linear regression.ipynb

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      "name": "Untitled0.ipynb",
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        "<a href=\"https://colab.research.google.com/github/spoorthy24/Linear-regression/blob/master/Untitled0.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.datasets import load_boston\n",
        "\n",
        "%matplotlib inline\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EUHJ6HuHjMZ2",
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      "source": [
        "boston=load_boston()\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
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        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 884
        }
      },
      "source": [
        "print(boston.DESCR)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            ".. _boston_dataset:\n",
            "\n",
            "Boston house prices dataset\n",
            "---------------------------\n",
            "\n",
            "**Data Set Characteristics:**  \n",
            "\n",
            "    :Number of Instances: 506 \n",
            "\n",
            "    :Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.\n",
            "\n",
            "    :Attribute Information (in order):\n",
            "        - CRIM     per capita crime rate by town\n",
            "        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\n",
            "        - INDUS    proportion of non-retail business acres per town\n",
            "        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
            "        - NOX      nitric oxides concentration (parts per 10 million)\n",
            "        - RM       average number of rooms per dwelling\n",
            "        - AGE      proportion of owner-occupied units built prior to 1940\n",
            "        - DIS      weighted distances to five Boston employment centres\n",
            "        - RAD      index of accessibility to radial highways\n",
            "        - TAX      full-value property-tax rate per $10,000\n",
            "        - PTRATIO  pupil-teacher ratio by town\n",
            "        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\n",
            "        - LSTAT    % lower status of the population\n",
            "        - MEDV     Median value of owner-occupied homes in $1000's\n",
            "\n",
            "    :Missing Attribute Values: None\n",
            "\n",
            "    :Creator: Harrison, D. and Rubinfeld, D.L.\n",
            "\n",
            "This is a copy of UCI ML housing dataset.\n",
            "https://archive.ics.uci.edu/ml/machine-learning-databases/housing/\n",
            "\n",
            "\n",
            "This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\n",
            "\n",
            "The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\n",
            "prices and the demand for clean air', J. Environ. Economics & Management,\n",
            "vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\n",
            "...', Wiley, 1980.   N.B. Various transformations are used in the table on\n",
            "pages 244-261 of the latter.\n",
            "\n",
            "The Boston house-price data has been used in many machine learning papers that address regression\n",
            "problems.   \n",
