftJKPwZ3cnXaENiB2koZBvZkcJuwNu2Zyn1Lu4Nvzl1EviEib4nI845j20SkICKTlf+ud3zvHhF5SUSOiMjGdp04Nc9uCOZVHuc3sntjqsiP9gliWq7yxaGr8MCWNdy3tAsFGbl/E8D/APBw3fEHVPUfnAdE5H0APgFgFYBLAPxYRP5YVTm8S4ig7XuvvXKJ52bKdvBnrj0ZvD5pcUel7uQ7clfVnwI4GfD1bgLwbVU9q6qvAHgJwAdaOD+KWJCWv2MTBew8UDAGdkE5qE+fm2G5Vcy8FooRObWSc/+MiHwKwDiAu1X1FIA8gP2Ox7xeOdZARG4HcDsALF++vIXToDC8Wv4GrXyxgz5r1+OX67PwTmmuoV0Ec+hUr9mB11cBXA5gDYDjAO4P+wKq+qCqDqrq4JIl3N4rLqYRXq7PqnZ0pOSami41NH5jDp3cNDVyV9U37a9F5GsAvl/5awHAMsdD31s5RgkxvHGla6MwVVa+xM3qQeg2C7k+izl0CqSp4C4iS1X1eOWvHwVgV9LsAvAtEfkSyhOqVwD4RctnSU2r36D62iuXYGFvTzWQ2wuS7tox2eEz7S7rL1+MR//Tv6n+PegmJ2+/M4OxiQKDO/nyDe4i8hiADwF4j4i8DmArgA+JyBqU06+vAvgrAFDVwyLyOIBfAZgBcAcrZTrHrTLmkf1Hax5jL0jya8lL0frZyyerQbr+Buz1cyjNlfc5dQb3+uebdmCi7sJ+7ilmb73mx96SrT5dY2UEM7PKPU/bJCOCW69Zhp0HCqFSYs4e7aZ+/MzDdwf2c+9SQRcZ2TeAhb3nfx3snXk+uY6VTO0yq4pH9x8NPdfhnBQPUtpK3YnBPcWC9lDvEeCeJw/V9JKx0zVPv3iiLedGZWE/FdWXPXqVtlJ3Y2+ZFAuacZtzqZQplmZxJydZOy6XtbBoYa8xn27K0XNREzG4p9TYRMHY1ZHik6lUvvT3WZgqlgLfcG2niyVMbr3O+H1TaSsXNRHTMilkT7JR582qQlBezXvRBRasTG0DgayVwfrLFxuf7zcCHxrIc1ETueLIPYXcJtlsVkawaEEvR/UxsgfrU8USrB4pj+KnSzVpls+PHWq6NS8XNZEbBvcU8ppM2/Iny/D0iycY3DukNKfoW9CLiS/Uplq+OHQVBi9dzHp1igyD+zxmWrximmTLZa3QNdXkzp7obGbhl+nmyxE4RYk593nKzqsXpopQnO/LPjZRcN30OmtlIML+MVEQANtuXOV6nYNgJQvFgSP3hAi7hNy0eOXuxw9iThW5PgsLe3twung+t8v+MdFQnN/YZPy1k3jsmWPGXjD1BOWNUIjajSP3BPAahZuYPtrParldwKnpEqaKJVyUtWrSNa3oQbm0r9vlK9fR3tQkaGAHyjeGnQcKnj9boiiwt0wCmHrA5HNZ7BvZEOo5bgTAJ9ctx+Cli7kwKQLrL1+MV/+lGOj6C9xXoWZEMKfKiVNqCXvLJFwzS8jD5HsVwCP7j2LbrsPNnN68tmhBBrlssDYMQe17+WSgwJ4RMbYXsD9hBfmURtQMBvcEMKVLLnF8/F8/uheXjezG+tG91VaxzsUrQXRj+eOclic/O/PeWk3heGGjL2oHBvcEMFW3DG9c6ZmPHxrIY9/IBrwyuiny0Wla2JPMnWCnXIJ8wmKjL4oag3sCeC0hD9rSdduNq2D1cLLTTZgJz6jYN+f6n61pQprlkRQ1lkImhGkBS9B8vP3c7XuOcEeliNiToXbzr3wui5NnzqLosvFp1urB4kULXUtZnT9b0+YabPRFUWNwT7gwLV2HBvIYf+1kQ48Sao6isWJpbKKA4ScOojR3/gpbPYL7bn5/oIoX502YbQaonRjcEy5MS9exiUJbA7tI8B7x80neY99Sr09IzQZnthmgODC4x6iZjYzDBJPte460dcSuWr6xpKmFQS5rYd/IBuO6AdMnJAZnSjoG95jU51rtqhcAgQK86THOG0a7B9X2Rtppyuvb5aHXXrkEj+w/2vB9tgqg+YrVMjFpx0bG9WWS7XbtlUswNJDH8MaVqWtDYNorlnvI0nzFkXtMgla9hEndeG3K0Q6P7D/qOrqdz/orm4hzo2lKG47cY+K3ChUI30AsTOBhCby7rTeUV68G+fkQzScM7jFxW6koKAdwu6VA2NRN0MCTtTL4D9csb+q802z95Yurn4q8VgkTzUcM7jFxrlQEarsF2iP0oOV4tqBL2zevzWP3c8ebOe1U++XR0zWfii6wzv9zyGUtbjRN8xpz7jGyq17cyu6KpdnqSsh69akbZ07eDtynps1Nwfy+H7U+qwcigjPnkl0y6fxUVL+W4OxM4ypUovmEI/cO8Npowys14JaT3/HsMd+FRXEGdgBQCD56dR5WJt5Ev13BU/+uXp9u3pgqtqWSiajTGNw7wJQrtxuGuTUQA9yrY0qzmrhWvsXSLB7ZfxQzc/EuZ7X7v3xy3fKaa7h5bd6zYRcrZSiNmJbpAK+WAm4LluxUTDsWDlmZck8Bl15YLetEq4LCVBE7DxSqN0X7045busu+5qZry0oZms8Y3GPilit/+sUTKEwVIVIe7d65YxLbdh3Gv1+9FE+/eAJvTBWR67Pw9jszNY2qorJoQQbFc7NIW3bZTqmYWiYD5RSO81MROzVS2jC4R8htARIA3PvU4Zq8tz263Lw2jx3PHkNp9nzgniqWahYKtSNfnhHB/besxvY9R3DmXDpTD3ZKxZRamVOtackLsFMjpQuDe0TcescMP3EQENQEb1uxNIvHnjnW0kYS/U2M6rNWpjpiTdJm2VE3JLNTKkFbJrMZGKWN74SqiHxDRN4SkecdxxaLyI9E5NeVP/srx0VE/lFEXhKR50Tk6naefJK4TnbOqWtgt7US2PO5LCa+cB22f3x1zeShvZze9BxnLjopi1adE8nA+aqX+j+DcqZUuDiJupWoT4ARkT8F8DaAh1X1X1eO/XcAJ1V1VERGAPSr6mdF5HoAfw3gegDXAPiKql7jdxKDg4M6Pj7e4v9KZ60Y2R3bezlH3/VMO/3UP97U4jZuAuCBLWs8R82Xjez2bYxmLwrr77OgCpwulmpSY0y5UBqJyAFVHXT7nm9aRlV/KiIr6g7fBOBDla8fAvBPAD5bOf6wlu8Y+0UkJyJLVTX1yyNNC5Da8T5XL78I2/ccwV07Jl23dAP8g1kSyvwEwCfXLa/Zgs7tvC/KWp7lnnlHEHdrq3zfzVfV7KZE1A2azblf7AjYvwVwceXrPIBjjse9XjnWENxF5HYAtwPA8uXzv+9JXJswz6pi38snq3936wtv54/tYHnXjkls33OkJsibctHtlhHBnGrDTcer370pK9PfZ2HiC9dV/75+dK9xMRJH6tRtWl7EVBmlh45sqvqgqg6q6uCSJfN/QwRTXtjOhdt/5rLmnHiz6ldTjk0UMPB3P8SdOyaNHSaHN66MfQUpUK5SeWV0U3UkvX50Ly4b2Y27Hz9oDMxThoqhU9OlatM1gG17iZyaHbm/aadbRGQpgLcqxwsAljke997KsdQzjdwVaNhguT4n3gO0XGtemCriis/t9lyM5LwJ3PvUYc/J3naxq1Tqr4Pp+tkpGtOnDOcIP8xm4kRp1+zIfReA2ypf3wbge47jn6pUzawDcDqp+faxiUJ11Ogc/TX7+LwhgLgdr+8+eJFHhUsYQVaZ2sEw7n4zQG2VStCNRuz0jVd/GPumxcoYovOClEI+BuDnAFaKyOsi8mkAowD+nYj8GsC/rfwdAH4A4DcAXgLwNQD/uS1n3aKwm2IEeXyQwGK/jjOwnp2Ziz3Qxrl7k52uqu+TEyRVIji/tZ+zVNLNG1PFmse59eYh6iZBqmVuNXzrwy6PVQB3tHpS7ebVBdAtEAR5fJAqFdPr+OmzejDdjuYvbZbPZY1VKkEmdBXAzgMFDF662LNdsv16ABcjEdm6sitk2Im3oMeHBvLYN7KhOmEYRflh1srgv938/tDPM4l6X+tc1nKdJPZLh5h2pqpXP1nM1AtRMF0Z3MPulxnV/pphH+/cDcgrJRGKYQ41a/U0VT1Tmp1rqEHvkfLuT14jaLcUiml613lTZOqFKJiuDO5hR39RjRaDbotnW7Sw13OPTysjyGUtCODZdsDJLYDmshZe+K8fwfaPrQ59E3HbbWlOgR3PHnOdw3BOTNuToPYnHdN7u/WB8fqERERdGtzDjv7CPN6rqsZ+naDq0zgLe8//uBYtyGDRgt7qMvtN718augeL7XRl5G0HzVdHN+HLW9YEvih8pLEAAAt0SURBVGG4Kc1qw05GfhPTTLkQRYddIQMKMlHntcrSOfFa3wLYxFQTDtgj5vPv42wTHJbzfZwTwltvWFWz4UXYKpv6m5PfxDRb7xJFpyuDe5Ag3IygVThbb1iF4e8c9FxE1ExNeLOGN64MdE2cQffM2Rnf7f3q0ylBJqZZ7UIUja4M7mFLIYMKErzs0bFbYLc7G+brRqxxLJ8PMqp2XpuxiYLnDcrKSEM6xdQA7KI2tGQg6nZdmXNvVw8Sv6oaZ87ZjR3Y6ycJm10+n89l8eUta3wfZ4/I3bgdd96gelzS/P19FrZ/bHXDjdI0JRB1eSYRdenIvV09SLw2vgaCpVcKU0WsH91bM3J3e90gTp05G2i3Ja/+LfX5+MJUsfoJAyhXxnj1l3cyNQAzHSei5nXlyL1dVRl+VTVBPxkUpoq4a8ckVlQqbgDgvpuvCl0NE3RVq6l/i738v/4TR30ipn6hkdf7hDlORM3rypF7q1UZpk0l7Nc2vU6YHup2AHVuOHH/LasbRvBWRrBoQa/v5KaJfVMbGshj/LWTeHT/0ep728v/v3/wuO+nBtONy3mtLspasDJSk6dnqSNRe/husxeH+bTNntc2doD7DcOU0gDQ8HeTjAjuv2W18T2CbEVXr7/PqpY7Aq1tvefWR8btWlk9ggsv6MXUdImljkQtammbPSpzBuh6xdIstu06jLMzcw2lhOOvncTOA4XqcUVjVczdjx/03clpVhV37ZisPq9+39FmdlZy7mIEND+hbBp9mzYN71vQ2/DeRBStrsy5A+H6uftVuQDAVLHkWkr42DPHGo7XV8UE3aKvPlXj13LYi9tSf1Puu7/PMjb58lqty52RiDqnK0fuYRcxtbKIyGuHIVu+iVF3sTSLO132RrVTNn0LMq59X4Bynv7M2RlcNrK7JjXiVpVjZQSq5fezNwGvr8M34c5IRJ3TlSN3rwU7bvxGmlkrY+zDYqpwcQa4sKNuJ+co3tlQK9e3wPic0qxiqlhq6O8yNJDH5rX56jmLALNzWp2snVWtmYD1w14xRJ3TlcE9bLrAa6RppyW23rDKNZDdes0y3wDnVkL55+uWBw74bjemMJ8E7OePTRSw80Ch+mlDtVzH7vdeJmzPS9Q5XZmWCZsuMC1OcgtUbpUsg5cu9i27dCuhHLx0caDJVqCxxUHQKhzn84Omn8LkzNkrhqgzujK4+60krRe0Lt4UyJoNcEMDedwVYIUpUHtj2r7nSOiyyEty2cBBmzlzouTryuDezCKmdo9ATQujgpQ41t+Ywlaj2M83lXp6vRcRJVOqgrvXytF6XsE6zOtEcS5e1TumChbnRh31rx3khmDqQMlFR0TpkJrgHlWP9iheJ4pSS3vi0l71GeZmY2o0ZgroNm6WQZQeqQnuUfVoj+J1wr6GX/VO2JSQ/dj6HZ8U8C1l5AQoUTqkphQyqtWQpsfbrXiDrGiNqtSylYnLoYE8+hY03rvDlDIS0fyVmuAeVYA0PV4A48bOrZ5Luxb7NHvDC9OagYiSKTXBPaoAaeprHqaHedhzaddin2ZueM4+OkFuZESUTKlq+dtqlUtNa14pr9D0I4Dre0VRcdMqr/bEpnMxtf11a+lLRJ3VNS1/W5kMrA+EQe95ztGtfQ6tnktUmql+YSdHonRIVXBvRSudH4HGapgkjNyB8DcZdnIkSofU5NxtzU4GRjEytV9jPuet2cmRKB1SNXJvZQFSkFWd9gYXpsfZo1u/lsJJGNGbcCETUTqkKri3sgDJtKrTZo9evRp52aNbr1r5KFbRtlsS5guIqDUtpWVE5FUROSQikyIyXjm2WER+JCK/rvzZH82p1nJLv7QyGVhfjpjLWujvsxpKE02551zWqgZE02MyIqE2CSEialYUI/drVfV3jr+PAPiJqo6KyEjl75+N4H2qTOmXXJ9Vs9zeFnQyMMiI1dQueNuNqzwfAwTbco+IKArtSMvcBOBDla8fAvBPiDi4m9IvC3t7kLUygfu0OwWtbgmSk7a/3rbrcHWLOi+sRCGiqLUa3BXAD0VEAfxvVX0QwMWqerzy/d8CuLjF92hgGumeLpbwwJY1oScDg0zEhi1tHBrIY/ueI77BnZUoRNQOrQb3D6pqQUT+FYAficiLzm+qqlYCfwMRuR3A7QCwfPnyUG/qVYvdzGSg30Rss1U4XukW08pWIqIotDShqqqFyp9vAfgugA8AeFNElgJA5c+3DM99UFUHVXVwyZIlod436lpsv4lYv9JGE1O6JZ/L4pXRTdg3soGBnYjaoungLiKLRORd9tcArgPwPIBdAG6rPOw2AN9r9STrRd1oy6/BVrNVOFwQRESd0kpa5mIA3xUR+3W+par/V0SeBfC4iHwawGsAbmn9NBtFWYvtt2F2s0vyuSCIiDql6eCuqr8BsNrl+L8A+HArJxU3vyDsF/z9XpvBnIjilqoVqq3wCsIcgRPRfMPgHhBH4EQ0n6SuKyQRETG4ExGlEoM7EVEKMbgTEaUQgzsRUQoxuBMRpRCDOxFRCjG4ExGlEIM7EVEKMbgTEaUQgzsRUQqxt0xMwm7TR0TUCgb3GDS7TR8RUbOYlolBs9v0ERE1i8E9Bs1u00dE1CwG9xj47dFKRBQ1BvcYcKNsIoobJ1RjwG36iChuDO4x4TZ9RBQnpmWIiFKIwZ2IKIUY3ImIUojBnYgohRjciYhSSFS10+cAETkB4DWPh7wHwO9iOp35htfGjNfGG6+P2Xy5Npeq6hK3byQiuPsRkXFVHez0eSQRr40Zr403Xh+zNFwbpmWIiFKIwZ2IKIXmS3B/sNMnkGC8Nma8Nt54fczm/bWZFzl3IiIKZ76M3ImIKAQGdyKiFEp0cBeRPxORIyLykoiMdPp8kkBEXhWRQyIyKSLjlWOLReRHIvLryp/9nT7POIjIN0TkLRF53nHM9VpI2T9WfpeeE5GrO3fm7We4NttEpFD53ZkUkesd37uncm2OiMjGzpx1PERkmYg8LSK/EpHDIvI3leOp+t1JbHAXkQyA/wngIwDeB+BWEXlfZ88qMa5V1TWOOtwRAD9R1SsA/KTy927wTQB/VnfMdC0+AuCKyn+3A/hqTOfYKd9E47UBgAcqvztrVPUHAFD5d/UJAKsqz/lflX9/aTUD4G5VfR+AdQDuqFyDVP3uJDa4A/gAgJdU9Teqeg7AtwHc1OFzSqqbADxU+fohAEMdPJfYqOpPAZysO2y6FjcBeFjL9gPIicjSeM40foZrY3ITgG+r6llVfQXASyj/+0slVT2uqr+sfP0HAC8AyCNlvztJDu55AMccf3+9cqzbKYAfisgBEbm9cuxiVT1e+fq3AC7uzKklgula8Pep7DOV1MI3HOm7rr02IrICwACAZ5Cy350kB3dy90FVvRrlj4p3iMifOr+p5dpW1reC18LFVwFcDmANgOMA7u/s6XSWiFwIYCeAO1X1987vpeF3J8nBvQBgmePv760c62qqWqj8+RaA76L88flN+2Ni5c+3OneGHWe6Fl3/+6Sqb6rqrKrOAfgazqdeuu7aiIiFcmB/VFWfrBxO1e9OkoP7swCuEJHLRGQByhM+uzp8Th0lIotE5F321wCuA/A8ytfltsrDbgPwvc6cYSKYrsUuAJ+qVD6sA3Da8RG8K9TliT+K8u8OUL42nxCRhSJyGcoTh7+I+/ziIiIC4OsAXlDVLzm+la7fHVVN7H8Argfw/wC8DOBvO30+nf4PwB8BOFj577B9TQC8G+XZ/V8D+DGAxZ0+15iux2MopxdKKOdBP226FgAE5eqrlwEcAjDY6fPvwLX5P5X/9+dQDlhLHY//28q1OQLgI50+/zZfmw+inHJ5DsBk5b/r0/a7w/YDREQplOS0DBERNYnBnYgohRjciYhSiMGdiCiFGNyJiFKIwZ2IKIUY3ImIUuj/AwF1dGlrFFgtAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YSnbe2H5CW89"
      },
      "source": [
        "df.head()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7QdAkpfgC0Wk"
