Atharv_Patawar_A4_Linear_Regression.ipynb

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        "<a href=\"https://colab.research.google.com/github/savioratharv/Compute_tasks/blob/main/Atharv_Patawar_Linear_Regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "markdown",
      "source": [
        "# Linear Regression\n",
        "Implementing Linear Regression for predicting profit of a food truck given the population and profits of different cities\n"
      ],
      "metadata": {
        "id": "XbA5XjSilR4j"
      }
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      "execution_count": 1,
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        "id": "5_cw35relJgl"
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      "source": [
        "import os\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.metrics import r2_score,mean_squared_error\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#in dataset both the column has values in multiple of 10k"
      ],
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        "id": "36GyLOkigQAq"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Reading the dataset"
      ],
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        "id": "6WCVaXe8lll3"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#load dataset\n",
        "df = pd.read_csv(\"Data1.txt\", sep=\",\",header=None)"
      ],
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        "id": "i4huSnTRloPT"
      },
      "execution_count": 3,
      "outputs": []
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      "source": [
        "df"
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      "execution_count": 4,
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              "          0         1\n",
              "0    6.1101  17.59200\n",
              "1    5.5277   9.13020\n",
              "2    8.5186  13.66200\n",
              "3    7.0032  11.85400\n",
              "4    5.8598   6.82330\n",
              "..      ...       ...\n",
              "92   5.8707   7.20290\n",
              "93   5.3054   1.98690\n",
              "94   8.2934   0.14454\n",
              "95  13.3940   9.05510\n",
              "96   5.4369   0.61705\n",
              "\n",
              "[97 rows x 2 columns]"
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        "#describe the dataframe\n",
        "df.describe()"
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          "data": {
            "text/plain": [
              "               0          1\n",
              "count  97.000000  97.000000\n",
              "mean    8.159800   5.839135\n",
              "std     3.869884   5.510262\n",
              "min     5.026900  -2.680700\n",
              "25%     5.707700   1.986900\n",
              "50%     6.589400   4.562300\n",
              "75%     8.578100   7.046700\n",
              "max    22.203000  24.147000"
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              "      <th>count</th>\n",
              "      <td>97.000000</td>\n",
              "      <td>97.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>8.159800</td>\n",
              "      <td>5.839135</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>3.869884</td>\n",
              "      <td>5.510262</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>5.026900</td>\n",
              "      <td>-2.680700</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>5.707700</td>\n",
              "      <td>1.986900</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>6.589400</td>\n",
              "      <td>4.562300</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>8.578100</td>\n",
              "      <td>7.046700</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>22.203000</td>\n",
              "      <td>24.147000</td>\n",
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              "                                                     [key], {});\n",
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              "\n",
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          "metadata": {},
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    },
    {
      "cell_type": "markdown",
      "source": [
        "### Scatter plot of Population vs Profit"
      ],
      "metadata": {
        "id": "-utpyHE8l8XX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#plot"
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      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import seaborn as sns\n",
        "sns.scatterplot(x=df[0],y=df[1],palette='mako')\n",
        "plt.xlabel('Population')\n",
        "plt.ylabel('Profit')"
      ],
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      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Profit')"
            ]
          },
          "metadata": {},
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Function to compute the cost function "
      ],
      "metadata": {
        "id": "iGFXAq_YoWZq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "### Function to compute the cost function "
      ],
      "metadata": {
        "id": "_8d1sdJmoVGb"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def computeCost(X, y, theta):\n",
        "    inner_product = np.power(((X * theta.T) - y) , 2)\n",
