BOSTON HOUSE PREDICTION.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9249c6df",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "359919dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "boston = load_boston()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ca497f4b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "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 black people 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"
     ]
    }
   ],
   "source": [
    "print(boston.DESCR)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "79babfcd",
   "metadata": {},
   "outputs": [],
   "source": [
    "boston_df = boston.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c139215b",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "array([[6.3200e-03, 1.8000e+01, 2.3100e+00, ..., 1.5300e+01, 3.9690e+02,\n",
       "        4.9800e+00],\n",
       "       [2.7310e-02, 0.0000e+00, 7.0700e+00, ..., 1.7800e+01, 3.9690e+02,\n",
       "        9.1400e+00],\n",
       "       [2.7290e-02, 0.0000e+00, 7.0700e+00, ..., 1.7800e+01, 3.9283e+02,\n",
       "        4.0300e+00],\n",
       "       ...,\n",
       "       [6.0760e-02, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9690e+02,\n",
       "        5.6400e+00],\n",
       "       [1.0959e-01, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9345e+02,\n",
       "        6.4800e+00],\n",
       "       [4.7410e-02, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9690e+02,\n",
       "        7.8800e+00]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8e8b76b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.DataFrame(boston.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "368412de",
   "metadata": {},
   "outputs": [
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       "        0     1     2    3      4      5     6       7    8      9     10  \\\n",
       "0  0.00632  18.0  2.31  0.0  0.538  6.575  65.2  4.0900  1.0  296.0  15.3   \n",
       "1  0.02731   0.0  7.07  0.0  0.469  6.421  78.9  4.9671  2.0  242.0  17.8   \n",
       "2  0.02729   0.0  7.07  0.0  0.469  7.185  61.1  4.9671  2.0  242.0  17.8   \n",
       "3  0.03237   0.0  2.18  0.0  0.458  6.998  45.8  6.0622  3.0  222.0  18.7   \n",
       "4  0.06905   0.0  2.18  0.0  0.458  7.147  54.2  6.0622  3.0  222.0  18.7   \n",
       "\n",
       "       11    12  \n",
       "0  396.90  4.98  \n",
       "1  396.90  9.14  \n",
       "2  392.83  4.03  \n",
       "3  394.63  2.94  \n",
       "4  396.90  5.33  "
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   ],
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    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2700b29e",
   "metadata": {},
   "outputs": [
    {
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       "  <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",
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       "      <th>LSTAT</th>\n",
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       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
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       "      <td>242.0</td>\n",
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       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
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       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
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      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  \n",
       "0     15.3  396.90   4.98  \n",
       "1     17.8  396.90   9.14  \n",
       "2     17.8  392.83   4.03  \n",
       "3     18.7  394.63   2.94  \n",
       "4     18.7  396.90   5.33  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.columns = boston.feature_names\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3cd638f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CRIM       0\n",
       "ZN         0\n",
       "INDUS      0\n",
       "CHAS       0\n",
       "NOX        0\n",
       "RM         0\n",
       "AGE        0\n",
       "DIS        0\n",
       "RAD        0\n",
       "TAX        0\n",
       "PTRATIO    0\n",
       "B          0\n",
       "LSTAT      0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "257776cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "data['PRICE'] = boston.target "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "fd795046",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data.drop(['PRICE'], axis = 1)\n",
    "y = data['PRICE']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f542d1b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y, test_size = 0.3, random_state = 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5258c8e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# Create a Linear regressor\n",
    "lm = LinearRegression()\n",
    "\n",
    "# Train the model using the training sets \n",
    "lm.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "76432166",
   "metadata": {},
   "outputs": [
    {
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       "      <th>CRIM</th>\n",
       "      <td>-0.122570</td>\n",
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       "      <th>ZN</th>\n",
       "      <td>0.055678</td>\n",
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       "    <tr>\n",
       "      <th>INDUS</th>\n",
       "      <td>-0.008834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CHAS</th>\n",
       "      <td>4.693448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NOX</th>\n",
       "      <td>-14.435783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RM</th>\n",
       "      <td>3.280080</td>\n",
       "    </tr>\n",
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       "      <th>AGE</th>\n",
       "      <td>-0.003448</td>\n",
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       "      <th>DIS</th>\n",
       "      <td>-1.552144</td>\n",
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       "      <th>RAD</th>\n",
       "      <td>0.326250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TAX</th>\n",
       "      <td>-0.014067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PTRATIO</th>\n",
       "      <td>-0.803275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.009354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LSTAT</th>\n",
       "      <td>-0.523478</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Coefficient\n",
       "CRIM       -0.122570\n",
       "ZN          0.055678\n",
       "INDUS      -0.008834\n",
       "CHAS        4.693448\n",
       "NOX       -14.435783\n",
       "RM          3.280080\n",
       "AGE        -0.003448\n",
       "DIS        -1.552144\n",
       "RAD         0.326250\n",
       "TAX        -0.014067\n",
       "PTRATIO    -0.803275\n",
       "B           0.009354\n",
       "LSTAT      -0.523478"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coeff_df = pd.DataFrame(lm.coef_,X.columns,columns=['Coefficient'])\n",
    "coeff_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "926cc514",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = lm.predict(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "45492788",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "5cd0bdd9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2: 0.7465991966746854\n",
      "Adjusted R^2: 0.736910342429894\n",
      "MAE: 3.0898610949711265\n",
      "MSE: 19.07368870346903\n",
      "RMSE: 4.367343437774162\n"
     ]
    }
   ],
   "source": [
    "print('R^2:',metrics.r2_score(y_train, y_pred))\n",
    "print('Adjusted R^2:',1 - (1-metrics.r2_score(y_train, y_pred))*(len(y_train)-1)/(len(y_train)-X_train.shape[1]-1))\n",
    "print('MAE:',metrics.mean_absolute_error(y_train, y_pred))\n",
    "print('MSE:',metrics.mean_squared_error(y_train, y_pred))\n",
    "print('RMSE:',np.sqrt(metrics.mean_squared_error(y_train, y_pred)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5117f7d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(y_train, y_pred)\n",
    "plt.xlabel(\"Prices\")\n",
    "plt.ylabel(\"Predicted prices\")\n",
    "plt.title(\"Prices vs Predicted prices\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "80777ed0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(y_pred,y_train-y_pred)\n",
    "plt.title(\"Predicted vs residuals\")\n",
    "plt.xlabel(\"Predicted\")\n",
    "plt.ylabel(\"Residuals\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "eed05bf2",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_test_pred = lm.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "b18456c4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2: 0.7121818377409193\n",
      "Adjusted R^2: 0.6850685326005711\n",
      "MAE: 3.859005592370745\n",
      "MSE: 30.053993307124163\n",
      "RMSE: 5.482152251362978\n"
     ]
    }
   ],
   "source": [
    "acc_linreg = metrics.r2_score(y_test, y_test_pred)\n",
    "print('R^2:', acc_linreg)\n",
    "print('Adjusted R^2:',1 - (1-metrics.r2_score(y_test, y_test_pred))*(len(y_test)-1)/(len(y_test)-X_test.shape[1]-1))\n",
    "print('MAE:',metrics.mean_absolute_error(y_test, y_test_pred))\n",
    "print('MSE:',metrics.mean_squared_error(y_test, y_test_pred))\n",
    "print('RMSE:',np.sqrt(metrics.mean_squared_error(y_test, y_test_pred)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "01764756",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}