      },
      "source": [
        "Now let's calculate Pearson Correlation Coefficient with Pandas .corr() and prove that we are dealing with the positive correlation.\n",
        "\n",
        "You will need to run  df.corr(method ='pearson') to get Pearson correlation coefficient for your dataframe."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 111
        },
        "id": "Or567hoJCkCd",
        "outputId": "719beaed-3169-43b1-ed99-081176bea20b"
      },
      "source": [
        "df.corr(method='pearson')\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Column1</th>\n",
              "      <th>Column2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Column1</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.831948</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Column2</th>\n",
              "      <td>0.831948</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "          Column1   Column2\n",
              "Column1  1.000000  0.831948\n",
              "Column2  0.831948  1.000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BwF9rXnYDYSm"
      },
      "source": [
        "This is what we expected for the dataframe as it was created to show a positive correlation.\n",
        "\n",
        "A correlation coefficient close to +1 demonstrates a large positive relationship. Any column correlation with self will result in 1. Here the correlation between column1 and column2 is **0.83**, which is close to +1, and so this confirms that we are dealing with positive correlation."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "03x9yYWVDfuz"
      },
      "source": [
        "Let's calculate **Spearman  Correlation Coefficient** with Pandas .corr() and prove that we are dealing with the positive correlation.\n",
        "\n",
        "You will need to run  df.corr(method ='spearman') to get Pearson Correlation Coefficient for your dataframe."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 111
        },
        "id": "TktcLx62DnPM",
        "outputId": "204a05b7-75aa-4818-8726-5680dbbff9e8"
      },
      "source": [
        "df.corr(method='spearman')\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Column1</th>\n",
              "      <th>Column2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Column1</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.808668</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Column2</th>\n",
              "      <td>0.808668</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "          Column1   Column2\n",
              "Column1  1.000000  0.808668\n",
              "Column2  0.808668  1.000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-hnF9aaSDx9-"
      },
      "source": [
        "Finally, let's calculate **Kendall  Correlation Coefficient**with Pandas .corr() and prove that we are dealing with the positive correlation.\n",
        "\n",
        "You will need to run  df.corr(method ='kendall') to get Pearson Correlation Coefficient for your dataframe.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 111
        },
        "id": "R9f1MD-ID247",
        "outputId": "209af6d2-5452-45ab-ccde-24cefb499fe3"
      },
      "source": [
        "df.corr(method='kendall')\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Column1</th>\n",
              "      <th>Column2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Column1</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.615858</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Column2</th>\n",
              "      <td>0.615858</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "          Column1   Column2\n",
              "Column1  1.000000  0.615858\n",
              "Column2  0.615858  1.000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B8mtE--MEInd"
      },
      "source": [
        "The first thing that strikes when comparing correlation coefficients for the test dataframe computed by Pearson and Spearman and Kendall correlation coefficients is the difference between them. Why are they different? We can understand the difference if we understand the assumption of each method.\n",
        "\n",
        "As mentioned before, Pearson's correlation assumes the data is normally distributed. However, Spearman's and Kendall's correlations don't make any assumption on the distribution of the data. That is the main reason for the difference."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Yc-u2NC0_Xqs"
      },
      "source": [
        "## **Correlation Calculation in SciPy**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "COw52KbEEOeU"
      },
      "source": [
        "**Correlation Calculation in SciPy**\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VQPHsvDUGDeB"
      },
      "source": [
        "Pandas does not have a function that calculates **p-values**, so it is better to use **SciPy **to calculate correlation as it will give you both **p-value** and **correlation coefficient.**\n",
        "\n",
        "SciPy library has many statistics routines contained in **scipy.stats.** You can use the following methods to calculate the three correlation coefficients you saw earlier:\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ASBGA6ehGj6h"
      },
      "source": [
        "- pearsonr()\n",
        "- spearmanr()\n",
        "- kendalltau()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GL7q2PxkGvow"
      },
      "source": [
        "That's how you would use these functions in Python:\n",
        "\n",
        "We will create a new test dataframe this time with negative correlation."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Yv1qMHL8GOeJ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "outputId": "241a82b6-774a-483f-f585-531ef5414ce0"
      },
      "source": [
        "# creating a datasets to illustrate negative correlation.\n",
        "\n",
        "# importing libraries\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import scipy\n",
        "\n",
        "from numpy import mean\n",
        "from numpy import std\n",
        "from numpy.random import randn\n",
        "from numpy.random import seed\n",
        "from matplotlib import pyplot\n",
        "\n",
        "# seed random number generator\n",
        "seed(24)\n",
        "\n",
        "# prepare data\n",
        "d1 = 30 * randn(1000) + 100\n",
        "d2 = d1 * -1 + (20 * randn(1000) + 50)\n",
        "\n",
        "# let's convert to a dataframe\n",
        "df = pd.DataFrame({'Column1': d1, 'Column2': d2})\n",
        "\n",
        "# summarize\n",
        "print('d1: mean=%.3f stdv=%.3f' % (mean(d1), std(d1)))\n",
        "print('d2: mean=%.3f stdv=%.3f' % (mean(d2), std(d2)))\n",
        "\n",
        "# plot\n",
        "pyplot.scatter(d1, d2)\n",
        "pyplot.show()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "d1: mean=100.408 stdv=30.396\n",
            "d2: mean=-51.359 stdv=36.784\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0sg2wC8UHDZK"
      },
      "source": [
        "he **scipy.stats.pearsonr(x, y)** calculates a Pearson correlation coefficient and the **p-value** for testing non-correlation.\n",
        "\n",
        "The Pearson correlation coefficient measures the linear relationship between two datasets.\n",
        "\n",
        "The **p-value** roughly indicates the probability of an uncorrelated system producing datasets that have a Pearson correlation at least as extreme as the one computed from these datasets. The p-values are not entirely reliable but are probably reasonable for datasets larger than 500 or so."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vGMRIH5pHjnL",
        "outputId": "694811fa-932d-4f76-f920-e64a3535ac94"
      },
      "source": [
        "scipy.stats.pearsonr(df['Column1'], df['Column2'])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-0.8494613723907997, 2.370666878292138e-279)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AnicM6FGH4b3"
      },
      "source": [
        "corr, pvalue=scipy.stats.pearsonr(df['Column1'], df['Column2'])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UbriSqINH97P",
        "outputId": "460d374e-1001-41fc-949b-ad952a288896"
      },
      "source": [
