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【キカガク流】人工知能・機械学習 脱ブラックボックス講座 - 中級編 -
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20180225_multiple-linear-regression_1.ipynb
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20180225_multiple-linear-regression_2.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 68,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": 69,
"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>x1</th>\n",
" <th>x2</th>\n",
" <th>x3</th>\n",
" <th>x4</th>\n",
" <th>x5</th>\n",
" <th>x6</th>\n",
" <th>x7</th>\n",
" <th>x8</th>\n",
" <th>x9</th>\n",
" <th>x10</th>\n",
" <th>x11</th>\n",
" <th>x12</th>\n",
" <th>x13</th>\n",
" <th>y</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</td>\n",
" <td>0.538</td>\n",
" <td>6.575</td>\n",
" <td>65.2</td>\n",
" <td>4.0900</td>\n",
" <td>1</td>\n",
" <td>296</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</td>\n",
" <td>0.469</td>\n",
" <td>6.421</td>\n",
" <td>78.9</td>\n",
" <td>4.9671</td>\n",
" <td>2</td>\n",
" <td>242</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</td>\n",
" <td>0.469</td>\n",
" <td>7.185</td>\n",
" <td>61.1</td>\n",
" <td>4.9671</td>\n",
" <td>2</td>\n",
" <td>242</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</td>\n",
" <td>0.458</td>\n",
" <td>6.998</td>\n",
" <td>45.8</td>\n",
" <td>6.0622</td>\n",
" <td>3</td>\n",
" <td>222</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</td>\n",
" <td>0.458</td>\n",
" <td>7.147</td>\n",
" <td>54.2</td>\n",
" <td>6.0622</td>\n",
" <td>3</td>\n",
" <td>222</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": [
" x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 \\\n",
"0 0.00632 18.0 2.31 0 0.538 6.575 65.2 4.0900 1 296 15.3 396.90 \n",
"1 0.02731 0.0 7.07 0 0.469 6.421 78.9 4.9671 2 242 17.8 396.90 \n",
"2 0.02729 0.0 7.07 0 0.469 7.185 61.1 4.9671 2 242 17.8 392.83 \n",
"3 0.03237 0.0 2.18 0 0.458 6.998 45.8 6.0622 3 222 18.7 394.63 \n",
"4 0.06905 0.0 2.18 0 0.458 7.147 54.2 6.0622 3 222 18.7 396.90 \n",
"\n",
" x13 y \n",
"0 4.98 24.0 \n",
"1 9.14 21.6 \n",
"2 4.03 34.7 \n",
"3 2.94 33.4 \n",
"4 5.33 36.2 "
]
},
"execution_count": 69,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# CSV ファイルの読み込み\n",
"df = pd.read_csv('housing.csv')\n",
"df.head(5)"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"506"
]
},
"execution_count": 70,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# レコード数の確認\n",
"len(df)"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style>\n",
" .dataframe thead tr:only-child th {\n",
" text-align: right;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: left;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>x1</th>\n",
" <th>x2</th>\n",
" <th>x3</th>\n",
" <th>x4</th>\n",
" <th>x5</th>\n",
" <th>x6</th>\n",
" <th>x7</th>\n",
" <th>x8</th>\n",
" <th>x9</th>\n",
" <th>x10</th>\n",
" <th>x11</th>\n",
" <th>x12</th>\n",
" <th>x13</th>\n",
" <th>y</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>3.677082</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",
"</div>"
],
"text/plain": [
" x1 x2 x3 x4 x5 x6 \\\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% 3.677082 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",
" x7 x8 x9 x10 x11 x12 \\\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",
" x13 y \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": 71,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 統計量の算出\n",
"df.describe()"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# 分布の確認\n",
"%matplotlib inline\n",
"import seaborn as sns"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1a1cb07b70>"
]
},