            "     \n",
            ".. topic:: References\n",
            "\n",
            "   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\n",
            "   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\n",
            "\n"
          ],
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      "source": [
        "\n",
        "features=pd.DataFrame(boston.data, columns=boston.feature_names)\n",
        "target=pd.DataFrame(boston.target,columns=['Target'])\n",
        "data=pd.concat([features,target],axis=1)"
      ],
      "execution_count": 0,
      "outputs": []
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        ""
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      "outputs": []
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      "source": [
        ""
      ],
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      "outputs": []
    },
    {
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        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        }
      },
      "source": [
        "data2=data.corr('pearson')\n",
        "data2"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>CRIM</th>\n",
              "      <th>ZN</th>\n",
              "      <th>INDUS</th>\n",
              "      <th>CHAS</th>\n",
              "      <th>NOX</th>\n",
              "      <th>RM</th>\n",
              "      <th>AGE</th>\n",
              "      <th>DIS</th>\n",
              "      <th>RAD</th>\n",
              "      <th>TAX</th>\n",
              "      <th>PTRATIO</th>\n",
              "      <th>B</th>\n",
              "      <th>LSTAT</th>\n",
              "      <th>Target</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>CRIM</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.200469</td>\n",
              "      <td>0.406583</td>\n",
              "      <td>-0.055892</td>\n",
              "      <td>0.420972</td>\n",
              "      <td>-0.219247</td>\n",
              "      <td>0.352734</td>\n",
              "      <td>-0.379670</td>\n",
              "      <td>0.625505</td>\n",
              "      <td>0.582764</td>\n",
              "      <td>0.289946</td>\n",
              "      <td>-0.385064</td>\n",
              "      <td>0.455621</td>\n",
              "      <td>-0.388305</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>ZN</th>\n",
              "      <td>-0.200469</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.533828</td>\n",
              "      <td>-0.042697</td>\n",
              "      <td>-0.516604</td>\n",
              "      <td>0.311991</td>\n",
              "      <td>-0.569537</td>\n",
              "      <td>0.664408</td>\n",
              "      <td>-0.311948</td>\n",
              "      <td>-0.314563</td>\n",
              "      <td>-0.391679</td>\n",
              "      <td>0.175520</td>\n",
              "      <td>-0.412995</td>\n",
              "      <td>0.360445</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>INDUS</th>\n",
              "      <td>0.406583</td>\n",
              "      <td>-0.533828</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.062938</td>\n",
              "      <td>0.763651</td>\n",
              "      <td>-0.391676</td>\n",
              "      <td>0.644779</td>\n",
              "      <td>-0.708027</td>\n",
              "      <td>0.595129</td>\n",
