Rによる実行結果
> data923 <- read.csv("Table923.csv")
> data923
Y X1 X2 X3 X4 X5 X6 X7
1 44000 95 59.2 10.0 80 7 8 125
2 50000 95 62.5 15.0 200 14 12 200
3 110000 90 54.8 15.0 98 0 15 250
4 16000 12 54.5 10.0 60 5 6 70
5 10000 66 48.0 13.0 42 3 3 40
6 160000 95 67.5 5.0 100 18 17 200
7 100000 95 70.5 8.0 100 3 4 150
8 6500 65 48.3 12.0 50 4 3 50
9 1500 66 51.0 8.0 16 2 2 25
10 164000 138 75.0 7.0 200 1 26 220
11 1300 19 43.0 23.0 18 1 0 20
12 13000 62 67.0 22.0 75 0 0 120
13 40000 66 60.3 0.5 100 7 6 130
14 2200 22 47.5 17.0 34 3 1 30
15 50000 95 62.9 5.0 80 2 4 110
16 200000 95 68.7 7.0 90 3 18 300
> attach(data923)
> cor(data923)#相関行列
Y X1 X2 X3 X4 X5 X6 X7
Y 1.0000000 0.7104306 0.7444810 -0.4511601 0.5785899 0.2154686 0.8772393 0.8949123
X1 0.7104306 1.0000000 0.7533081 -0.4767957 0.7251732 0.1728760 0.7145366 0.7167610
X2 0.7444810 0.7533081 1.0000000 -0.4572787 0.7317957 0.2101435 0.6316771 0.7501950
X3 -0.4511601 -0.4767957 -0.4572787 1.0000000 -0.2687331 -0.3194164 -0.4044195 -0.3163315
X4 0.5785899 0.7251732 0.7317957 -0.2687331 1.0000000 0.3602120 0.7444591 0.7197530
X5 0.2154686 0.1728760 0.2101435 -0.3194164 0.3602120 1.0000000 0.2803295 0.2307346
X6 0.8772393 0.7145366 0.6316771 -0.4044195 0.7444591 0.2803295 1.0000000 0.8372739
X7 0.8949123 0.7167610 0.7501950 -0.3163315 0.7197530 0.2307346 0.8372739 1.0000000
> model1 <- lm(Y~X6)#公開授業の数
> summary(model1)
Call:
lm(formula = Y ~ X6)
Residuals:
Min 1Q Median 3Q Max
-42259 -17664 -6756 13336 68355
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1337 11912 0.112 0.912
X6 7577 1108 6.837 8.1e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 32730 on 14 degrees of freedom
Multiple R-squared: 0.7695, Adjusted R-squared: 0.7531
F-statistic: 46.75 on 1 and 14 DF, p-value: 8.095e-06
> AIC(model1)
[1] 381.9441
>
>
> model2 <- lm(Y~X7)#企画数
> summary(model2)
Call:
lm(formula = Y ~ X7)
Residuals:
Min 1Q Median 3Q Max
-59716 -16683 4578 15884 50284
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -25966.95 13810.87 -1.880 0.0811 .
X7 678.42 90.41 7.504 2.86e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 30430 on 14 degrees of freedom
Multiple R-squared: 0.8009, Adjusted R-squared: 0.7866
F-statistic: 56.31 on 1 and 14 DF, p-value: 2.863e-06
> AIC(model2)
[1] 379.607
>
>
> model3 <- lm(Y~X6+X7)#企画数、公開授業の数
> summary(model3)
Call:
lm(formula = Y ~ X6 + X7)
Residuals:
Min 1Q Median 3Q Max
-55501 -15037 732 11354 44409
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -20210.8 12475.7 -1.620 0.1292
X6 3696.5 1664.6 2.221 0.0448 *
X7 406.8 146.1 2.784 0.0155 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 26880 on 13 degrees of freedom
Multiple R-squared: 0.8556, Adjusted R-squared: 0.8334
F-statistic: 38.52 on 2 and 13 DF, p-value: 3.441e-06
> AIC(model3)
[1] 376.4618
> step(model3)
Start: AIC=329.06
Y ~ X6 + X7
Df Sum of Sq RSS AIC
<none> 9.3962e+09 329.06
- X6 1 3564006627 1.2960e+10 332.20
- X7 1 5602366191 1.4999e+10 334.54
Call:
lm(formula = Y ~ X6 + X7)
Coefficients:
(Intercept) X6 X7
-20210.8 3696.5 406.8
>
> # 標準偏回帰係数（β）を求める
> z <- scale(data923) # 得点を標準化
> z <- data.frame(z) # データフレーム形式に戻す
> summary(lm(Y~X6+X7, z))
Call:
lm(formula = Y ~ X6 + X7, data = z)
Residuals:
Min 1Q Median 3Q Max
-0.84258 -0.22828 0.01111 0.17237 0.67419
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.074e-17 1.020e-01 0.000 1.0000
X6 4.280e-01 1.927e-01 2.221 0.0448 *
X7 5.366e-01 1.927e-01 2.784 0.0155 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.4081 on 13 degrees of freedom
Multiple R-squared: 0.8556, Adjusted R-squared: 0.8334
F-statistic: 38.52 on 2 and 13 DF, p-value: 3.441e-06
>
>
#多重共線性のチェック
> zx <- z[7:8]
> r <- cor(zx)
> VIF <- diag(solve(r))
> tolerance = 1/VIF
> data.frame(tolerance, VIF)
tolerance VIF
X6 0.2989725 3.34479
X7 0.2989725 3.34479
>
VIF >5 （tolerance < 0.2 ）の時、多重共線性が疑われる。