Housing_price_prediction_using_Regularised_linear_regression_.ipynb

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    "colab": {
      "name": "Housing price prediction using Regularised linear regression .ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3nppKaoi4Lr3",
        "colab_type": "text"
      },
      "source": [
        "# **Housing price prediction using linear regression** \n",
        "(*Regularised Gradient Descent and Regularised Normal equation*)\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zDCzcBQ8Q1u4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dHiaTyNZ5CMc",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "1.   *Delete unnecessary column*\n",
        "2.   *Normalised the data with mean*\n",
        " "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "outputId": "1d7588ca-1e3e-4cc9-9861-f1aa2fee86b6",
        "id": "Z_1MXqR2-08l",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        }
      },
      "source": [
        "data = pd.read_csv('Housing Price data set.csv')\n",
        "data=data.drop(['Unnamed: 0','driveway','recroom','fullbase','airco','prefarea', 'gashw'],axis=1)\n",
        "mean = data.mean()[0]\n",
        "stddev = data.std()[0]\n",
        "data = (data - data.mean())/data.std()\n",
        "\n",
        "data.head()"
      ],
      "execution_count": 0,
      "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>price</th>\n",
              "      <th>lotsize</th>\n",
              "      <th>bedrooms</th>\n",
              "      <th>bathrms</th>\n",
              "      <th>stories</th>\n",
              "      <th>garagepl</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-0.978239</td>\n",
              "      <td>0.322732</td>\n",
              "      <td>0.047192</td>\n",
              "      <td>-0.568973</td>\n",
              "      <td>0.221501</td>\n",
              "      <td>0.357239</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-1.109312</td>\n",
              "      <td>-0.530526</td>\n",
              "      <td>-1.308947</td>\n",
              "      <td>-0.568973</td>\n",
              "      <td>-0.930304</td>\n",
              "      <td>-0.803788</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-0.697368</td>\n",
              "      <td>-0.964074</td>\n",
              "      <td>0.047192</td>\n",
              "      <td>-0.568973</td>\n",
              "      <td>-0.930304</td>\n",
              "      <td>-0.803788</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-0.285425</td>\n",
              "      <td>0.691709</td>\n",
              "      <td>0.047192</td>\n",
              "      <td>-0.568973</td>\n",
              "      <td>0.221501</td>\n",
              "      <td>-0.803788</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-0.266700</td>\n",
              "      <td>0.557955</td>\n",
              "      <td>-1.308947</td>\n",
              "      <td>-0.568973</td>\n",
              "      <td>-0.930304</td>\n",
              "      <td>-0.803788</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "      price   lotsize  bedrooms   bathrms   stories  garagepl\n",
              "0 -0.978239  0.322732  0.047192 -0.568973  0.221501  0.357239\n",
              "1 -1.109312 -0.530526 -1.308947 -0.568973 -0.930304 -0.803788\n",
              "2 -0.697368 -0.964074  0.047192 -0.568973 -0.930304 -0.803788\n",
              "3 -0.285425  0.691709  0.047192 -0.568973  0.221501 -0.803788\n",
              "4 -0.266700  0.557955 -1.308947 -0.568973 -0.930304 -0.803788"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 168
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "mPI-h9ER6Ah4"
      },
      "source": [
        "\n",
        "3.   *Separate out the Feature and Target matrices\n",
