1-LinearRegression_boston_hourse.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 波士顿房价预测"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1、数据分析以及可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm\n",
    "from sklearn.datasets import load_boston\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import linear_model\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.metrics import r2_score\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import LinearRegression, SGDRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = load_boston()\n",
    "x = dataset.data\n",
    "target = dataset.target\n",
    "y = np.reshape(target,(len(target), 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "boston_date = pd.DataFrame(dataset.data, columns=dataset.feature_names)\n",
    "boston_date['price'] = target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "float64    14\n",
       "dtype: int64"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston_date.get_dtype_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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",
       "price      0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston_date.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
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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",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <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",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "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  price  \n",
       "0     15.3  396.90   4.98   24.0  \n",
       "1     17.8  396.90   9.14   21.6  \n",
       "2     17.8  392.83   4.03   34.7  \n",
       "3     18.7  394.63   2.94   33.4  \n",
       "4     18.7  396.90   5.33   36.2  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston_date.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "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>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.613524</td>\n",
       "      <td>11.363636</td>\n",
       "      <td>11.136779</td>\n",
       "      <td>0.069170</td>\n",
       "      <td>0.554695</td>\n",
       "      <td>6.284634</td>\n",
       "      <td>68.574901</td>\n",
       "      <td>3.795043</td>\n",
       "      <td>9.549407</td>\n",
       "      <td>408.237154</td>\n",
       "      <td>18.455534</td>\n",
       "      <td>356.674032</td>\n",
       "      <td>12.653063</td>\n",
       "      <td>22.532806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>8.601545</td>\n",
       "      <td>23.322453</td>\n",
       "      <td>6.860353</td>\n",
       "      <td>0.253994</td>\n",
       "      <td>0.115878</td>\n",
       "      <td>0.702617</td>\n",
       "      <td>28.148861</td>\n",
       "      <td>2.105710</td>\n",
       "      <td>8.707259</td>\n",
       "      <td>168.537116</td>\n",
       "      <td>2.164946</td>\n",
       "      <td>91.294864</td>\n",
       "      <td>7.141062</td>\n",
       "      <td>9.197104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.006320</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.460000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.385000</td>\n",
       "      <td>3.561000</td>\n",
       "      <td>2.900000</td>\n",
       "      <td>1.129600</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>187.000000</td>\n",
       "      <td>12.600000</td>\n",
       "      <td>0.320000</td>\n",
       "      <td>1.730000</td>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.082045</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.190000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.449000</td>\n",
       "      <td>5.885500</td>\n",
       "      <td>45.025000</td>\n",
       "      <td>2.100175</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>279.000000</td>\n",
       "      <td>17.400000</td>\n",
       "      <td>375.377500</td>\n",
       "      <td>6.950000</td>\n",
       "      <td>17.025000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.256510</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>9.690000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.538000</td>\n",
       "      <td>6.208500</td>\n",
       "      <td>77.500000</td>\n",
       "      <td>3.207450</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>330.000000</td>\n",
       "      <td>19.050000</td>\n",
       "      <td>391.440000</td>\n",
       "      <td>11.360000</td>\n",
       "      <td>21.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.677083</td>\n",