        "print('correlation coefficent', corr)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "correlation coefficent -0.8494613723907997\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2BWjYJT6IGk4",
        "outputId": "7cedbd0f-4cc5-4e03-f87e-bc1f2e52ec46"
      },
      "source": [
        "print('P-VALUE', pvalue)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "P-VALUE 2.370666878292138e-279\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YMdbG7ArIZkf",
        "outputId": "4bf74aac-155d-4b4f-810a-bf35f31592e0"
      },
      "source": [
        "print('P-value without a notations','{:0.300f}'.format(pvalue))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "P-value without a notations 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002370666878292137817821\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "93NrdJJOJS9Y"
      },
      "source": [
        "As expected, the function produced correlation coefficient -0.8494613, that is close to -1, and it confirms a strong negative correlation. The returned p-value is < 0.001, and so it confirms strong certainty in the result."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "06nM5ydzJU0V"
      },
      "source": [
        "**Spearman correlation coefficient and the p-value**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ME6JpPxN8QlN"
      },
      "source": [
        "The scipy.stats.spearmanr(a, b=None, axis=0, nan_policy='propagate') calculates a Spearman correlation coefficient with associated p-value.\n",
        "\n",
        "The Spearman rank-order correlation coefficient is a nonparametric measure of the monotonicity of the relationship between two datasets. Unlike the Pearson correlation, the Spearman correlation does not assume that both datasets are normally distributed."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z_D2zBlz8ZkI"
      },
      "source": [
        "The p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Spearman correlation at least as extreme as the one computed from these datasets."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1IsEmFHj8gp0"
      },
      "source": [
        "**Parameters:**\n",
        "\n",
        "- a, b: 1D or 2D array_like, b is optional. One or two 1-D or 2-D arrays containing multiple variables and observations. When these are 1-D, each represents a vector of observations of a single variable. For the behavior in the 2-D case, see under axis, below. Both arrays need to have the same length in the axis dimension.\n",
        "- axis : int or None, optional. If axis=0 (default), then each column represents a variable, with observations in the rows. If axis=1, the relationship is transposed: each row represents a variable, while the columns contain observations. If axis=None, then both arrays will be raveled.\n",
        "- nan_policy : {‘propagate’, ‘raise’, ‘omit’}, optional. Defines how to handle when input contains nan. The following options are available (default is propagate): propagate: returns nan, raise: throws an error, and omit: performs the calculations ignoring nan values"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ziufmStY89gr"
      },
      "source": [
        "The scipy.stats.spearmanr(a, b=None, axis=0, nan_policy='propagate') function returns:\n",
        "\n",
        "- **correlation** : float or ndarray (2-D square). Spearman correlation matrix or correlation coefficient (if only 2 variables are given as parameters. Correlation matrix is square with length equal to total number of variables (columns or rows) in a and b combined.\n",
        "- **p-value :** float. The two-sided p-value for a hypothesis test whose null hypothesis is that two sets of data are uncorrelated, has same dimension as rho."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FCBvFVmo9M6p",
        "outputId": "0290fa8f-16d5-420e-da71-018d21d61740"
      },
      "source": [
        "scipy.stats.spearmanr(df)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SpearmanrResult(correlation=-0.8516826716826716, pvalue=2.5840062112066416e-282)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-YqCFoj39sQ6"
      },
      "source": [
        "corr, Pvalue=scipy.stats.spearmanr(df)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "apKmgTn_97m0"
      },
      "source": [
        "print('correlation coefficent', corr)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lg6yESx0-B1f",
        "outputId": "cbd6cc05-814a-4246-b411-1c15a2f7cc39"
      },
      "source": [
        "print('P-VALUE', Pvalue)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "P-VALUE 2.5840062112066416e-282\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sMMx2MkJ-nDq"
      },
      "source": [
        "We know that the data is Gaussian and that the relationship between the variables is linear. Nevertheless, the nonparametric rank-based approach shows a strong correlation between the variables of 0.85. Returned p-value is < 0.001 and so confirms strong certainty in the result."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pZLPbHHf_p_O"
      },
      "source": [
        "**Kendall correlation coefficient and the p-value**\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YO3nUnbR_si1"
      },
      "source": [
        "The scipy.stats.kendalltau(x, y, nan_policy='propagate', method='auto') calculates Kendall’s tau, a correlation measure for ordinal data.\n",
        "\n",
        "Kendall’s tau is a measure of the correspondence between two rankings. Values close to 1 indicate strong agreement, values close to -1 indicate strong disagreement."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qwm9l6YS_9cA"
      },
      "source": [
        "**Parameters:**\n",
        "\n",
        "- **x, yarray_like.**  Arrays of rankings, of the same shape. If arrays are not 1-D, they will be flattened to 1-D.\n",
        "- **nan_policy : {‘propagate’, ‘raise’, ‘omit’}, optional.** Defines how to handle when input contains nan. The following options are available (default is propagate): propagate: returns nan, raise: throws an error, and omit: performs the calculations ignoring nan values.\n",
        "- method: {‘auto’, ‘asymptotic’, ‘exact’}, optional. Defines which method is used to calculate the p-value. The following options are available (default is auto): auto: selects the appropriate method based on a trade-off between speed and accuracy. asymptotic: uses a normal approximation valid for large samples. exact: computes the exact p-value, but can only be used if no ties are present.\n",
        "The scipy.stats"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n7DUeEYIAM5s"
      },
      "source": [
        "The scipy.stats.kendalltau(x, y, nan_policy='propagate', method='auto') function returns:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HcznpJE1AQwt"
      },
      "source": [
        "**correlation float**\n",
        "- The tau statistic - p-value float. The two-sided p-value for a hypothesis test whose null hypothesis is an absence of association, tau = 0."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_eZB-edwAbjx",
        "outputId": "940c5717-e4c1-4047-db9c-2e60a254d392"
      },
      "source": [
        "scipy.stats.kendalltau(df['Column1'], df['Column2'])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "KendalltauResult(correlation=-0.6591271271271271, pvalue=7.67043823229759e-214)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o2leSjFWAmRN"
      },
      "source": [
        "corr, pvalue=scipy.stats.kendalltau(df['Column1'], df['Column2'])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UB5cyjCfAteu",
        "outputId": "342b4775-eaf2-4e4b-b667-0bf30cea7507"
      },
      "source": [
        "print('correlation coefficent', corr)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "correlation coefficent -0.6591271271271271\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iWTkPtG5AxxX",
        "outputId": "55397a31-e87c-4c51-c5b4-0548672cec20"
      },
      "source": [
        "print('P-VALUE', pvalue)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "P-VALUE 7.67043823229759e-214\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qwK2bzqjA86s"
      },
      "source": [
        "## **Visualization of Correlation with Matplotlib and Seaborn**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p5a_9D2VMVbj"
      },
      "source": [