        "    return np.sum(inner_product) / (2 * len(X))"
      ],
      "metadata": {
        "id": "Az8pJnBMoa1N"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Appending 1s to the front of the dataset"
      ],
      "metadata": {
        "id": "v31Nvikf2xYm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#insert column with 1s\n",
        "df.insert(0,\"ones\",1)"
      ],
      "metadata": {
        "id": "XQlQ0VvR23gJ"
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df"
      ],
      "metadata": {
        "id": "GQSPt0HRX_WL",
        "outputId": "c909bd74-e46a-4b88-e725-2506c4310245",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        }
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    ones        0         1\n",
              "0      1   6.1101  17.59200\n",
              "1      1   5.5277   9.13020\n",
              "2      1   8.5186  13.66200\n",
              "3      1   7.0032  11.85400\n",
              "4      1   5.8598   6.82330\n",
              "..   ...      ...       ...\n",
              "92     1   5.8707   7.20290\n",
              "93     1   5.3054   1.98690\n",
              "94     1   8.2934   0.14454\n",
              "95     1  13.3940   9.05510\n",
              "96     1   5.4369   0.61705\n",
              "\n",
              "[97 rows x 3 columns]"
            ],
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              "\n",
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              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>7.0032</td>\n",
              "      <td>11.85400</td>\n",
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              "    <tr>\n",
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              "    <tr>\n",
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              "      <td>8.2934</td>\n",
              "      <td>0.14454</td>\n",
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              "    <tr>\n",
              "      <th>95</th>\n",
              "      <td>1</td>\n",
              "      <td>13.3940</td>\n",
              "      <td>9.05510</td>\n",
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              "      <td>5.4369</td>\n",
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              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-798cddb7-0dde-4aa9-95c9-e35512f91e81 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-798cddb7-0dde-4aa9-95c9-e35512f91e81');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Set training data (X) and target variable (y)"
      ],
      "metadata": {
        "id": "HQbvSZFcsExq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "cols = df.shape[1]\n",
        "x = df.iloc[:,0:cols-1]\n",
        "y = df.iloc[: , cols-1:cols]"
      ],
      "metadata": {
        "id": "WVCVPoznsMms"
      },
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Converting dataframe to numpy matrices and creating a parameter (theta) matrix"
      ],
      "metadata": {
        "id": "bY6E4Mc2sSSC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#converting X,y into numpy matrix\n",
        "x_mat = np.matrix(x.values)\n",
        "y_mat = np.matrix(y.values)"
      ],
      "metadata": {
        "id": "qr-CsrRAsV0_"
      },
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#converting theta into numpy matrix\n",
        "# take initial values as [0,0] for theta\n",
        "theta = np.matrix(np.array([0,0]))\n",
        "\n",
        "print(theta)"
      ],
      "metadata": {
        "id": "xgRDEMANaCGu",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "29e7b381-211f-435f-a6ed-1f1dbeb4df15"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0 0]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(theta.ravel())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yvqJU0tfOnTz",
        "outputId": "2ddb2f2c-ea41-42a5-efdb-6bfb88ffda7c"
      },
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0 0]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(computeCost(x_mat,y_mat,theta))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "remLvAAxOqwW",
        "outputId": "1ef6523b-ac7f-489d-a294-1654582fabbc"
      },
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "32.072733877455676\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Function to perform gradient descent on parameters theta by repeatedly updating the parameters"
      ],
      "metadata": {
        "id": "cbfeP2qas_4o"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def gradiantDescent(x,y,theta,alpha,n):\n",
        "    temp = np.matrix(np.zeros(theta.shape))\n",
        "    parameters = theta.ravel().shape[1]\n",
        "    cost = np.zeros(n)\n",
        "\n",
        "    # With each iteration, we are calculating the changes to be made to the\n",
        "    # parameter (theta) value to reduce the error (cost)\n",
        "    for i in range(n):\n",
        "        \n",
        "        error = (x *theta.T)-y\n",
        "        # number of parameters to be calculated,here we have 2 parameters theta [0,0] and theta [0,1]\n",
        "        for j in range (parameters):\n",
        "        \n",
        "        \n",
        "            term = np.multiply(error , x[: , j])\n",
        "            temp[0,j] = theta[0,j] - ((alpha /len(x)) *np.sum(term))\n",
        "        \n",
        "        theta = temp\n",