              "      <td>0.720760</td>\n",
              "      <td>0.383248</td>\n",
              "      <td>-0.356977</td>\n",
              "      <td>0.603800</td>\n",
              "      <td>-0.483725</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>CHAS</th>\n",
              "      <td>-0.055892</td>\n",
              "      <td>-0.042697</td>\n",
              "      <td>0.062938</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.091203</td>\n",
              "      <td>0.091251</td>\n",
              "      <td>0.086518</td>\n",
              "      <td>-0.099176</td>\n",
              "      <td>-0.007368</td>\n",
              "      <td>-0.035587</td>\n",
              "      <td>-0.121515</td>\n",
              "      <td>0.048788</td>\n",
              "      <td>-0.053929</td>\n",
              "      <td>0.175260</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NOX</th>\n",
              "      <td>0.420972</td>\n",
              "      <td>-0.516604</td>\n",
              "      <td>0.763651</td>\n",
              "      <td>0.091203</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.302188</td>\n",
              "      <td>0.731470</td>\n",
              "      <td>-0.769230</td>\n",
              "      <td>0.611441</td>\n",
              "      <td>0.668023</td>\n",
              "      <td>0.188933</td>\n",
              "      <td>-0.380051</td>\n",
              "      <td>0.590879</td>\n",
              "      <td>-0.427321</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>RM</th>\n",
              "      <td>-0.219247</td>\n",
              "      <td>0.311991</td>\n",
              "      <td>-0.391676</td>\n",
              "      <td>0.091251</td>\n",
              "      <td>-0.302188</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.240265</td>\n",
              "      <td>0.205246</td>\n",
              "      <td>-0.209847</td>\n",
              "      <td>-0.292048</td>\n",
              "      <td>-0.355501</td>\n",
              "      <td>0.128069</td>\n",
              "      <td>-0.613808</td>\n",
              "      <td>0.695360</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>AGE</th>\n",
              "      <td>0.352734</td>\n",
              "      <td>-0.569537</td>\n",
              "      <td>0.644779</td>\n",
              "      <td>0.086518</td>\n",
              "      <td>0.731470</td>\n",
              "      <td>-0.240265</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.747881</td>\n",
              "      <td>0.456022</td>\n",
              "      <td>0.506456</td>\n",
              "      <td>0.261515</td>\n",
              "      <td>-0.273534</td>\n",
              "      <td>0.602339</td>\n",
              "      <td>-0.376955</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>DIS</th>\n",
              "      <td>-0.379670</td>\n",
              "      <td>0.664408</td>\n",
              "      <td>-0.708027</td>\n",
              "      <td>-0.099176</td>\n",
              "      <td>-0.769230</td>\n",
              "      <td>0.205246</td>\n",
              "      <td>-0.747881</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.494588</td>\n",
              "      <td>-0.534432</td>\n",
              "      <td>-0.232471</td>\n",
              "      <td>0.291512</td>\n",
              "      <td>-0.496996</td>\n",
