相関係数と重回帰

stat R言語 Excel

まず今回用いる各説明変数と従属変数との単回帰による相関係数を見ておこう。

  • 居住地：R^2=.007　R=-.084　***
  • 性別：R^2=.011　R=.105　***
  • 年齢：R^2=.174　R=-.418　***
  • 婚姻経験：R^2=.023　R=.153　***
  • 主観的階層：R^2=.000　R=-.004
  • 教育年数：R^2=.049　R=.222　***
  • 旧制・新制：R^2=.062　R=.250　***
  • 世帯収入：R^2=.006　R=.080　***
    • ***p<.001 **p<.01 *p<.05

主観的階層変数以外はすべて有意である（すべて0.1％水準で有意）。有意な各相関係数からそのまま解釈すれば、都市部に住み、女性で、若く、婚姻経験がなく、学歴が高く、戦後の教育を受けており、世帯収入が高い、という属性をもっているほうが、より同性間の性的関係に「寛容」ということになる。

Rによる単回帰分析の出力は以下を参照：

> x1<-size;x2<-sex;x3<-age;x4<-donemarr;x5<-strat_sub;x6<-edulong_q
> x7<-oldnew;x8<-incm_q

> summary(lm(y~x1))

Call:
lm(formula = y ~ x1)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.2738 -1.0202 -0.1470  0.8530  1.9798 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  2.40068    0.07595  31.608  < 2e-16 ***
x1          -0.12683    0.03600  -3.523 0.000438 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.951 on 1760 degrees of freedom
Multiple R-Squared: 0.007002,   Adjusted R-squared: 0.006438 
F-statistic: 12.41 on 1 and 1760 DF,  p-value: 0.0004378 
> summary(lm(y~x2))

Call:
lm(formula = y ~ x2)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.24409 -1.04467 -0.04467  0.75591  1.95533 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.84525    0.07170   25.74  < 2e-16 ***
x2           0.19942    0.04522    4.41 1.10e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.9491 on 1760 degrees of freedom
Multiple R-Squared: 0.01093,    Adjusted R-squared: 0.01037 
F-statistic: 19.45 on 1 and 1760 DF,  p-value: 1.097e-05 
> summary(lm(y~x3))

Call:
lm(formula = y ~ x3)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.8562 -0.8384  0.1438  0.6527  2.6705 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  3.11067    0.05417   57.42   <2e-16 ***
x3          -0.25445    0.01320  -19.28   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.8671 on 1760 degrees of freedom
Multiple R-Squared: 0.1744,     Adjusted R-squared: 0.1739 
F-statistic: 371.7 on 1 and 1760 DF,  p-value: < 2.2e-16
> summary(lm(y~x4))

Call:
lm(formula = y ~ x4)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.57778 -1.09608 -0.09608  0.90392  1.90392 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  2.09608    0.02371  88.403  < 2e-16 ***
x4           0.48170    0.07418   6.493 1.09e-10 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.9431 on 1760 degrees of freedom
Multiple R-Squared: 0.0234,     Adjusted R-squared: 0.02284 
F-statistic: 42.16 on 1 and 1760 DF,  p-value: 1.089e-10
> summary(lm(y~x5))

Call:
lm(formula = y ~ x5)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.1724 -1.1373 -0.1373  0.8510  1.8744 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  2.18415    0.09847  22.181   <2e-16 ***
x5          -0.01171    0.02886  -0.406    0.685    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.9543 on 1760 degrees of freedom
Multiple R-Squared:  9.348e-05, Adjusted R-squared: -0.0004746 
F-statistic: 0.1645 on 1 and 1760 DF,  p-value: 0.685 
> summary(lm(y~x6))

Call:
lm(formula = y ~ x6)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.6538 -0.9079 -0.1210  0.8790  2.1987 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.58819    0.06231  25.490   <2e-16 ***
x6           0.10656    0.01114   9.567   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.9304 on 1760 degrees of freedom
Multiple R-Squared: 0.04944,    Adjusted R-squared: 0.0489 
F-statistic: 91.53 on 1 and 1760 DF,  p-value: < 2.2e-16 
> summary(lm(y~x7))

Call:
lm(formula = y ~ x7)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.2529 -0.6187 -0.2529  0.7471  2.3813 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.61873    0.05344   30.29   <2e-16 ***
x7           0.63418    0.05865   10.81   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.9241 on 1760 degrees of freedom
Multiple R-Squared: 0.06229,    Adjusted R-squared: 0.06176 
F-statistic: 116.9 on 1 and 1760 DF,  p-value: < 2.2e-16
> summary(lm(y~x8))

Call:
lm(formula = y ~ x8)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.30558 -1.09332 -0.09332  0.82178  2.03404 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.92351    0.06940  27.715  < 2e-16 ***
x8           0.04245    0.01256   3.381 0.000739 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.9512 on 1760 degrees of freedom
Multiple R-Squared: 0.006452,   Adjusted R-squared: 0.005888 
F-statistic: 11.43 on 1 and 1760 DF,  p-value: 0.0007385