        "        cost[i] = computeCost(x,y,theta)\n",
        "    \n",
        "    return theta , cost"
      ],
      "metadata": {
        "id": "Qz1wNo7PPMWf"
      },
      "execution_count": 56,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Set values for learning rate and number of iterations\n",
        "- alpha here denotes the learning rate that helps to determine how quickly the algorithm\n",
        "    will converge to the optimal solution\n",
        "- iters denotes the number of iterations"
      ],
      "metadata": {
        "id": "Adv1nVcItTJs"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# take alpha 0.01 \n",
        "# iters=1000\n",
        "alpha = 0.01\n",
        "n = 1000\n",
        "\n",
        "\n",
        "theta, cost = gradiantDescent(x_mat,y_mat,theta,alpha,n)"
      ],
      "metadata": {
        "id": "FBz7ob7vtRLr"
      },
      "execution_count": 57,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "theta"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UIqK_JiVNo7P",
        "outputId": "1bf247c2-398a-4b06-e733-f11848a06ae3"
      },
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "matrix([[-3.87805118,  1.1912525 ]])"
            ]
          },
          "metadata": {},
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "\n",
        "### Using Matplotlib library to visualize our solution using scatter plot"
      ],
      "metadata": {
        "id": "W3HlzF5pt_0Z"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# linspace function will create an evenly-spaced series of points within the range of our data\n",
        "x = np.linspace(df[0].min(), df[1].max(), 100)  \n",
        "f = theta[0, 0] + (theta[0, 1] * x)\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(10, 7))  \n",
        "ax.plot(x, f, 'r', label='Prediction')  \n",
        "ax.scatter(df[0], df[1], label='Traning Data')  \n",
        "ax.legend(loc=2)  \n",
        "ax.set_xlabel('Population')  \n",
        "ax.set_ylabel('Profit')  \n",
        "ax.set_title('Predicted Profit vs. Population Size')\n"
      ],
      "metadata": {
        "id": "gXP5psuyuAPr",
        "outputId": "ecfe3eec-5fa2-4e0d-89a5-8ab4dab7beae",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 475
        }
      },
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Predicted Profit vs. Population Size')"
            ]
          },
          "metadata": {},
          "execution_count": 59
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x504 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(f)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vTL4mr-eNclP",
        "outputId": "aa9c4d29-8f7e-43c7-e9b4-5d4bc0ad750c"
      },
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 2.11025603  2.3403254   2.57039476  2.80046412  3.03053349  3.26060285\n",
            "  3.49067221  3.72074158  3.95081094  4.1808803   4.41094967  4.64101903\n",
            "  4.8710884   5.10115776  5.33122712  5.56129649  5.79136585  6.02143521\n",
            "  6.25150458  6.48157394  6.7116433   6.94171267  7.17178203  7.40185139\n",
            "  7.63192076  7.86199012  8.09205948  8.32212885  8.55219821  8.78226757\n",
            "  9.01233694  9.2424063   9.47247567  9.70254503  9.93261439 10.16268376\n",
            " 10.39275312 10.62282248 10.85289185 11.08296121 11.31303057 11.54309994\n",
            " 11.7731693  12.00323866 12.23330803 12.46337739 12.69344675 12.92351612\n",
            " 13.15358548 13.38365484 13.61372421 13.84379357 14.07386294 14.3039323\n",
            " 14.53400166 14.76407103 14.99414039 15.22420975 15.45427912 15.68434848\n",
            " 15.91441784 16.14448721 16.37455657 16.60462593 16.8346953  17.06476466\n",
            " 17.29483402 17.52490339 17.75497275 17.98504211 18.21511148 18.44518084\n",
            " 18.6752502  18.90531957 19.13538893 19.3654583  19.59552766 19.82559702\n",
            " 20.05566639 20.28573575 20.51580511 20.74587448 20.97594384 21.2060132\n",
            " 21.43608257 21.66615193 21.89622129 22.12629066 22.35636002 22.58642938\n",
            " 22.81649875 23.04656811 23.27663747 23.50670684 23.7367762  23.96684557\n",
            " 24.19691493 24.42698429 24.65705366 24.88712302]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots(figsize = (12, 8))\n",
        "ax.plot(np.arange(n), cost, 'r')\n",
        "ax.set_xlabel('Iterations')\n",
        "ax.set_ylabel('Cost')\n",
        "ax.set_title('Error vs Training epoch')"
      ],
      "metadata": {
        "id": "iaOPcKBtuG7v",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 530
        },
        "outputId": "8f7fd4ea-4c9c-4bff-aa69-9a9e6ac06282"
      },
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Error vs Training epoch')"
            ]
          },
          "metadata": {},
          "execution_count": 61
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "SCIKIT LEARN IMPLEMENTATION\n",
        "\n",
        "-Implement various type of errors,\n",
        " eg.Mean squared error,R_squared_score\n",
        "choose best for the evaluting model,\n",
        "and justify why it is best\n"
      ],
      "metadata": {
        "id": "jgmRYwlXWEX4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "pgpkAwSNQ39J",
        "outputId": "6f2fc8f8-3195-437b-edc5-08707a974e22"
      },