        "The fastest way to learn more about your data is to use data visualization. In this section, you’ll learn how to visually represent the relationship between two features with an x-y plot. You’ll also use heatmaps to visualize a correlation matrix and scatterplot matrix."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_ZprdPZzMYnI"
      },
      "source": [
        "**Scatterplot matrix**\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BvkUFWZFMmTs"
      },
      "source": [
        "Scatter plots are useful for spotting structured relationships between variables, like whether you could summarize the relationship between two variables with a line. Attributes with structured relationships may also be correlated and good candidates for removal from your dataset. You don't need to delete anything from the test dataframe, but when dealing with real world data this can be necessary."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Je9SxHgPMvhg"
      },
      "source": [
        "pandas.plotting.scatter_matrix(frame, alpha=0.5, figsize=None, ax=None, grid=False, diagonal='hist', marker='.', density_kwds=None, hist_kwds=None, range_padding=0.05, **kwargs) - The command syntax for a scatterplot matrix.\n",
        "\n",
        "For scatterplt matrix we are using the same test df as in SciPy section."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 502
        },
        "id": "arpVQbDAM1Oe",
        "outputId": "7fa5238c-e712-4ab0-bc08-f072de9de77c"
      },
      "source": [
        "#Scatterplot Matrix - Histogram plots\n",
        "\n",
        "#import pandas\n",
        "#from matplotlib import pyplot\n",
        "\n",
        "from pandas.plotting import scatter_matrix\n",
        "\n",
        "scatter_matrix(df, figsize = (14,8))\n",
        "pyplot.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1008x576 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 502
        },
        "id": "-Vg_GPioNR55",
        "outputId": "1f17a43e-af85-43a8-e3b4-1a02840499d8"
      },
      "source": [
        "# Scatterplot Matrix - Kernel Density Estimation\n",
        "\n",
        "scatter_matrix(df, alpha = 0.3, figsize = (14,8), diagonal = 'kde')\n",
        "pyplot.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1008x576 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7bGUdImiNhGv"
      },
      "source": [
        "**X-Y Plots With a Regression Line**\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iB6ja21HNn2n"
      },
      "source": [
        "Now you’ll see how to create an x-y plot with the regression line, its equation, and the Pearson correlation coefficient. The slope and the intercept of the regression line, as well as the correlation coefficient are calculated with linregress()."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        },
        "id": "IAlcpwCvNpZC",
        "outputId": "24372d6a-3bca-4b7a-8f02-02d924568400"
      },
      "source": [
        "# creating X-Y Plots With a Regression Line\n",
        "\n",
        "# slope, intersept, and correlation coefficient calculation \n",
        "slope, intercept, r, p, stderr = scipy.stats.linregress(df['Column1'], df['Column2'])\n",
        "\n",
        "line = f'Regression line: y={intercept:.2f}+{slope:.2f}x, r={r:.2f}'\n",
        "\n",
        "# plotting\n",
        "fig, ax = pyplot.subplots(figsize = (14,8))\n",
        "ax.plot(df['Column1'], df['Column2'], linewidth=0, marker='s', label='Data points')\n",
        "ax.plot(df['Column1'], intercept + slope * df['Column1'], label=line)\n",
        "ax.set_xlabel('Column1')\n",
        "ax.set_ylabel('Column2')\n",
        "ax.legend(facecolor='white')\n",
        "pyplot.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1008x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-8gYFlxXN54v"
      },
      "source": [
        "**Heatmaps of Correlation Matrices**\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eT79s3T8N8Nv"
      },
      "source": [
        "You can calculate the correlation between each pair of attributes. This is called a correlation matrix. You can then plot the correlation matrix and get an idea of which variables have a high correlation with each other.\n",
        "\n",
        "The easiest way to get a pretty heatmap is to use seaborn library. So let's do this.\n",
        "\n",
        "seaborn.heatmap(data, vmin=None, vmax=None, cmap=None, center=None, robust=False, annot=None, fmt='.2g', annot_kws=None, linewidths=0, linecolor='white', cbar=True, cbar_kws=None, cbar_ax=None, square=False, xticklabels='auto', yticklabels='auto', mask=None, ax=None, **kwargs) - Plots rectangular data as a color-encoded matrix."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 504
        },
        "id": "DtGQc2WWODko",
        "outputId": "8f54be48-c5ac-4e86-a26a-22d353c0d2a3"
      },
      "source": [
        "import seaborn as sns\n",
        "\n",
        "f, ax = pyplot.subplots(figsize=(14, 8))\n",
        "corr = df.corr()\n",
        "sns.heatmap(corr, mask=np.zeros_like(corr, dtype=np.bool), cmap=sns.diverging_palette(220, 10, as_cmap=True),\n",
        "            square=True, annot=True, ax=ax)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f632cb39250>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1008x576 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pvrFbtyHONSG"
      },
      "source": [
        "The command returns a table with the coefficients. It sort of looks like the Pandas output with colored backgrounds. The colors help you interpret the output. In this example, the red color represents the number 1, blue corresponds to -0.85."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G2P752bnrNSr"
      },
      "source": [
        "## **Correlation Analysis — Heatmap**[4]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qpyMC7gIsbrB"
      },
      "source": [
        "Some algorithms demands the absence of collinearity in explanatory variables, including logistic regression which will be used for this exercise. Therefore, eliminating highly correlated features is an essential step to avoid this potential pitfall. Correlation analysis with heatmap visualization highlights pairs of features with high correlation coefficient."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_wT_K0O2vb04"
      },
      "source": [
        "import seaborn as sns  \n",
        "import matplotlib.pyplot as plt  "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zm3jcFdEu9MX"
      },
      "source": [
        "plt.figure (figsize = (20,20))\n",
        "correlation = data. corr()\n",
        "#sns.heatmap (correlation. cmap = 'GnBu\", annot = True)\n",
        "sns.heatmap (correlation, cmap='GnBu', annot= True)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gI8RNR0kYptd"
      },
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1gmU7vkrgvM425pVV7EdSyZVeoLChHlIF)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aWw6FHT5Yw2T"
      },
      "source": [
        "As shown, it is not hard to find following pairs of highly correlated features:\n",
        "\n",
        "- Customer_Age & Month_on_Book (0.79)\n",
        "- Total_Trans_Amt & Total_Trans_Ct (0.82)\n",
        "- Avg_Open_To_Buy & Credit_Limit (1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3DLXW7ToY_n0"
      },
      "source": [
        "# **Bivariate Analysis** [4]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "moP3RQPuZaxM"
      },
      "source": [
        "Bivariate EDA investigates the relationship between each explanatory variable and the target variable. Categorical features and numerical variables are addressed using grouped bar chart and box plot respectively, and this exploration can further facilitate the statistical tests used in the filter methods, e.g. Chi-Square and ANOVA test."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_aCxS42uZeqi"
      },
      "source": [
        "Grouped bar chart is used as the visual representation of Chi-Square Analysis"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NMF0pcrGaoDW"
      },
      "source": [
        "for i in range (0, len(X)):\n",
        "  primary_cat = X[i]\n",
        "  plt.figure (figsize = (8,8))\n",
        "  chart = sns.countplot(data =df, x= primary_cat, hue= \"Attrition_flag\", palette = 'GnBu')\n",
        "  \n",