        "and devide test and train data with 0.9 split ratio*\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hS6ya-6MWxha",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        " \n",
        "data=np.asarray(data)\n",
        "Y=data[:,0:1]\n",
        "X=data[:,1:]\n",
        "one = np.ones((len(X),1))\n",
        "X = np.concatenate((one,X),axis=1)\n",
        "split_ratio = 0.9\n",
        "split = int(split_ratio * X.shape[0])\n",
        "X_test = X[split+1:,:]\n",
        "X_train = X[:split+1, :]\n",
        "Y_test = Y[split+1:,:]\n",
        "Y_train = Y[:split+1, :]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "16F95s136lq3",
        "colab_type": "text"
      },
      "source": [
        "4. *Compute cost function*\n",
        "5. *denormalise price funcion*\n",
        "6. *compute error function*\n",
        "7. *plot graph function* "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tc5dfKZXWxmK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# helper Functions\n",
        "def computeCost(X,y,theta,lam):\n",
        "    tobesummed = np.power(((X.dot(theta.T))-y),2)+lam*np.sum(np.power(theta,2))\n",
        "    return np.sum(tobesummed)/(2 * len(X))\n",
        "\n",
        "def denormalise_price(price):\n",
        "    global mean\n",
        "    global stddev\n",
        "    ret = price * stddev + mean\n",
        "    return ret\n",
        "\n",
        "def computeError(predicted, actual):\n",
        "    error = 0\n",
        "    for i in range(len(predicted)):\n",
        "        error += abs(actual[i] - predicted[i]) / actual[i]\n",
        "    error /= len(actual)\n",
        "    return error[0]\n",
        "\n",
        "def plotGraph(x,y,labelX='X',labelY='Y',title='X vs Y'):\n",
        "  fig, ax = plt.subplots()  \n",
        "  ax.plot(x, y, 'r')\n",
        "  ax.set_xlabel(labelX) \n",
        "  ax.set_ylabel(labelY)  \n",
        "  ax.set_title(title)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oDkRDFBq7AD4",
        "colab_type": "text"
      },
      "source": [
        "7. *Gradient descent with regularisation to fint minimum theta*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vA1kkGh7Wxss",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Gradient Descent\n",
        "def gradientDescent(X,y,theta,iters,alpha, lam):\n",
        "    lam_matrix = lam * np.ones(theta.shape)\n",
        "    lam_matrix[0][0] = 0\n",
        "    for i in range(iters):\n",
        "        theta = theta*(1- lam_matrix / len(X)) - (alpha/len(X)) * np.sum(X * (X @ theta.T - y), axis=0)\n",
        "\n",
        "    return theta"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p2VgY1kK7T8b",
        "colab_type": "text"
      },
      "source": [
        "7. *Normal eqution function with regularisation to find minimum theta*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FdtX5XeoWxyE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Normal equation\n",
        "def normalEquation(X,Y,lam):\n",
        "    lam_matrix = lam * np.identity(X.shape[1])\n",
        "    lam_matrix[0][0] = 0\n",
        "    theta = np.linalg.inv(X.T.dot(X) + lam_matrix).dot(X.T).dot(Y)\n",
        "    return theta\n",
        "    "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lB5CnXQJ7h-k",
        "colab_type": "text"
      },
      "source": [
        "8. *Train the model with train data and predict the test data using gradient descent*\n",
        "9. *compute the minimum error and lambda* \n",
        "10. *plot error vs lambda graph*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IPet8YbFWx3G",
        "colab_type": "code",
        "outputId": "6be04329-cae3-45b8-d9de-ab6f60613ef9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 329