       "      <td>12.500000</td>\n",
       "      <td>18.100000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.624000</td>\n",
       "      <td>6.623500</td>\n",
       "      <td>94.075000</td>\n",
       "      <td>5.188425</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>666.000000</td>\n",
       "      <td>20.200000</td>\n",
       "      <td>396.225000</td>\n",
       "      <td>16.955000</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>88.976200</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>27.740000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.871000</td>\n",
       "      <td>8.780000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>12.126500</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>711.000000</td>\n",
       "      <td>22.000000</td>\n",
       "      <td>396.900000</td>\n",
       "      <td>37.970000</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "             CRIM          ZN       INDUS        CHAS         NOX          RM  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean     3.613524   11.363636   11.136779    0.069170    0.554695    6.284634   \n",
       "std      8.601545   23.322453    6.860353    0.253994    0.115878    0.702617   \n",
       "min      0.006320    0.000000    0.460000    0.000000    0.385000    3.561000   \n",
       "25%      0.082045    0.000000    5.190000    0.000000    0.449000    5.885500   \n",
       "50%      0.256510    0.000000    9.690000    0.000000    0.538000    6.208500   \n",
       "75%      3.677083   12.500000   18.100000    0.000000    0.624000    6.623500   \n",
       "max     88.976200  100.000000   27.740000    1.000000    0.871000    8.780000   \n",
       "\n",
       "              AGE         DIS         RAD         TAX     PTRATIO           B  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean    68.574901    3.795043    9.549407  408.237154   18.455534  356.674032   \n",
       "std     28.148861    2.105710    8.707259  168.537116    2.164946   91.294864   \n",
       "min      2.900000    1.129600    1.000000  187.000000   12.600000    0.320000   \n",
       "25%     45.025000    2.100175    4.000000  279.000000   17.400000  375.377500   \n",
       "50%     77.500000    3.207450    5.000000  330.000000   19.050000  391.440000   \n",
       "75%     94.075000    5.188425   24.000000  666.000000   20.200000  396.225000   \n",
       "max    100.000000   12.126500   24.000000  711.000000   22.000000  396.900000   \n",
       "\n",
       "            LSTAT       price  \n",
       "count  506.000000  506.000000  \n",
       "mean    12.653063   22.532806  \n",
       "std      7.141062    9.197104  \n",
       "min      1.730000    5.000000  \n",
       "25%      6.950000   17.025000  \n",
       "50%     11.360000   21.200000  \n",
       "75%     16.955000   25.000000  \n",
       "max     37.970000   50.000000  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston_date.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <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",
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       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>price</th>\n",
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       "  </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>price</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      CHAS       NOX        RM       AGE  \\\n",
       "CRIM     1.000000 -0.200469  0.406583 -0.055892  0.420972 -0.219247  0.352734   \n",
       "ZN      -0.200469  1.000000 -0.533828 -0.042697 -0.516604  0.311991 -0.569537   \n",
       "INDUS    0.406583 -0.533828  1.000000  0.062938  0.763651 -0.391676  0.644779   \n",
       "CHAS    -0.055892 -0.042697  0.062938  1.000000  0.091203  0.091251  0.086518   \n",
       "NOX      0.420972 -0.516604  0.763651  0.091203  1.000000 -0.302188  0.731470   \n",
       "RM      -0.219247  0.311991 -0.391676  0.091251 -0.302188  1.000000 -0.240265   \n",
       "AGE      0.352734 -0.569537  0.644779  0.086518  0.731470 -0.240265  1.000000   \n",
       "DIS     -0.379670  0.664408 -0.708027 -0.099176 -0.769230  0.205246 -0.747881   \n",
       "RAD      0.625505 -0.311948  0.595129 -0.007368  0.611441 -0.209847  0.456022   \n",
       "TAX      0.582764 -0.314563  0.720760 -0.035587  0.668023 -0.292048  0.506456   \n",
       "PTRATIO  0.289946 -0.391679  0.383248 -0.121515  0.188933 -0.355501  0.261515   \n",
       "B       -0.385064  0.175520 -0.356977  0.048788 -0.380051  0.128069 -0.273534   \n",