        "  "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cUhtYA5AuMMZ"
      },
      "source": [
        "# **Descriptive Statistics**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vBMaSiSnuZf8"
      },
      "source": [
        "Descriptive Statistics is that branch of Statistics which analyzes brief descriptive coefficients that summarize a given data set. Those coefficients are called ‘descriptive statistics’[5]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dzxGZkceur8T"
      },
      "source": [
        "Descriptive statistics hence provides information about the data you want to analyze and describes them in some manners. More specifically, it collects from the target dataset (population) some descriptive measurements (called parameters). It differs from Inferential Statistics since the latter aims at making assumptions and inference about a population starting from a smaller representation of it, called sample. Indeed, it often happens that the size of the population is far too large to be manipulated, and you’d rather rely on a smaller representation of it. The latter is called sample. From your sample then, you can compute some sample measurements (sample mean, sample variance and so forth) which will be the estimates (or statistics) of the real parameters[5]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wJOYwP49u4Qz"
      },
      "source": [
        "## **Central Tendency**[5]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gXnEpP_kvHpA"
      },
      "source": [
        "Those metrics tell us how our data behave like in their ‘middle’. What does it mean ‘middle’ though? Well, it depends on the metric we are talking about, hence let’s see all of them:[5]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8hz_qsXOvRtu"
      },
      "source": [
        "**Mean:** it is the average value of our data and it has a very easy computation. Just take the sum of your values, divide it by the number of values and, voilà, you have your mean."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qw3iUFPmvb9G"
      },
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1rm5XR4WYshnqpH-boXRcjHOLoXua4feJ)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LPKk-WoewYVx"
      },
      "source": [
        "mean=x.sum()/len(x)\n",
        "print('Mean: {}'.format(mean))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oKNiInx_wesf"
      },
      "source": [
        "import statistics\n",
        "print('Mean: {}'.format(x.mean()))\n",
        "Output: Mean: 5.84333333333333"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CodLKGO3wrGT"
      },
      "source": [
        "**Median:** it is the number that lies in the middle of a list of ordered numbers (which may be an ascending or descending order)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E_eVmFtBxlPp"
      },
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1k06IXmnpYaoPgMvSdNjcetRMKCvwBwio)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AYOwoKyT0T43"
      },
      "source": [
        "If the number of values is even, the middle positional value is obtained as the average of the two central values:\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KBbkWZVw0kkL"
      },
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1gNhWesZlP9DqMPjFBpQa2huNdyvCzvI7\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NytDNv500vcT"
      },
      "source": [
        "print('Median: {}'.format(x.median()))\n",
        "Output: Median: 5.8"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "udggzYEP0w7_"
      },
      "source": [
        "**Mode:** it is defined as the value that appears the most frequently in our data. If a value appears repeatedly throughout the data, we also know it will influence the average towards the modal value, hence it is an important measure of central tendency of our data."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "He_7J2IN1WIO"
      },
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1P20OMsNpfWdUahlWfczyqeNaKZKreWiZ)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YGvELmY01go9"
      },
      "source": [
        "mode=x.mode()\n",
        "print('Mode: {}'.format(mode))\n",
        "Output: Mode: 5.0"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jdAV9Ev91kg2"
      },
      "source": [
        "Now, before concluding this paragraph about the measures of central tendency, it is worth spending some words about the relationship among mean, median and mode.\n",
        "As anticipated, all of them describe the behavior of data in their ‘middle’. Furthermore, if compared to each other, they can also suggest something about the shape of the probability distribution of our data. Indeed, whenever mean=median=mode, the distribution is known to be symmetric ( that means, the probability of being any given distance on one side of the value about which symmetry occurs is the same as the probability of being the same distance on the other side of that value)[5]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tSbhwkL31p0-"
      },
      "source": [
        "Namely, Normal distribution is symmetric, hence can easily demonstrate that mean=median=mode."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S61Gdzav5HxO"
      },
      "source": [
        "![](https://drive.google.com/uc?export=view&id=14j8H33wyYryudTsnkUehMZK-0Byi3IyT)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f2ivBwR45U6C"
      },
      "source": [
        "On the other hand, if have either mode>median>mean or mean>median>mode, we are facing an asymmetric distribution:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "87GCAVPo5wJj"
      },
      "source": [
        "![](https://drive.google.com/uc?export=view&id=11QTnsldSkZpntxxJYKVfOaemi-WVRkbS)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8Svhba3e6Cw7"
      },
      "source": [
        "The first picture (mean>median>mode) shows a positive asymmetric distribution, while the second one (mode>median>mean) exhibits a negative asymmetry. A way to check the symmetry of distribution is thought the measure of Skewness:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j26sDhTP7SAr"
      },
      "source": [
        "![](\n",
        "https://drive.google.com/uc?export=view&id=1ujtOaPQ-lUoBQ5C6gMhnLtFXxHUCFcf4)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fMu2-71n7cch"
      },
      "source": [
        "Positive skewness indicates a positive asymmetry, while a negative skewness indicates negative asymmetry.\n",
        "Now, recalling the parameters obtained from our dataset:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WxfO6ccx7frw"
      },
      "source": [
        "Mean: 5.843333333333335\n",
        "Median: 5.8\n",
        "Mode: 5.0"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ni7SblGd7iU6"
      },
      "source": [
        "We can see that mean>median>mode, hence the distribution should exhibit a positive skewness. Let’s check it out:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vK-uxNmM7qSp"
      },
      "source": [
        "f, (ax_box, ax_hist) = plt.subplots(2, sharex=True, gridspec_kw= {\"height_ratios\": (0.2, 1)})\n",
        "sns.boxplot(x, ax=ax_box)\n",
        "ax_box.axvline(mean, color='r', linestyle='--')\n",
        "ax_box.axvline(median, color='g', linestyle='-')\n",
        "ax_box.axvline(mode, color='b', linestyle='-')\n",
        "sns.distplot(x, ax=ax_hist)\n",
        "ax_hist.axvline(mean, color='r', linestyle='--')\n",
        "ax_hist.axvline(median, color='g', linestyle='-')\n",
        "ax_hist.axvline(mode, color='b', linestyle='-')\n",
        "plt.legend({'Mean':mean,'Median':median,'Mode':mode})\n",
        "ax_box.set(xlabel='')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qfm5ZyUp8PFF"
      },
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1Swic-5ssEwe_9eoeC6t-EJ3kP9Oj4n2B)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wDY-S3GR7wYW"
      },
      "source": [
        "Let’s compute the Skewness:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G54SGMfl71K8"
      },
      "source": [
        "from scipy.stats import skew\n",
        "print('Skewness: {}'.format(skew(x)))\n",
        "Output: Skewness: 0.3117530585022963"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xoYyYpe974-9"
      },
      "source": [