"execution_count": 73,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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6+2p3X004bvAed984P+HO2Uz+Xv+ScPAbM2skbMHsJ7pmcs2HgGsBzOxiwoTe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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a1e243d30>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.distplot(df['x4'], bins=10)"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style>\n",
" .dataframe thead tr:only-child th {\n",
" text-align: right;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: left;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>x1</th>\n",
" <th>x2</th>\n",
" <th>x3</th>\n",
" <th>x4</th>\n",
" <th>x5</th>\n",
" <th>x6</th>\n",
" <th>x7</th>\n",
" <th>x8</th>\n",
" <th>x9</th>\n",
" <th>x10</th>\n",
" <th>x11</th>\n",
" <th>x12</th>\n",
" <th>x13</th>\n",
" <th>y</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>x1</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>x2</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>x3</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>x4</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>x5</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>x6</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>x7</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>x8</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>x9</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>x10</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>x11</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>x12</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>x13</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>y</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": [
" x1 x2 x3 x4 x5 x6 x7 \\\n",
"x1 1.000000 -0.200469 0.406583 -0.055892 0.420972 -0.219247 0.352734 \n",
"x2 -0.200469 1.000000 -0.533828 -0.042697 -0.516604 0.311991 -0.569537 \n",
"x3 0.406583 -0.533828 1.000000 0.062938 0.763651 -0.391676 0.644779 \n",
"x4 -0.055892 -0.042697 0.062938 1.000000 0.091203 0.091251 0.086518 \n",
"x5 0.420972 -0.516604 0.763651 0.091203 1.000000 -0.302188 0.731470 \n",
"x6 -0.219247 0.311991 -0.391676 0.091251 -0.302188 1.000000 -0.240265 \n",
"x7 0.352734 -0.569537 0.644779 0.086518 0.731470 -0.240265 1.000000 \n",
"x8 -0.379670 0.664408 -0.708027 -0.099176 -0.769230 0.205246 -0.747881 \n",
"x9 0.625505 -0.311948 0.595129 -0.007368 0.611441 -0.209847 0.456022 \n",
"x10 0.582764 -0.314563 0.720760 -0.035587 0.668023 -0.292048 0.506456 \n",
"x11 0.289946 -0.391679 0.383248 -0.121515 0.188933 -0.355501 0.261515 \n",
"x12 -0.385064 0.175520 -0.356977 0.048788 -0.380051 0.128069 -0.273534 \n",
"x13 0.455621 -0.412995 0.603800 -0.053929 0.590879 -0.613808 0.602339 \n",
"y -0.388305 0.360445 -0.483725 0.175260 -0.427321 0.695360 -0.376955 \n",
"\n",
" x8 x9 x10 x11 x12 x13 y \n",
"x1 -0.379670 0.625505 0.582764 0.289946 -0.385064 0.455621 -0.388305 \n",
"x2 0.664408 -0.311948 -0.314563 -0.391679 0.175520 -0.412995 0.360445 \n",
"x3 -0.708027 0.595129 0.720760 0.383248 -0.356977 0.603800 -0.483725 \n",
"x4 -0.099176 -0.007368 -0.035587 -0.121515 0.048788 -0.053929 0.175260 \n",
"x5 -0.769230 0.611441 0.668023 0.188933 -0.380051 0.590879 -0.427321 \n",
"x6 0.205246 -0.209847 -0.292048 -0.355501 0.128069 -0.613808 0.695360 \n",
"x7 -0.747881 0.456022 0.506456 0.261515 -0.273534 0.602339 -0.376955 \n",
"x8 1.000000 -0.494588 -0.534432 -0.232471 0.291512 -0.496996 0.249929 \n",
"x9 -0.494588 1.000000 0.910228 0.464741 -0.444413 0.488676 -0.381626 \n",
"x10 -0.534432 0.910228 1.000000 0.460853 -0.441808 0.543993 -0.468536 \n",
"x11 -0.232471 0.464741 0.460853 1.000000 -0.177383 0.374044 -0.507787 \n",
"x12 0.291512 -0.444413 -0.441808 -0.177383 1.000000 -0.366087 0.333461 \n",
"x13 -0.496996 0.488676 0.543993 0.374044 -0.366087 1.000000 -0.737663 \n",
"y 0.249929 -0.381626 -0.468536 -0.507787 0.333461 -0.737663 1.000000 "
]
},