              "      <td>0.249929</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>RAD</th>\n",
              "      <td>0.625505</td>\n",
              "      <td>-0.311948</td>\n",
              "      <td>0.595129</td>\n",
              "      <td>-0.007368</td>\n",
              "      <td>0.611441</td>\n",
              "      <td>-0.209847</td>\n",
              "      <td>0.456022</td>\n",
              "      <td>-0.494588</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.910228</td>\n",
              "      <td>0.464741</td>\n",
              "      <td>-0.444413</td>\n",
              "      <td>0.488676</td>\n",
              "      <td>-0.381626</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>TAX</th>\n",
              "      <td>0.582764</td>\n",
              "      <td>-0.314563</td>\n",
              "      <td>0.720760</td>\n",
              "      <td>-0.035587</td>\n",
              "      <td>0.668023</td>\n",
              "      <td>-0.292048</td>\n",
              "      <td>0.506456</td>\n",
              "      <td>-0.534432</td>\n",
              "      <td>0.910228</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.460853</td>\n",
              "      <td>-0.441808</td>\n",
              "      <td>0.543993</td>\n",
              "      <td>-0.468536</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>PTRATIO</th>\n",
              "      <td>0.289946</td>\n",
              "      <td>-0.391679</td>\n",
              "      <td>0.383248</td>\n",
              "      <td>-0.121515</td>\n",
              "      <td>0.188933</td>\n",
              "      <td>-0.355501</td>\n",
              "      <td>0.261515</td>\n",
              "      <td>-0.232471</td>\n",
              "      <td>0.464741</td>\n",
              "      <td>0.460853</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.177383</td>\n",
              "      <td>0.374044</td>\n",
              "      <td>-0.507787</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>B</th>\n",
              "      <td>-0.385064</td>\n",
              "      <td>0.175520</td>\n",
              "      <td>-0.356977</td>\n",
              "      <td>0.048788</td>\n",
              "      <td>-0.380051</td>\n",
              "      <td>0.128069</td>\n",
              "      <td>-0.273534</td>\n",
              "      <td>0.291512</td>\n",
              "      <td>-0.444413</td>\n",
              "      <td>-0.441808</td>\n",
              "      <td>-0.177383</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.366087</td>\n",
              "      <td>0.333461</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>LSTAT</th>\n",
              "      <td>0.455621</td>\n",
              "      <td>-0.412995</td>\n",
              "      <td>0.603800</td>\n",
              "      <td>-0.053929</td>\n",
              "      <td>0.590879</td>\n",
              "      <td>-0.613808</td>\n",
              "      <td>0.602339</td>\n",
              "      <td>-0.496996</td>\n",
              "      <td>0.488676</td>\n",
              "      <td>0.543993</td>\n",
              "      <td>0.374044</td>\n",
              "      <td>-0.366087</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.737663</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Target</th>\n",
              "      <td>-0.388305</td>\n",
              "      <td>0.360445</td>\n",