        "As you can see, the skewness is greater than zero, hence it indicates a positive asymmetry, confirming the fact that mean>median>mode."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9b6VryzlCS_g"
      },
      "source": [
        "## **Measures of Dispersion [5]**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "urt0LQBkCeSf"
      },
      "source": [
        "If the measures of central tendency dwell on the ‘average’ behavior of our data, on the other hand, measures of dispersion focus on how much our data tend to vary."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fFUCXvgKCoo4"
      },
      "source": [
        "**Range:** it is the most intuitive measure of dispersion. It is computed as the difference between the maximum and minimum values, and it suggests how spread our data are."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6DNc36XvCtKw"
      },
      "source": [
        "r=x.max()-x.min()\n",
        "print('Range: ',r)\n",
        "Output: Range: 3.6000000000000005"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ayT8BKK9CwCI"
      },
      "source": [
        "We can also visualize that dispersion with the aid of a boxplot:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9vsDNnyoC0Ef"
      },
      "source": [
        "fig1, ax1 = plt.subplots()\n",
        "ax1.set_title('BoxPlot')\n",
        "ax1.boxplot(x)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0w_nhojCDKgp"
      },
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1bVSCi81RHPvu3K21Vw7_M-sdjwpRG3cq)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Wd5PTvrwDYtP"
      },
      "source": [
        "**Interquantile Range:** quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities. More specifically, the 0.x quantile (also called x percentile) leaves at its left x% of the probability. Furthermore, the 0, 0.25, 0.5, 0.75 and 1 quantiles are known as, respectively, 0, 1st, 2nd,3rd and 4th quartiles. Note that the Second Quartile (Q2) corresponds to the median value, since it leaves 50% of the probability to its left and 50% of probability to its right."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CqrR13JrDdJW"
      },
      "source": [
        "Q1=np.percentile(x, 25) \n",
        "Q2=np.percentile(x, 50)  \n",
        "Q3=np.percentile(x, 75)\n",
        "print('Q1: {}'.format(Q1))\n",
        "print('Q2: {}'.format(Q2))\n",
        "print('Q3: {}'.format(Q3))\n",
        "Output: Q1: 5.1 \n",
        "        Q2: 5.8 \n",
        "        Q3: 6.4"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lQ2vNCcGJ0X2"
      },
      "source": [
        "Let’s visualize them on our distribution graph:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NWsW1gO4J4UD"
      },
      "source": [
        "f, (ax_box, ax_hist) = plt.subplots(2, sharex=True, gridspec_kw= {\"height_ratios\": (0.2, 1)})\n",
        "sns.boxplot(x, ax=ax_box)\n",
        "ax_box.axvline(Q1, color='r', linestyle='--')\n",
        "ax_box.axvline(Q2, color='g', linestyle='-')\n",
        "ax_box.axvline(Q3, color='b', linestyle='-')\n",
        "sns.distplot(x, ax=ax_hist)\n",
        "ax_hist.axvline(Q1, color='r', linestyle='--')\n",
        "ax_hist.axvline(Q2, color='g', linestyle='-')\n",
        "ax_hist.axvline(Q3, color='b', linestyle='-')\n",
        "plt.legend({'Q1':Q1,'Q2':Q2,'Q3':Q3})\n",
        "ax_box.set(xlabel='')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8sYAR6GeKflD"
      },
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1enOVPXgMPjbyYQtx28LkiMalhp1fAAep)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-r9kvLUtK27r"
      },
      "source": [
        "Interquantiles ranges are the difference between two quantiles. In particular, in the boxplot above you can see the interquartile range, computed as the difference between Q3 and Q1."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UDvNjVK4K87p"
      },
      "source": [
        "IQR=Q3-Q1\n",
        "print('Interquartile Range: ',IQR)\n",
        "Output: Interquartile Range:  1.3000000000000007"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CGQZR_JDLCIx"
      },
      "source": [
        "**Variance:**it summarizes how much your data differs from the mean and it is computed as follows:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8El0U8CjLT0y"
      },
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1nhu7CbZ0CJx4sNVLIF5rySZuf_0I9lgc)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_eBAJXy5L0w5"
      },
      "source": [
        "Where mu is the mean of the population.\n",
        "However, since it often happens that the square of your unit of measurement is meaningless (namely, what does it means “the variance of my portfolio is 120 squared dollars”?), a more manageable measure it’s used: the standard deviation, which is nothing but the square root of the variance:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CXVqsSY7MfDq"
      },
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1GjxPwUvexQ0HcuMjCTq8ikPOf3r5La3P)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZgqELJ31L-PF"
      },
      "source": [
        "sigma=np.std(x)\n",
        "print('Standard Deviation: ',sigma)\n",
        "Output: Standard Deviation: 0.8253012917851409"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Inferential Statistics**"
      ],
      "metadata": {
        "id": "KtKeFnj_8xbw"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**What is meant by Inferential Statistics?**\n",
        "\n",
        "In simple words, inferential statistics is a technique we used to find the conclusion using some data and on basis of some conclusions, we are doing the prediction [**7**]"
      ],
      "metadata": {
        "id": "MG4dNzd19FnI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Why do we use inferential statistics?**\n",
        "\n",
        "We are using inferential statistics when we have population data and we need to estimate or compare the result with sample data which is drawn from population data.\n",
        "For eg., You randomly select a sample of 12th graders in your state and collect data on their Board results and other characteristics.\n",
        "You can use inferential statistics to make estimates and test hypotheses about the whole population of 12th graders in the state based on your sample data.\n",
        "Now, Let’s discuss the different concepts in Inferential statistics [7]"
      ],
      "metadata": {
        "id": "_ZXR3tev9byX"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Gaussian/Normal Distribution**:\n"
      ],
      "metadata": {
        "id": "B9TdUPPh91Bu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "A variable is said to be normally distributed or have a normal distribution if its distribution has the shape of a normal curve — a special bell-shaped curve. In Normal Distribution both sides of the curve are symmetric and the value of the mean, median, and mode are the same. The graph of a normal distribution is called the normal curve. In Normal Distribution, values range from 0 to 1.[7]"
      ],
      "metadata": {
        "id": "BQmBql0l96Vt"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](\n",
        "https://drive.google.com/uc?export=view&id=12BB9fYa_Xxnqm1O9f4GvH9uqxUxALOeb)"
      ],
      "metadata": {
        "id": "IWz_bkPw2dzP"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=10Bdz5-vK7x84BCWMDY5u_9DUUinYwd3a)"
      ],
      "metadata": {
        "id": "kzSQsyqn26OQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Standard Normal Distribution**\n",
        "\n",
        "Standard Normal Distribution is an extended version of Normal distribution with mean 0 and standard deviation 1. In Standard Normal Distribution we are using use Z-score to calculate the values. In Standard Normal Distribution values range from -1 to 1.[6]"
      ],
      "metadata": {
        "id": "CsubwtzK3SZV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1n1NZNjy4lyaC_x3zrM2TtA-RJZNKZkIl)"
      ],
      "metadata": {
        "id": "6lot0dMJ4qLP"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Hypothesis Testing**\n"
      ],
      "metadata": {
        "id": "8D92AMr_7SeG"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Hypothesis testing is a statistical method that is used in making statistical decisions using experimental data to either accept or reject statistical hypotheses. Statistical hypotheses are of two types:[7]"