"execution_count": 74,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 相関係数(correlation)の算出\n",
"df.corr()"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# 相関関係を目視で確認\n",
"# sns.pairplot(df)"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style>\n",
" .dataframe thead tr:only-child th {\n",
" text-align: right;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: left;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>x1</th>\n",
" <th>x2</th>\n",
" <th>x3</th>\n",
" <th>x4</th>\n",
" <th>x5</th>\n",
" <th>x6</th>\n",
" <th>x7</th>\n",
" <th>x8</th>\n",
" <th>x9</th>\n",
" <th>x10</th>\n",
" <th>x11</th>\n",
" <th>x12</th>\n",
" <th>x13</th>\n",
" <th>y</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</td>\n",
" <td>0.538</td>\n",
" <td>6.575</td>\n",
" <td>65.2</td>\n",
" <td>4.0900</td>\n",
" <td>1</td>\n",
" <td>296</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</td>\n",
" <td>0.469</td>\n",
" <td>6.421</td>\n",
" <td>78.9</td>\n",
" <td>4.9671</td>\n",
" <td>2</td>\n",
" <td>242</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</td>\n",
" <td>0.469</td>\n",
" <td>7.185</td>\n",
" <td>61.1</td>\n",
" <td>4.9671</td>\n",
" <td>2</td>\n",
" <td>242</td>\n",
" <td>17.8</td>\n",
" <td>392.83</td>\n",
" <td>4.03</td>\n",
" <td>34.7</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 \\\n",
"0 0.00632 18.0 2.31 0 0.538 6.575 65.2 4.0900 1 296 15.3 396.90 \n",
"1 0.02731 0.0 7.07 0 0.469 6.421 78.9 4.9671 2 242 17.8 396.90 \n",
"2 0.02729 0.0 7.07 0 0.469 7.185 61.1 4.9671 2 242 17.8 392.83 \n",
"\n",
" x13 y \n",
"0 4.98 24.0 \n",
"1 9.14 21.6 \n",
"2 4.03 34.7 "
]
},
"execution_count": 76,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.head(3)"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# df.iloc[行, 列]\n",
"X = df.iloc[:, :-1]\n",
"y = df.iloc[:, -1]"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# モデル構築と検証\n",
"from sklearn.linear_model import LinearRegression"
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
]
},
"execution_count": 79,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model = LinearRegression()\n",
"model.fit(X, y)"
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.74064266410940938"
]
},
"execution_count": 82,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 検証（決定係数の計算）\n",
"model.score(X, y)"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ -1.08011358e-01 4.64204584e-02 2.05586264e-02 2.68673382e+00\n",
" -1.77666112e+01 3.80986521e+00 6.92224640e-04 -1.47556685e+00\n",
" 3.06049479e-01 -1.23345939e-02 -9.52747232e-01 9.31168327e-03\n",
" -5.24758378e-01]\n",
"36.4594883851\n"
]
}
],
"source": [
"print(model.coef_)\n",
"print(model.intercept_)"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# 訓練データ(train)と検証データ(test)\n",
"# \n",
"# 例）受験勉強用 10 年分の過去問を購入\n",
"# - 駄目なケース\n",
"# - 10 年分で勉強（学習）\n",
"# - 10 年分で実力テスト（検証）\n",
"# - 良いケース\n",
"# - 前半の 5 年分で勉強（学習） ← 訓練データ\n",
"# - 後半の 5 年分で勉強（検証） ← 検証データ"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from sklearn.model_selection import train_test_split"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# 訓練データと検証データの分割\n",
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=1)"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
]
},
"execution_count": 87,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# モデルの学習\n",
"model.fit(X_train, y_train)"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.720905667266176"
]
},
"execution_count": 88,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 検証 ← 検証データ\n",
"model.score(X_test, y_test)"
]
},
{
"cell_type": "code",
"execution_count": 89,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.74683165201406265"
]
},
"execution_count": 89,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 検証 ← 訓練データ\n",
"model.score(X_train, y_train)"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"x1 0.00632\n",