              "      <td>-0.483725</td>\n",
              "      <td>0.175260</td>\n",
              "      <td>-0.427321</td>\n",
              "      <td>0.695360</td>\n",
              "      <td>-0.376955</td>\n",
              "      <td>0.249929</td>\n",
              "      <td>-0.381626</td>\n",
              "      <td>-0.468536</td>\n",
              "      <td>-0.507787</td>\n",
              "      <td>0.333461</td>\n",
              "      <td>-0.737663</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "             CRIM        ZN     INDUS  ...         B     LSTAT    Target\n",
              "CRIM     1.000000 -0.200469  0.406583  ... -0.385064  0.455621 -0.388305\n",
              "ZN      -0.200469  1.000000 -0.533828  ...  0.175520 -0.412995  0.360445\n",
              "INDUS    0.406583 -0.533828  1.000000  ... -0.356977  0.603800 -0.483725\n",
              "CHAS    -0.055892 -0.042697  0.062938  ...  0.048788 -0.053929  0.175260\n",
              "NOX      0.420972 -0.516604  0.763651  ... -0.380051  0.590879 -0.427321\n",
              "RM      -0.219247  0.311991 -0.391676  ...  0.128069 -0.613808  0.695360\n",
              "AGE      0.352734 -0.569537  0.644779  ... -0.273534  0.602339 -0.376955\n",
              "DIS     -0.379670  0.664408 -0.708027  ...  0.291512 -0.496996  0.249929\n",
              "RAD      0.625505 -0.311948  0.595129  ... -0.444413  0.488676 -0.381626\n",
              "TAX      0.582764 -0.314563  0.720760  ... -0.441808  0.543993 -0.468536\n",
              "PTRATIO  0.289946 -0.391679  0.383248  ... -0.177383  0.374044 -0.507787\n",
              "B       -0.385064  0.175520 -0.356977  ...  1.000000 -0.366087  0.333461\n",
              "LSTAT    0.455621 -0.412995  0.603800  ... -0.366087  1.000000 -0.737663\n",
              "Target  -0.388305  0.360445 -0.483725  ...  0.333461 -0.737663  1.000000\n",
              "\n",
              "[14 rows x 14 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6PAWotvHmCFw",
        "colab_type": "code",
        "outputId": "45e17529-216c-4131-9f8c-ad140874da42",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 272
        }
      },
      "source": [
        "abs(data2.loc['Target']).sort_values(ascending=False)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Target     1.000000\n",
              "LSTAT      0.737663\n",
              "RM         0.695360\n",
              "PTRATIO    0.507787\n",
              "INDUS      0.483725\n",
              "TAX        0.468536\n",
              "NOX        0.427321\n",
              "CRIM       0.388305\n",
              "RAD        0.381626\n",
              "AGE        0.376955\n",
              "ZN         0.360445\n",
              "B          0.333461\n",
              "DIS        0.249929\n",
              "CHAS       0.175260\n",
              "Name: Target, dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
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    {
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      "metadata": {
        "id": "UvuStcp0ntbd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X=data['RM']\n",
        "Y=data['Target']"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rwnyCgYdlfU2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X=np.array(X/X.mean())\n",