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    ones        0         1\n",
              "0      1   6.1101  17.59200\n",
              "1      1   5.5277   9.13020\n",
              "2      1   8.5186  13.66200\n",
              "3      1   7.0032  11.85400\n",
              "4      1   5.8598   6.82330\n",
              "..   ...      ...       ...\n",
              "92     1   5.8707   7.20290\n",
              "93     1   5.3054   1.98690\n",
              "94     1   8.2934   0.14454\n",
              "95     1  13.3940   9.05510\n",
              "96     1   5.4369   0.61705\n",
              "\n",
              "[97 rows x 3 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-b26de1d8-1a57-4f92-bceb-61e9b8bbaa58\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>ones</th>\n",
              "      <th>0</th>\n",
              "      <th>1</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>6.1101</td>\n",
              "      <td>17.59200</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>5.5277</td>\n",
              "      <td>9.13020</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1</td>\n",
              "      <td>8.5186</td>\n",
              "      <td>13.66200</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>7.0032</td>\n",
              "      <td>11.85400</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1</td>\n",
              "      <td>5.8598</td>\n",
              "      <td>6.82330</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>92</th>\n",
              "      <td>1</td>\n",
              "      <td>5.8707</td>\n",
              "      <td>7.20290</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>93</th>\n",
              "      <td>1</td>\n",
              "      <td>5.3054</td>\n",
              "      <td>1.98690</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>94</th>\n",
              "      <td>1</td>\n",
              "      <td>8.2934</td>\n",
              "      <td>0.14454</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>95</th>\n",
              "      <td>1</td>\n",
              "      <td>13.3940</td>\n",
              "      <td>9.05510</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>96</th>\n",
              "      <td>1</td>\n",
              "      <td>5.4369</td>\n",
              "      <td>0.61705</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>97 rows × 3 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-b26de1d8-1a57-4f92-bceb-61e9b8bbaa58')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-b26de1d8-1a57-4f92-bceb-61e9b8bbaa58 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-b26de1d8-1a57-4f92-bceb-61e9b8bbaa58');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 68
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X=df.iloc[:,1]    #defining X and y\n",
        "y=df.iloc[:,2]"
      ],
      "metadata": {
        "id": "UVTfFSfvQ6CU"
      },
      "execution_count": 80,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "y"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UoXdH_kxRGvr",
        "outputId": "7a354871-1f0d-46ae-ea6e-c73531fe7680"
      },
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0     17.59200\n",
              "1      9.13020\n",
              "2     13.66200\n",
              "3     11.85400\n",
              "4      6.82330\n",
              "        ...   \n",
              "92     7.20290\n",
              "93     1.98690\n",
              "94     0.14454\n",
              "95     9.05510\n",
              "96     0.61705\n",
              "Name: 1, Length: 97, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 82
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x=np.array(X).reshape(-1,1) "
      ],
      "metadata": {
        "id": "8aDiu4zCRcC6"
      },
      "execution_count": 85,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#fit the model\n",
        "lr=LinearRegression()\n",
        "lr.fit(x,y)"
      ],
      "metadata": {
        "id": "_-Z2iJXUWDvk",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "940d20cd-10f0-4c7c-994b-5cdfbff10593"
      },
      "execution_count": 86,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression()"
            ]
          },
          "metadata": {},
          "execution_count": 86
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#predict the target values\n",
        "y_pred=lr.predict(x)"
      ],
      "metadata": {
        "id": "EKb8ME-ma-ex"
      },
      "execution_count": 87,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#evalute the model\n",
        "r2_score(y,y_pred)"
      ],
      "metadata": {
        "id": "9mxBzwgnbF3Y",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "60a45152-8462-4541-8b72-41975981efd8"
      },
      "execution_count": 89,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7020315537841397"
            ]
          },
          "metadata": {},
          "execution_count": 89
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "mean_squared_error(y,y_pred)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9IhvLDNoR7cW",
        "outputId": "9ac9e6ed-2d37-4af9-b6c1-1d18943dd52a"
      },
      "execution_count": 90,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "8.953942751950358"
            ]
          },
          "metadata": {},
          "execution_count": 90
        }
      ]
    }
  ]
}