      ],
      "metadata": {
        "id": "gAMeGaj-7gRn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Null hypothesis,**\n",
        "\n",
        " H0 represents a hypothesis of chance basis. A null hypothesis is a general statement that says there is no statistical significance between any two variables in the hypothesis. The null-hypothesis is considered an accepted truth. for eg. suppose we wanted to check whether a coin was fair and balanced. A null hypothesis might say, that half flips will be of the head and half will of tails."
      ],
      "metadata": {
        "id": "bljgISb97rgm"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Alternative hypothesis**\n",
        "\n",
        " H1 represents a hypothesis of observations that are influenced by some non-random cause. The alternative hypothesis is the hypothesis used in hypothesis testing that is contrary to the null hypothesis. For eg. alternative hypothesis might say that flips of head and tail may be very different [7]."
      ],
      "metadata": {
        "id": "ddB1HUho8BuE"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=157uRWK2AHZHQ19ZqLp0jr9nDkBytQGCY)"
      ],
      "metadata": {
        "id": "CkXNskx58ro6"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Steps to perform Hypothesis testing:**\n",
        "\n",
        "1. Define Null-hypothesis. For eg. Coin is fair\n",
        "2. Define Alternate-hypothesis. For eg. Coin is unfair.\n",
        "3. Perform an experiment to test whether we should reject/accept null-hypothesis\n",
        "4. Reject/Accept null-hypothesis [7]"
      ],
      "metadata": {
        "id": "onvCldkp81tK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Level of significance:**\n",
        "\n",
        "It means the degree of significance in which we accept or reject the null-hypothesis. Since in most of the experiments 100% accuracy is not possible for accepting or rejecting a hypothesis, so we, therefore, select a level of significance. It is denoted by alpha (∝).[7]"
      ],
      "metadata": {
        "id": "sSL-IGBNAklt"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**P-Value**\n",
        "\n",
        "P-value is used to find extreme values when the null hypothesis (h0) is true. In simpler words, it is used to reject or support the null hypothesis during hypothesis testing.[7]"
      ],
      "metadata": {
        "id": "hC3yS_hPBAcD"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "During hypothesis testing, we assume a significance level (α), generally 5% (α = 0.05). It is the probability of rejecting the null hypothesis when it is true. It is observed that the lower the p-value, the higher is the probability of rejecting the null hypothesis. When:\n",
        "\n",
        "- p ≤ (α = 0.05) : reject h0.\n",
        "- p > (α = 0.05) : reject h1 (or accept h0"
      ],
      "metadata": {
        "id": "UArldgTYBLrK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1h6GHmt6Oy5ul3qSGYrcxohFmnjp0XvQJ)"
      ],
      "metadata": {
        "id": "SU14ln9gBwvC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Hypothesis testing types**"
      ],
      "metadata": {
        "id": "FbtPZYWnCvKo"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now Let’s see some of the widely used hypothesis testing types and implement them using Python.\n",
        "\n",
        "- Z-Test\n",
        "- T-Test\n",
        "- ANOVA Test (F-test)\n",
        "- Chi-Square Test"
      ],
      "metadata": {
        "id": "ZBRmU273C0Hx"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Z-Test**\n",
        "\n",
        "Z-test is a statistical method to determine whether the distribution of the test statistics can be approximated by a normal distribution.\n",
        "It is used when the sample size is greater than 30 and the population standard deviation is known.[7]"
      ],
      "metadata": {
        "id": "TplCXImKC-Bx"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Steps to do Z-test:**\n",
        "\n",
        "- First, identify the null and alternate hypotheses.\n",
        "- Determine the level of significance (∝).\n",
        "- Find the critical value of z in the z-test using\n",
        "- Calculate the z-test statistics."
      ],
      "metadata": {
        "id": "27JumqPWDcmR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1vJ7QEwvlp66VTXrfkhYMW7GZ8Oj8XFKr)"
      ],
      "metadata": {
        "id": "h0XJkt3WFyAR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here,\n",
        "\n",
        "- X¯: mean of the sample.\n",
        "- Mu: mean of the population.\n",
        "- Sd: Standard deviation of the population.\n",
        "- n: sample size"
      ],
      "metadata": {
        "id": "s20bqQlEF-i9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Python Implementation**"
      ],
      "metadata": {
        "id": "iwTDDSxYGD99"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now, let’s see the python implementation of Z-test\n",
        "There are two types of Z-test"
      ],
      "metadata": {
        "id": "-c3xzcyKGj7p"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "One sample Z-test\n",
        "Suppose the IQ in a certain population is normally distributed with a mean of μ = 100 and a standard deviation of σ = 15.\n",
        "A researcher wants to know if a new drug affects IQ levels, so he recruits 20 patients to try it and records their IQ levels.[7]"
      ],
      "metadata": {
        "id": "riLzheKrIGlW"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The following code shows how to perform a one sample z-test in Python to determine if the new drug causes a significant difference in IQ levels:"
      ],
      "metadata": {
        "id": "-ZzoDIT6IOl-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1bwNrd3chF87y3cbPyj67Tvxc06pa46CJ)"
      ],
      "metadata": {
        "id": "kevJTDYoKmCh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The test statistic for the one sample z-test is 1.5976 and the corresponding p-value is 0.1101.\n",
        "\n",
        "Since this p-value is not less than .05, we do not have sufficient evidence to reject the null hypothesis. In other words, the new drug does not significantly affect IQ level.[7]"
      ],
      "metadata": {
        "id": "hGQtG4J1KyZ3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Two sample Z-test**\n",
        "\n",
        "Suppose the IQ levels among individuals in two different cities are known to be normally distributed with known standard deviations.\n",
        "A researcher wants to know if the mean IQ level between individuals in city A and city B are different, so she selects a simple random sample of 20 individuals from each city and records their IQ levels.[7]"
      ],
      "metadata": {
        "id": "3QOLQyjmK6bV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**T-test**\n",
        "\n",
        "A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related to certain features. It is mostly used when the data sets, like the set of data recorded as an outcome from flipping a coin a 100 times and where population standard deviation is unknown.[7]"
      ],
      "metadata": {
        "id": "jFwYVzXTLIkN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Steps to do T-test**\n",
        "\n",
        "- Determining a Null and Alternate Hypothesis\n",
        "- Determining a Degrees of Freedom\n",
        "- Calculating the T-Statistics\n",
        "- Calculating the critical T-value from the T-Distribution\n",
        "- Comparing the critical T-values with the calculated T-Statistics"
      ],
      "metadata": {
        "id": "9n861EcOMOOi"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**One sample t-test:**"
      ],
      "metadata": {
        "id": "BxrPsomWMX1Z"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](\n",
        "https://drive.google.com/uc?export=view&id=1p84FML7Zw6jm26kLY3AdGicqmGrPmGRk)"
      ],
      "metadata": {
        "id": "PmmJ93QEM2r4"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here, p-value is not less than .05, we do not have sufficient evidence to reject the null hypothesis. In other words, the new drug does not significantly affect IQ level."