        }
      },
      "source": [
        "theta = np.zeros([1,X.shape[1]])\n",
        "alpha = .1 #learning rate\n",
        "iters = 500 #epoch\n",
        "error_matrix = []\n",
        "lam_range = 600 #maximam lamda\n",
        "for lam in range(lam_range):\n",
        "    g = gradientDescent(X_train,Y_train,theta,iters,alpha, lam)\n",
        "    Cost = computeCost(X_train,Y_train,g,lam)\n",
        "\n",
        "    Y_pred = X_test.dot(g.T)\n",
        "    error = computeError(denormalise_price(Y_pred),denormalise_price(Y_test))\n",
        "    error_matrix.append(error*100)\n",
        "optimal_lambda = 0\n",
        "min_error = 9999\n",
        "for i in range(len(error_matrix)):\n",
        "    if error_matrix[i] < min_error:\n",
        "        optimal_lambda = i\n",
        "        min_error = error_matrix[i]\n",
        "\n",
        "print(\"min Error  : \", (min_error),'%')\n",
        "print(\"Optimal Lambda : \", optimal_lambda)\n",
        "plotGraph(np.arange(lam_range),error_matrix,'lambda','error','lambda vs error')"
      ],
      "execution_count": 173,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "min Error  :  13.960611355440056 %\n",
            "Optimal Lambda :  24\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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7iR/guONCj3z06HjO/8orcP/98Pe/w6GHxnMNEZFKkh+Jv00bqF4dXn658s/9\n8MNw4omw995www2Vf34RkUqWH4m/WjU48kgYNgxWraqcc65cCRdfDN26hV7+6NHhOiIiGS4/Ej+E\nypjffw9PPLHx51q0CI49Fu6+Gy67DF59VeWWRSRr5E/iP/54aN4crrsuLHa+oWbPhlatQg9/4MCw\nhm5Bble+EJHckj+J3wz694dZs+CUUzZsyGfaNDjwwDB7Z/hwOOecyo9TRCRm+ZP4AQ4+GB54IEzt\nvPhicK/4937zTbhJ/Ntv8J//wFFHxReniEiM8m+M4pxz4Isv4LbboFGjUCt/Xb79dk3SHzUK9tkn\n/jhFRGISW4/fzB42s3lmNqmMfZebmZtZnbiuv1Y33xymYF52Gbz44tqP/eknOOKIcF/gzTeV9EUk\n68U51DMIaFd6o5nVB44Evovx2mu3ySbw+OPQogWceiq89lrZx61YEX5BfPttGNPfd9/0xikiEoPY\nEr+7jwF+LmNXX+BKYD0G2GOwxRahfk/TptCxYxj3T7VkCXTpAmPGwKBB8Kc/JRKmiEhlS+vNXTPr\nAHzv7p+m87rl2mabkPAbN4YOHcL4vTu8917o3T/3HNx+O3TunHSkIiKVJm03d81sC6AnYZinIsd3\nB7oDNGjQIL7AatcOY/dt2oSx/K23hp9/DlU2R42C1q3ju7aISALSOatnV2Bn4FMLJYt3BD4xs/3d\nfW7pg919ADAAoLCwMN5hobp1wwNZ990H330XhnVOOklVNkUkJ6Ut8bv7Z8C2JZ/NbAZQ6O4/piuG\ntapbNyyiIiKS4+KczjkYGAs0MrNZZtYtrmuJiEjFxdbjd/e13hF194ZxXVtERMqXXyUbREREiV9E\nJN8o8YuI5BklfhGRPKPELyKSZ5T4RUTyjPn6LEaSEDObD3y7gd9eB8iMh8Q2ntqSmXKlLbnSDlBb\nSuzk7nVLb8yKxL8xzKzI3QuTjqMyqC2ZKVfakivtALVlXTTUIyKSZ5T4RUTyTD4k/gFJB1CJ1JbM\nlCttyZV2gNqyVjk/xi8iIr+XDz1+ERFJocQvIpJncjrxm1k7M/vCzKaZWY+k41kXM3vYzOaZ2aSU\nbbXM7E0z+yr6uk203cysf9S2iWa2b3KR/56Z1Tez0WY2xcwmm9kl0fZsbEs1M/vIzD6N2nJdtH1n\nM/swivkZM6sSba8afZ4W7W+YZPylmdmmZjbezIZHn7OyHRAWczKzz8xsgpkVRduy8WdsazN7zsym\nmtnnZnZg3O3I2cRvZpsC9wJHA02AzmbWJNmo1mkQ0K7Uth7ASHffHRgZfYbQrt2jV3fg/jTFWBGr\ngMvdvQnQErgw+rPPxrYsBxWsMMwAAATVSURBVA5z932AZkA7M2sJ3Ar0dffdgF+AkoWGugG/RNv7\nRsdlkkuAz1M+Z2s7SrRx92Yp89yz8WesHzDC3RsD+xD+fuJth7vn5As4EHg95fPVwNVJx1WBuBsC\nk1I+fwHUi97XA76I3j8AdC7ruEx7AS8BR2R7W4AtgE+AAwhPUhaU/lkDXgcOjN4XRMdZ0rFH8ewY\nJZHDgOGAZWM7UtozA6hTaltW/YwBNYFvSv/Zxt2OnO3xAzsAM1M+z4q2ZZvt3H1O9H4usF30Piva\nFw0RNAc+JEvbEg2PTADmAW8C04EF7r4qOiQ13v+2Jdq/EKid3ojLdRdwJVAcfa5NdrajhANvmNk4\nM+sebcu2n7GdgfnAI9EQ3ENmVp2Y25HLiT/nePgVnzXzb82sBvA8cKm7L0rdl01tcffV7t6M0GPe\nH2iccEjrzczaA/PcfVzSsVSig919X8Lwx4Vm1ip1Z5b8jBUA+wL3u3tzYAlrhnWAeNqRy4n/e6B+\nyucdo23Z5gczqwcQfZ0Xbc/o9pnZZoSk/6S7D402Z2VbSrj7AmA0YUhkazMrWbM6Nd7/tiXaXxP4\nKc2hluVPwPFmNgN4mjDc04/sa8d/ufv30dd5wAuEX8rZ9jM2C5jl7h9Gn58j/CKItR25nPg/BnaP\nZi1UAU4DhiUc04YYBnSN3ncljJeXbD8rusvfEliY8l/DRJmZAQOBz939zpRd2diWuma2dfR+c8K9\nis8JvwA6RYeVbktJGzsBo6IeW6Lc/Wp339HdGxL+LYxy9zPIsnaUMLPqZrZlyXvgSGASWfYz5u5z\ngZlm1ija1BaYQtztSPrmRsw3To4BviSMyf5f0vFUIN7BwBxgJaEn0I0wrjoS+Ap4C6gVHWuEWUvT\ngc+AwqTjT2nHwYT/mk4EJkSvY7K0LXsD46O2TAJ6Rdt3AT4CpgFDgKrR9mrR52nR/l2SbkMZbWoN\nDM/mdkRxfxq9Jpf8+87Sn7FmQFH0M/YisE3c7VDJBhGRPJPLQz0iIlIGJX4RkTyjxC8ikmeU+EVE\n8owSv4hInlHil7xlZr9W0nmuNbMrKnDcIDPrtK7jROKmxC8ikmeU+CXvmVkNMxtpZp9E9d07RNsb\nRjXSB5nZl2b2pJkdbmbvRXXS9085zT5mNjbafm70/WZm91hYE+ItYNuUa/Yys4/NbJKZDYiedhZJ\nCyV+EVgGdPRQ8KsN0CclEe8G9CEUZmsMnE54MvkKoGfKOfYm1L85EOhlZtsDHYFGhPUgzgIOSjn+\nHndv4e5Ngc2B9jG1TeQPCtZ9iEjOM+CmqLpjMaHMbUkZ3G/c/TMAM5tMWBzDzewzwtoJJV5y96XA\nUjMbTSgY1goY7O6rgdlmNirl+DZmdiWhxn8tQtmBl2NroUgKJX4ROAOoC+zn7iujCpbVon3LU44r\nTvlczO///ZSufVJuLRQzqwbcR6izMtPMrk25nkjsNNQjEkoOz4uSfhtgpw04RwcL6/PWJhRB+xgY\nA5waLeRSjzCMBGuS/I/RmgWa6SNppR6/CDwJvBwN3xQBUzfgHBMJJY7rANe7+2wze4Ew7j8F+A4Y\nC6Guv5k9SKj2OZfwS0IkbVSdU0Qkz2ioR0Qkzyjxi4jkGSV+EZE8o8QvIpJnlPhFRPKMEr+ISJ5R\n4hcRyTP/D0jT5M49YrU1AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u9VrkVqe1PXM",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "767df818-abfa-4227-ea63-7b72de7e39ef"
      },
      "source": [
        "print('pred price =',denormalise_price(Y_pred[2][0]),'actual price =',denormalise_price(Y_test[2][0]))"
      ],
      "execution_count": 174,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "pred price = 64257.57664950318 actual price = 58500.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M0LcIvFo8QLt",
        "colab_type": "text"
      },
      "source": [
        "11. *Train the model with train data and predict the test data using Normal Equation*\n",
        "12. *compute the minimum error and lambda* \n",
        "13. *plot error vs lambda graph*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e4DsK_VOWx5x",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 329
        },
        "outputId": "8755fe2d-8471-431d-94c4-f8a9d73d248f"
      },
      "source": [
        "error_mat = []\n",
        "lam_range = 600\n",
        "\n",
        "for lam in range(lam_range):\n",
        "    theta = normalEquation(X,Y,lam)\n",
        "    Cost = computeCost(X_train,Y_train,theta.T,lam)\n",
        "    Y_pred = X_test.dot(theta)\n",
        "    error = computeError(denormalise_price(Y_pred),denormalise_price(Y_test))\n",
        "    error_mat.append(error*100)\n",
        "\n",
        "optimal_lambda = 0\n",
        "min_error = 9999\n",
        "for i in range(len(error_mat)):\n",
        "    if error_mat[i] < min_error:\n",
        "        optimal_lambda = i\n",
        "        min_error = error_mat[i]\n",
        "print(\"min Error : \", min_error)\n",
        "print(\"Optimal Lambda : \", optimal_lambda)\n",
        "plotGraph(np.arange(lam_range),error_mat,'lambda','error','lambda vs error')"
      ],
      "execution_count": 175,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "min Error :  13.432288061521582\n",
            "Optimal Lambda :  311\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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am5HmNtoOGCxpbWA/oDdpPZLDge0Lzr86IraKiE2BFYC9S3RvZkW1\nX/wpZkaauuCibDbQetLUyQ1TK/8nIp4FkPQcaQGXkPQsae2OBvdExMfAx5LGkCaO2wkYGRELgdcl\nPVJw/q6STiOtMbEaabqI+0p2h2aNOEGYNc8Pga7AlhHxeTbbacfs2KcF59UXbNfz5b+xxvPaNDnP\njaSOwLWkOXRmSjqn4P3MysJVTGbNszJpnYTPJe0KrLcU1xigtH716qSJ8J4GxgIHZQsOrUWqvoIv\nksHb2XoZ7tlkZecShFnzjADuy6qN6oBpS3GNyaRps9cAzo+I1yXdTWqXeB54FRgHaV0JSTeQZod9\nk5RMzMrKs7mamVlRrmIyM7OinCDMzKwoJwgzMyvKCcLMzIpygjAzs6KcIMzMrCgnCDMzK+r/A+I8\nEbzumLeqAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jvnh2FTgdjBR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "56d36f4e-dead-4f71-ee2c-e62ef1741b2d"
      },
      "source": [
        "print('pred price =',denormalise_price(Y_pred[2][0]),'actual price =',denormalise_price(Y_test[2])[0])"
      ],
      "execution_count": 176,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "pred price = 57100.426317244695 actual price = 58500.0\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}