"x2 18.00000\n",
"x3 2.31000\n",
"x4 0.00000\n",
"x5 0.53800\n",
"x6 6.57500\n",
"x7 65.20000\n",
"x8 4.09000\n",
"x9 1.00000\n",
"x10 296.00000\n",
"x11 15.30000\n",
"x12 396.90000\n",
"x13 4.98000\n",
"Name: 0, dtype: float64"
]
},
"execution_count": 90,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 予測値の計算\n",
"x = X.iloc[0, :]\n",
"x"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 29.42368847])"
]
},
"execution_count": 91,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y_pred = model.predict([x])\n",
"y_pred"
]
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# モデルの保存\n",
"from sklearn.externals import joblib"
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"['model.pkl']"
]
},
"execution_count": 93,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"joblib.dump(model, 'model.pkl')"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 29.42368847])"
]
},
"execution_count": 94,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# モデルの読み込み\n",
"model_new = joblib.load('model.pkl')\n",
"model_new.predict([x])"
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ -8.95714048e-02, 6.73132853e-02, 5.04649248e-02,\n",
" 2.18579583e+00, -1.72053975e+01, 3.63606995e+00,\n",
" 2.05579939e-03, -1.36602886e+00, 2.89576718e-01,\n",
" -1.22700072e-02, -8.34881849e-01, 9.40360790e-03,\n",
" -5.04008320e-01])"
]
},
"execution_count": 96,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# パラメータの確認\n",
"# この変数が重要なのかどうかが判別できる\n",
"model.coef_"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ -0.09 , 0.067, 0.05 , 2.186, -17.205, 3.636, 0.002,\n",
" -1.366, 0.29 , -0.012, -0.835, 0.009, -0.504])"
]
},
"execution_count": 99,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.set_printoptions(precision=3, suppress=True) # 指数関数での表示が禁止\n",
"model.coef_"
]
},
{
"cell_type": "code",
"execution_count": 102,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style>\n",
" .dataframe thead tr:only-child th {\n",
" text-align: right;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: left;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>x1</th>\n",
" <th>x2</th>\n",
" <th>x3</th>\n",
" <th>x4</th>\n",
" <th>x5</th>\n",
" <th>x6</th>\n",
" <th>x7</th>\n",
" <th>x8</th>\n",
" <th>x9</th>\n",
" <th>x10</th>\n",
" <th>x11</th>\n",
" <th>x12</th>\n",
" <th>x13</th>\n",
" <th>y</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</td>\n",
" <td>0.538</td>\n",
" <td>6.575</td>\n",
" <td>65.2</td>\n",
" <td>4.0900</td>\n",
" <td>1</td>\n",
" <td>296</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</td>\n",
" <td>0.469</td>\n",
" <td>6.421</td>\n",
" <td>78.9</td>\n",
" <td>4.9671</td>\n",
" <td>2</td>\n",
" <td>242</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</td>\n",
" <td>0.469</td>\n",
" <td>7.185</td>\n",
" <td>61.1</td>\n",
" <td>4.9671</td>\n",
" <td>2</td>\n",
" <td>242</td>\n",
" <td>17.8</td>\n",
" <td>392.83</td>\n",
" <td>4.03</td>\n",
" <td>34.7</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 \\\n",
"0 0.00632 18.0 2.31 0 0.538 6.575 65.2 4.0900 1 296 15.3 396.90 \n",
"1 0.02731 0.0 7.07 0 0.469 6.421 78.9 4.9671 2 242 17.8 396.90 \n",
"2 0.02729 0.0 7.07 0 0.469 7.185 61.1 4.9671 2 242 17.8 392.83 \n",
"\n",
" x13 y \n",
"0 4.98 24.0 \n",
"1 9.14 21.6 \n",
"2 4.03 34.7 "
]
},
"execution_count": 102,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.head(3)"
]
},
{
"cell_type": "code",
"execution_count": 104,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# 重み（パラメータw）をみるだけでは、どの変数が影響を与えているかわからない"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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@rakuishi
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rakuishi commented Mar 3, 2018

pairplot

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