        "Y=np.array(Y/Y.mean())"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "95NiwjWJlwv1",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "n=int(0.8*len(X))\n",
        "x_train=X[:n]\n",
        "y_train=Y[:n]\n",
        "x_test=X[n:]\n",
        "y_test=Y[n:]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kwZ1Xp1tm9Qz",
        "colab_type": "code",
        "outputId": "3b79db83-bbff-4f53-9e47-1d90d246de44",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "plt.plot(x_train,y_train,'r.')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f674c02efd0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ErfVGxwsKBXdMPW8URtuwNMWG0UmazQr55JNBMe9CwS03k0o4aerjcGy9Hy8oFLq7tm6O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\nYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fXMFlxm5nGWp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def hypothesis(a,b,x):\n",
        "  return a * x + b\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QPUZJZKHoyfd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def error(a,b,x,y):\n",
        "  e=0\n",
        "  m=len(x)\n",
        "  for i in range(m):\n",
        "    e+= np.power((hypothesis(a,b,x[i])-y[i]),2)\n",
        "  return (1/(2*m))*e\n",
        "    "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZVUX-tTHprtF",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def step_gradient(a,b,x,y,learning_rate):\n",
        "  grad_a=0\n",
        "  grad_b=0\n",
        "  m=len(x)\n",
        "  for i in range(m):\n",
        "     grad_a +=1/m * (hypothesis(a,b,x[i])-y[i])*x[i]\n",
        "     grad_b +=1/m *(hypothesis(a,b,x[i])-y[i])\n",
        "  a=a-(grad_a * learning_rate)\n",
        "  b=b-(grad_b * learning_rate)\n",
        "  return a,b"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bdTyMNr_spgq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def descend(initial_a,initial_b,x,y,learning_rate,iterations):\n",
        "  a=initial_a\n",
        "  b=initial_b\n",
        "  for i in range(iterations):\n",
        "    e=error(a,b,x,y)\n",
        "    if i %1000 ==0:\n",
        "      print(f\"Error: {e}, a:{a}, b:{b}\")\n",
        "    a,b= step_gradient(a,b,x,y,learning_rate)\n",
        "  return a,b "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HHPtkPj6ujXx",
        "colab_type": "code",
        "outputId": "6b19e41f-f6dc-4488-a42f-b9097d656dce",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 187
        }
      },
      "source": [
        "a=0\n",
        "b=1\n",
        "learning_rate=0.01\n",
        "iterations=10000\n",
        "final_a,final_b = descend(a,b,x_train,y_train,learning_rate,iterations)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Error: 0.08691047391394598, a:0, b:1\n",
            "Error: 0.07708926030401912, a:0.21314461782342037, b:0.8745784354256118\n",
            "Error: 0.07209296957251596, a:0.37003145582037533, b:0.7154166649597727\n",
            "Error: 0.0677224328969421, a:0.5167652148513465, b:0.5665551977359419\n",
            "Error: 0.0638992785092092, a:0.6540029610039395, b:0.42732744002236356\n",
            "Error: 0.06055495021329734, a:0.782359237660549, b:0.29710993726992707\n",
            "Error: 0.05762947804645947, a:0.9024088174520268, b:0.1753195823755791\n",
            "Error: 0.0550704029073936, a:1.0146892760591748, b:0.061411004559502984\n",
            "Error: 0.05283183586798675, a:1.1197033994482735, b:-0.04512587277644767\n",