      ],
      "metadata": {
        "id": "pQHtC-AINAMw"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Two-sample t-test:**\n"
      ],
      "metadata": {
        "id": "Q3bu9BifQREz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![image.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "O5vqWabhQVLa"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here, p-value is less than .05, we have sufficient evidence to reject the null hypothesis. In other words, the mean IQ level is significantly different between the two cities."
      ],
      "metadata": {
        "id": "BFQB9EhMQdJz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**ANOVA Test (F-Test)**\n"
      ],
      "metadata": {
        "id": "MmGYhsSZQoFb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The t-test works well when dealing with two groups, but sometimes we want to compare more than two groups at the same time. For example, if we wanted to test whether voter age differs based on some categorical variable like race, we have to compare the means of each level or group the variable. In common words, ANOVA is a statistical inference test that lets you compare multiple groups at the same time.[7]"
      ],
      "metadata": {
        "id": "Jkjx0pPrQsqD"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](\n",
        "https://drive.google.com/uc?export=view&id=1IqqOifqewIaDX0bVVA94636SfG2mewwQ)"
      ],
      "metadata": {
        "id": "ICUWOd3-RK-b"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**One-Way ANOVA:**\n",
        "\n",
        "A one-way ANOVA has just one independent variable. For example, differences in Corona cases can be assessed by Country, and a Country can have 2, 20, or more different categories to compare [7]"
      ],
      "metadata": {
        "id": "ThJ84-1gRTrC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1XagpifgCQRQGgyqzyFBmjLquJxeCNbxh)"
      ],
      "metadata": {
        "id": "lrtw9bPpRsfD"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here, we can see that value is <0.05 hence we can reject the null hypothesis"
      ],
      "metadata": {
        "id": "mPwD5ejaRz5C"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Two-sample t-test:**"
      ],
      "metadata": {
        "id": "Khy6iJP0BcRI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=11NuKFniEKz9ulePt7n2Ntp5kIge-ET05)"
      ],
      "metadata": {
        "id": "FNcEjmkqBegm"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here, p-value is less than .05, we have sufficient evidence to reject the null hypothesis. In other words, the mean IQ level is significantly different between the two cities.[7]"
      ],
      "metadata": {
        "id": "3LgV4RC-COI9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**ANOVA Test (F-Test)**"
      ],
      "metadata": {
        "id": "2Vvvvz5pCTP-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1ZUNnXhZHxKley1bIldxLdGgqidOca7vg)"
      ],
      "metadata": {
        "id": "lfbLdWhfCz6t"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The t-test works well when dealing with two groups, but sometimes we want to compare more than two groups at the same time. For example, if we wanted to test whether voter age differs based on some categorical variable like race, we have to compare the means of each level or group the variable. In common words, ANOVA is a statistical inference test that lets you compare multiple groups at the same time**[7]**"
      ],
      "metadata": {
        "id": "jupWpcimCa29"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**1-One-Way ANOVA:** A one-way ANOVA has just one independent variable. For example, differences in Corona cases can be assessed by Country, and a Country can have 2, 20, or more different categories to compare[7]"
      ],
      "metadata": {
        "id": "J-P4Q4poC_88"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1u5D3J-i3voBklzyyOn0mOJ_JiKEhHbiB)"
      ],
      "metadata": {
        "id": "Naxp6FapEnj7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here, we can see that value is <0.05 hence we can reject the null hypothesis"
      ],
      "metadata": {
        "id": "60knI0KzEu8j"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Two Way ANOVA Test:**"
      ],
      "metadata": {
        "id": "psSfs0hREyf5"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "An Analysis of Variance Test that has two independent variables is known as a Two-way ANOVA test. This test is also known as Factorial ANOVA Test.[7]"
      ],
      "metadata": {
        "id": "aK0V0MYYE2qQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](\n",
        "https://drive.google.com/uc?export=view&id=1AKH2ANwCn6ZEjQZb6zqMCGqbna-MfnKL)"
      ],
      "metadata": {
        "id": "8ETkaRgoFWRU"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Chi-Square Test:**"
      ],
      "metadata": {
        "id": "FNWdvVHQFf4j"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Chi-square test claims about the population proportions. It is a Non-parametric that is performed on categorical (nominal/ordinal) data.\n",
        "For eg. A research scholar is interested in the relationship between the placement of students in the statistics department of a reputed University and their C.G.P.A (their final assessment score).\n",
        "He obtains the placement records of the past five years from the placement cell database (at random). He records how many students who got placed fell into each of the following C.G.P.A. categories — 9–10, 8–9, 7–8, 6–7, and below 6.[7]"
      ],
      "metadata": {
        "id": "DDsCbTe8FkXK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1b7l-BYfnKSAhNRBpXoOVXW23Rz2MnaK7)"
      ],
      "metadata": {
        "id": "uiT6fwmKHvFT"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![](https://drive.google.com/uc?export=view&id=1WuNk76Nijz2Gefa2iLQDx6pRWEDjeTBE)"
      ],
      "metadata": {
        "id": "0TVrNliAH_Iz"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5CKqdX86iIBc"
      },
      "source": [
        "# **References**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OZF79FvqiNhO"
      },
      "source": [
        "[1-Exploring Correlation in Python: Pandas, SciPy](https://re-thought.com/exploring-correlation-in-python/)\n",
        "\n",
        "[2- How to find the correlation between continuous variables and visualise it using python?](https://medium.com/geekculture/how-to-find-the-correlation-between-continuous-variables-and-visualise-it-using-python-7faf5b028ae0)\n",
        "\n",
        "[3-Statistical Analysis in Python](https://medium.com/mlearning-ai/statistical-analysis-in-python-9a04cf7705b7)\n",
        "\n",
        "[4-Feature Selection and EDA in Machine Learning](https://towardsdatascience.com/feature-selection-and-eda-in-python-c6c4eb1058a3)\n",
        "\n",
        "[5-Descriptive Statistics with Python](https://medium.com/dataseries/descriptive-statistics-with-python-75e2b1249e8d)\n",
        "\n",
        "[6- Choosing the appropriate correlation coefficient](https://medium.com/@vatvenger/choosing-the-appropriate-correlation-coefficient-a167a65203ff)\n",
        "\n",
        "[7-Inferential Statistics using Python](https://patelayush176.medium.com/inferential-statistics-using-python-e1e563810ca0)\n",
        "\n",
        "[Python Tricks for Data Science](https://medium.com/analytics-vidhya/python-tricks-for-data-science-fd038ab838a)\n",
        "\n",
        "[23 great Pandas codes for Data Scientists](https://towardsdatascience.com/23-great-pandas-codes-for-data-scientists-cca5ed9d8a38)\n",
        "\n",
        "[statsmodels](https://www.statsmodels.org/stable/index.html)\n",
        "\n",
        "[Skewness — Everything you need to know about Skewness](https://aayushmaan1306.medium.com/skewness-everything-you-need-to-know-about-skewness-d94e88508e92)\n",
        "\n"
      ]
    }
  ]
}