       "LSTAT    0.455621 -0.412995  0.603800 -0.053929  0.590879 -0.613808  0.602339   \n",
       "price   -0.388305  0.360445 -0.483725  0.175260 -0.427321  0.695360 -0.376955   \n",
       "\n",
       "              DIS       RAD       TAX   PTRATIO         B     LSTAT     price  \n",
       "CRIM    -0.379670  0.625505  0.582764  0.289946 -0.385064  0.455621 -0.388305  \n",
       "ZN       0.664408 -0.311948 -0.314563 -0.391679  0.175520 -0.412995  0.360445  \n",
       "INDUS   -0.708027  0.595129  0.720760  0.383248 -0.356977  0.603800 -0.483725  \n",
       "CHAS    -0.099176 -0.007368 -0.035587 -0.121515  0.048788 -0.053929  0.175260  \n",
       "NOX     -0.769230  0.611441  0.668023  0.188933 -0.380051  0.590879 -0.427321  \n",
       "RM       0.205246 -0.209847 -0.292048 -0.355501  0.128069 -0.613808  0.695360  \n",
       "AGE     -0.747881  0.456022  0.506456  0.261515 -0.273534  0.602339 -0.376955  \n",
       "DIS      1.000000 -0.494588 -0.534432 -0.232471  0.291512 -0.496996  0.249929  \n",
       "RAD     -0.494588  1.000000  0.910228  0.464741 -0.444413  0.488676 -0.381626  \n",
       "TAX     -0.534432  0.910228  1.000000  0.460853 -0.441808  0.543993 -0.468536  \n",
       "PTRATIO -0.232471  0.464741  0.460853  1.000000 -0.177383  0.374044 -0.507787  \n",
       "B        0.291512 -0.444413 -0.441808 -0.177383  1.000000 -0.366087  0.333461  \n",
       "LSTAT   -0.496996  0.488676  0.543993  0.374044 -0.366087  1.000000 -0.737663  \n",
       "price    0.249929 -0.381626 -0.468536 -0.507787  0.333461 -0.737663  1.000000  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston_date.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CRIM      -0.388305\n",
       "ZN         0.360445\n",
       "INDUS     -0.483725\n",
       "CHAS       0.175260\n",
       "NOX       -0.427321\n",
       "RM         0.695360\n",
       "AGE       -0.376955\n",
       "DIS        0.249929\n",
       "RAD       -0.381626\n",
       "TAX       -0.468536\n",
       "PTRATIO   -0.507787\n",
       "B          0.333461\n",
       "LSTAT     -0.737663\n",
       "price      1.000000\n",
       "Name: price, dtype: float64"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston_date.corr()['price']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1a1d3e42b0>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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(boston_date[\"RM\"],boston_date[\"price\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1a1d4f54e0>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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(boston_date[\"PTRATIO\"],boston_date[\"price\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1a1d540240>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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(boston_date[\"LSTAT\"],boston_date[\"price\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2、线性回归\n",
    "\n",
    "### 2-1、普通线性回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_x, test_x, train_y, test_y = train_test_split(x, y, random_state = 31, test_size = 0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(404, 13) (404, 1)\n"
     ]
    }
   ],
   "source": [
    "print(train_x.shape,train_y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "std_x = StandardScaler()\n",
    "train_x_std = std_x.fit_transform(train_x)\n",
    "test_x_std = std_x.transform(test_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE:  16.538367380923752\n",
      "R2:  0.7849023595572457\n"
     ]
    }
   ],
   "source": [
    "lr_normal = LinearRegression()\n",
    "lr_normal.fit(train_x_std, train_y)\n",
    "predict_y = lr_normal.predict(test_x_std)\n",
    "print(\"MSE: \",mean_squared_error(test_y, predict_y))\n",
    "print(\"R2: \",r2_score(test_y, predict_y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2-2、对y规范化-线性回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "std_y = StandardScaler()\n",
    "train_y_std = std_y.fit_transform(train_y)\n",
    "test_y_std = std_y.transform(test_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE:  16.538367380923745\n",
      "R2:  0.7849023595572459\n"
     ]
    }
   ],
   "source": [
    "lr_std_y = LinearRegression()\n",
    "lr_std_y.fit(train_x_std, train_y_std)\n",
    "predict_y = std_y.inverse_transform(lr_std_y.predict(test_x_std))\n",
    "print(\"MSE: \",mean_squared_error(test_y, predict_y))\n",
    "print(\"R2: \",r2_score(test_y, predict_y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE:  17.24879565224886\n",