            "Error: 0.05087363530035991, a:1.217921435320088, b:-0.1447681161448278\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gaEjIgmpvKzH",
        "colab_type": "code",
        "outputId": "b828697b-682a-403f-e5cb-3e77e74a4370",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "print(error(a,b,x_train,y_train))\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.08691047391394598\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zvltg5cr0hPM",
        "colab_type": "code",
        "outputId": "544c4f5a-3761-4d8a-b962-2ff13941be6d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        }
      },
      "source": [
        "plt.plot(x_test,y_test,'r.',x_test,hypothesis(final_a,final_b,x_test),'g')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f674bd20cf8>,\n",
              " <matplotlib.lines.Line2D at 0x7f674bd20e10>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PmSkKXOFlfaC5yFIa+wkT6FcCe5rZ7lQC/HHACX2OeR04DJhnZnsBQ4G3o2xorsVYBrh2\n+bVc+OiFgftKk70rcDUn6wPNRZbS2E/DQO/um83sXGAxlamTc919lZnNADrdfSHwfeBfzOwCKgOz\nkz2tK7GyKsIyQL3sffmpy2kfWbI/WgWu5mR9oLnIUhr70ZWxOXJ9x/V875HvBe4rTfYepFZGr3JO\nbfWWU47jefQeREZXxhZQvez9qVOf4qCRByXcogwKypJUzqmv57WI8zXSe5AZCvQZNXvFbC5YfEHg\nvlJn77X0LY2pnNNY3K+R3oPMUKDPkHrZ+5NTnmRM65iEW5RjWa5DZ6WcEfdrlOX3oGQU6DPghqdv\n4LsPfzdwn7L3AcrqBU9ZKmf0vEYLFtQ+ZjCdUlbfgxJSoE/Jlq4tbHVF8Mu/bMoyvtz65YRbVEBZ\nvOApi+WM+fMrbZk/v3fHE0WnlMX3oIQU6BN249M38p2HvxO4T9l7CWStnFGv44mjU8pK2apkFOgT\n0OVdtMxoCdy3dPJSvrLbVxJu0SDoD3VwslbOqNfxRN0pZalsVTIK9DF6eM3DTPjXCYH7cpm96w81\nGkmUM8J2yPXq9FF3SlksW5WEAn3EuryL7a/anj9t+lO/favOXsXeO+2dQqsioj/UfBhIh1yrTh9l\np5S1slWJKNBHZPGaxYz/1/H9to/7/DgWn7g4hRbFQH+o+dBsh5xUB561slWJKNAPgrvzrXu+xf3/\nfn+/fbnP3oPoDzUfmu2Qk+zANQsnFVrrZgBe+eMrHHHHEbz6zqu9th++x+E8etKjKbVKpEqzg+Ya\nZM+Ngax1o0Afkrtz9VNXM+2xab22jxk5hruPuZtdP71rSi0TkTLRomYxqJW9z//GfE7+wskptUok\nIcr0C0GBPoC785OnfsIlj13Sa/uYkWO4/9j72flTO6fUMpEEaTptYSjQV1m7cS1H3HEEazeu7bV9\n3sR5nPLFU1JqVYkpm0xXFLNx9B5mQukDvbsza/ksLv71xb22HzTyIB449gFl72lJK5tUYPrEYGfj\n6BNBZpQ20K/duJZxd4zjlY2v9Np++8TbmfzFyek0Sj6RxsVZRQtM1Z0WNN+BDXY6baP3UJ1qYkoV\n6N2da5Zfww9+/YNe29tHtPPAsQ/w19v9dUotk37SuDirSFf+VndaW20F7pXzarYDG8y893rvYdE6\n1YwrRaB/deOrjPvFONb8cU2v7XOPmsuU/aak1CqpK42Ls/Jw5W/YLLi60+rqqmxzT7YDq/ceFqlT\nzYHCBnp359qOa7no0Yt6bVf2niNJX0WZ9St/m8mCqzutnox+82YYMqRyQ/Ck1HoP89CpFkjhAv2r\nG1/lq7/4Kv/xx//otV3Zu4SS5Uv0m8mC+3ZaL74I55xT+d7zz4d99033PLPeqRZMIQJ9rez9wBEH\n8uCxDyp7l2JoNguu7rSWLKlk9V1dtTuJpAdHs9ypFkyuA32t7P3nR/2cU/c7NaVWidQw2EDa3g6z\nZ8N998GkSc39jEadRNiyUNKdgWbmRCKXgX72itlcsPiCXtsOGH4ADx73ILtst0tKrRKpI4pZJh0d\nlbLLpk2wbFlz5ZdGpZIwZaGkZ8poZk5khqTdgGa98IcXegX52/7Hbfh0Z8XpKxTkJbuCAmnSP6O9\nHaZNqz842tJSuywUxTk0I+nnK7DcZfR7DduLO46+g8P3OFyBvaiK+HE9ilkmcc5UCTM4mvRMGc3M\niUyoZYrNbDzwU6AFuM3drwo45p+AHwIOPO/uJ9T7mXlbplgSUsSP6z0d1447woYNg+vA0u4EVaNP\nXSzLFJtZC3AzcASwDlhpZgvdfXXVMXsC04Ax7r7RzLRAjAxMES6k6bv0QJQdV9ozVdK4tiFv738G\nhSndjAbWuPtaADO7C5gIrK465gzgZnffCODub0XdUCmJvH9c7/uJ5JRTmuu4ipDB6u5WmRMm0A8H\n3qh6vA44oM8xfwtgZk9RKe/80N0f7vuDzGwqMBWgtbV1IO2Vosv7hTR9P5FA+I6rXtkqL8Gw2dJb\nEUt1GRTVYOxWwJ7AWGAEsNTM9nX3d6oPcvc5wByo1Ogjem4pmjx/XO/7ieTkkyv/ml2fpjr7z1Mw\nbLb0VoRSXQ6ECfTrgZFVj0d0b6u2Dnja3T8CXjWzl6kE/pWRtFIkL2p9IgkTvGqVrZIIhlF9Ymi2\n9Jb3Ul1OhAn0K4E9zWx3KgH+OKDvjJoHgeOB281sGJVSzlpEymign0hqdRJxB8MoPzE0W3rLe6ku\nJxoGenffbGbnAoup1N/nuvsqM5sBdLr7wu5948xsNbAFuMjdN8TZcJFQ8lLb7hHUScQdDKP+xNBs\nR5fnUl1OhJpHHwfNo5fYZaG2nVRHM5jnycLrJKHFMo9eJLfSHuhLKoAO9nlUPik8BXoprrQH+pLq\naKJ4HpVPCk2BXoor7Uw1qY4m7Q5NMk81epE45aFGL7kykBq9Ar3ET0FIJDLlGIxV0MgXzejoT7/D\nkrB8BXoFjfxJe+ZL1uThd1gdUeHk6w5TuuNM/oS5c1EUOjpg5szK/1kW1e9wXOfb0xFddlnl/6y/\nnhJKvjJ6zS7InyRmvuQhS+4Rxe9wnOerT2CFlK9An/Z0ORmYuOdo5yk4RfE7HOf5KpkqpHwFetCF\nHdJf3oLTYH+H0753rOSOpldKMZRtALFs5ysfK8f0SpEgZfqkpyAvTVKgF8mTjg449NBPyjaPP65g\nLw3la3qlSBakOZVzwQL48ENwr/y/YEHybZDcUUYv0ow8TeUU6aaMXiSMnix+wYJ0L9o7+eRKB2P2\nyc3HRRpQRi/xy/vgYXUW39ICW3X/2aQxlbO9vfJa5vn1lMQp0Eu8ilDqqL5AqasLJk6E0aPTC7Rl\nmmEkkVDpRuJVhPWJxo79JIt3h0WLlE1LrijQS7ySWtQsTu3tMGVKpS4OlU4rjx2WlJYCvcSr55L6\nK67IZ9mmx8knw9Ch+e6wpLRUo5f4FaGmrDVgJMcU6EXCKkKHFVbeZ0pJLwr0ImVUL5AXYaaU9KJA\nL1I2jQJ5ntb3l1A0GCtSNo2mvBZhppT0EirQm9l4M/udma0xs0vqHDfJzNzMmlorWUQS1CiQF2Wm\nlHysYenGzFqAm4EjgHXASjNb6O6r+xz3aeC7wNNxNFREIhJmBlGZBp5LIEyNfjSwxt3XApjZXcBE\nYHWf464ArgYuirSFIhI9BfJSCVO6GQ68UfV4Xfe2j5nZ/sBId3+o3g8ys6lm1mlmnW+//XbTjRXJ\nlajWrU9z/XsphEHPujGzIcB1wORGx7r7HGAOVO4ZO9jnFsmsqKYoaqqjRCBMRr8eGFn1eET3th6f\nBvYBlpjZ74EDgYUakJXYZTnTjWoxtyIsCiepC5PRrwT2NLPdqQT444ATena6+7vAsJ7HZrYEuNDd\nO6NtqkiVrGa6PRci7bhjpV097RvoFMWeGTKD/Tl5pSt0I9Ew0Lv7ZjM7F1gMtABz3X2Vmc0AOt19\nYdyNFOknSxf1VAf388//JCjPng0bNgwuSJV5jZ2sduY5FKpG7+6LgEV9tl1e49ixg2+WpC7rmVRW\nMt3qYGRWuTFJV1fl8YYNMG3a4J+jrDNkstSZ55yWQJD+8pBJZSXTrQ5GQ4ZULkLquZ9r2cosUctK\nZ14ACvTSX14yqSxkun2DURTlGqnISmdeAAr00p8yqfAUjOKVhc68ABTopT8Fr+YoGEnGKdBLMAUv\nSUPWJwHklAK9iGRDHiYB5JTWoxeRirSvNNZVwLFRRi8i2cimNQkgNsroByvtLKho9HqmIwvZtG54\nEhtl9IORhSyoSPR6picr2bQmAcRCGf1gZCELKhK9nulRNl1oyugHIytZUFHo9UyXsunCUqAfDF1Y\nFC29niKxMPd0bvTU1tbmnZ1asl5EpBlm9qy7N3VjJ9XoRUQKToFeRKTgFOhFRApOgV5EpOAU6EVE\nCk6BXkSk4BToRUQKToFeRKTgFOhFRApOgV5EpOAU6KV8tOa9lIwWNZNy0Zr3UkLK6KVctOa9lFCo\nQG9m483sd2a2xswuCdj/PTNbbWYvmNljZrZb9E0ViUDPmvctLVrzXkqjYenGzFqAm4EjgHXASjNb\n6O6rqw77LdDm7n8xs7OAnwDHxtFgkUHRmvdSQmFq9KOBNe6+FsDM7gImAh8Hend/vOr4FcCJUTZS\nJFK6k5KUTJjSzXDgjarH67q31XIa8KugHWY21cw6zazz7bffDt9KEREZsEgHY83sRKANmBW0393n\nuHubu7fttNNOUT61iIjUEKZ0sx4YWfV4RPe2XszscOB/AYe4+4fRNE9ERAYrTEa/EtjTzHY3s22A\n44CF1QeY2X7APwNHuftb0TdTREQGqmGgd/fNwLnAYuDfgbvdfZWZzTCzo7oPmwVsB9xjZs+Z2cIa\nP05ERBIW6spYd18ELOqz7fKqrw+PuF0iIhIRc/d0ntjsbeC1VJ48nGHAf6XdiISU5VzLcp6gcy2q\nYcCn3L2p2SypBfqsM7NOd29Lux1JKMu5luU8QedaVAM9V611IyJScAr0IiIFp0Bf25y0G5Cgspxr\nWc4TdK5FNaBzVY1eRKTglNGLiBScAr2ISMGVPtCHuKnK9d1X+z5nZi+b2TtptHOwQpxnq5k9bma/\n7b6BzJFptDMKIc51t+4b5LxgZkvMbEQa7RwsM5trZm+Z2Us19puZ3dD9OrxgZvsn3caohDjXvzez\nDjP70MwuTLp9UQpxrt/ufj9fNLPlZvaFhj/U3Uv7D2gBXgH2ALYBngf2rnP8ecDctNsdx3lSGeQ5\nq/vrvYHfp93uGM/1HuCU7q//Ebgj7XYP8FwPBvYHXqqx/0gqS4YbcCDwdNptjvFcdwa+BFwJXJh2\ne2M+14OAz3Z/PSHM+1r2jP7jm6q4+yag56YqtRwP3JlIy6IV5jwd+Ez319sDbybYviiFOde9gd90\nf/14wP5ccPelwB/rHDIRWOAVK4AdzOxzybQuWo3O1d3fcveVwEfJtSoeIc51ubtv7H64gsqKwnWV\nPdCHvqlK931wd+eTAJEnYc7zh8CJZraOyrpG5yXTtMiFOdfngW92f3008Gkz2zGBtiWt2ZsGSf7U\nvNFTtbIH+mYcB9zr7lvSbkhMjgfmufsIKh/57zCzov5+XAgcYma/BQ6hcn+For6vUlBmdiiVQH9x\no2NDrV5ZYKFuqtLtOOCc2FsUjzDneRowHsDdO8xsKJUFlPJ2f4GG5+rub9Kd0ZvZdsAkd8/lIHsD\nzfx+S46Y2T8AtwET3H1Do+OLmrGF1fCmKlAZ0Qc+C3Qk3L6ohDnP14HDAMxsL2AokMcb+4a5Uc6w\nqk8r04C5CbcxKQuBk7tn3xwIvOvu/5l2o2RwzKwVuB84yd1fDvM9pc7o3X2zmfXcVKWFyoyaVWY2\nA+h0954AcRxwl3cPc+dNyPP8PvAvZnYBlYHZyXk835DnOhaYaWYOLCWnn9TM7E4q5zKse2xlOrA1\ngLv/jMpYy5HAGuAvwJR0Wjp4jc7VzHYBOqlMKOgys/OpzLZ6L6UmD1iI9/VyYEfgFjMD2OwNVrTU\nEggiIgVX9tKNiEjhKdCLiBScAr2ISMEp0IuIFJwCvYhIwSnQi4gUnAK9iEjB/X/LC5xfSwDphQAA\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NaM7B6bK0kd6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}