      "R2:  0.7756625451701186\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/supinyu/anaconda3/lib/python3.7/site-packages/sklearn/utils/validation.py:724: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    }
   ],
   "source": [
    "sgd = SGDRegressor()\n",
    "sgd.fit(train_x_std, train_y_std)\n",
    "predict_y_sgd = std_y.inverse_transform(sgd.predict(test_x_std))\n",
    "print(\"MSE: \",mean_squared_error(test_y, predict_y_sgd))\n",
    "print(\"R2: \",r2_score(test_y, predict_y_sgd))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2-3、numpy实现的线性回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "class liner_Regression:\n",
    "    \"\"\"\n",
    "    x : sample_num * dim\n",
    "    y : sample_num * 1\n",
    "    return :\n",
    "    weight , biase\n",
    "    \"\"\"\n",
    "    def __init__(self, x, y, learningRate = 0.001, epoch = 1000):\n",
    "        self.x = x\n",
    "        self.y = y\n",
    "        self.sample_num = x.shape[0]\n",
    "        self.dim = x.shape[1]\n",
    "        self.weight = np.ones(shape=(1, self.dim))\n",
    "        self.baise = np.array([[1]])\n",
    "        self.epoch = epoch\n",
    "        self.learningRate = learningRate\n",
    "        \n",
    "    def fit(self):\n",
    "        for num in range(self.epoch):\n",
    "            predict_y = np.dot(self.x, self.weight.T) + self.baise\n",
    "            loss =  (1.0 / 2) * np.dot((self.y - predict_y).T, self.y - predict_y) / self.sample_num\n",
    "            weight_grad = -1.0 /self.sample_num * np.dot((self.y - predict_y).T, self.x)\n",
    "            baise_grad = -1.0 /self.sample_num * np.dot((self.y - predict_y).T, np.ones(shape=[self.sample_num, 1]))\n",
    "\n",
    "            self.weight = self.weight - self.learningRate * weight_grad\n",
    "            self.baise = self.baise - self.learningRate * baise_grad\n",
    "            if num % 500 == 0:\n",
    "                print(\"loss: \", loss)\n",
    "    \n",
    "    def predict(self, test_x):\n",
    "        return np.dot(test_x, self.weight.T) + self.baise\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "self_linear = liner_Regression(train_x_std, train_y_std, epoch = 12000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss:  [[12.31029617]]\n",
      "loss:  [[1.98136196]]\n",
      "loss:  [[1.13928829]]\n",
      "loss:  [[0.73917842]]\n",
      "loss:  [[0.52578828]]\n",
      "loss:  [[0.40252083]]\n",
      "loss:  [[0.32630552]]\n",
      "loss:  [[0.27643966]]\n",
      "loss:  [[0.24227901]]\n",
      "loss:  [[0.21800169]]\n",
      "loss:  [[0.20023778]]\n",
      "loss:  [[0.18693465]]\n",
      "loss:  [[0.17678484]]\n",
      "loss:  [[0.16892292]]\n",
      "loss:  [[0.16275703]]\n",
      "loss:  [[0.15787117]]\n",
      "loss:  [[0.15396605]]\n",
      "loss:  [[0.15082203]]\n",
      "loss:  [[0.14827517]]\n",
      "loss:  [[0.14620125]]\n",
      "loss:  [[0.14450493]]\n",
      "loss:  [[0.14311221]]\n",
      "loss:  [[0.14196505]]\n",
      "loss:  [[0.14101752]]\n"
     ]
    }
   ],
   "source": [
    "self_linear.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "predict_y_self = std_y.inverse_transform(self_linear.predict(test_x_std))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE:  17.48076080782158\n",
      "R2:  0.7726456114861939\n"
     ]
    }
   ],
   "source": [
    "print(\"MSE: \",mean_squared_error(test_y, predict_y_self))\n",
    "print(\"R2: \",r2_score(test_y, predict_y_self))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2-4、选取部分特征"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = boston_date[['LSTAT','PTRATIO','RM','price']]\n",
    "y_select = np.array(data['price'])\n",
    "data = data.drop(['price'],axis=1)\n",
    "x_select = np.array(data)\n",
    "train_x_sel, test_x_sel, train_y_sel, test_y_sel = train_test_split(x_select, y_select, random_state = 31, test_size = 0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE:  20.613131629833926\n",
      "R2:  0.7319060658413352\n"
     ]
    }
   ],
   "source": [
    "std_x_sel = StandardScaler()\n",
    "train_x_sel_std = std_x.fit_transform(train_x_sel)\n",
    "test_x_sel_std = std_x.transform(test_x_sel)\n",
    "lr_select = LinearRegression()\n",
    "lr_select.fit(train_x_sel_std, train_y_sel)\n",
    "predict_y_sel = lr_select.predict(test_x_sel_std)\n",
    "print(\"MSE: \",mean_squared_error(test_y_sel, predict_y_sel))\n",
    "print(\"R2: \",r2_score(test_y_sel, predict_y_sel))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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