「直線回帰 (Fleiss)」の編集履歴（バックアップ）一覧はこちら

「直線回帰 (Fleiss)」(2006/05/09 (火) 06:09:23) の最新版変更点

追加された行は緑色になります。

削除された行は赤色になります。

#contents

----
Ch.2, "Simple Linear Regression Analysis" より (pp.34-36)

*プログラムと結果
**データ
>z <- c(1,2,4,6,7,8,10,15)
>x <- c(0.045, 0.114, 0.215, 0.346, 0.410, 0.520, 0.670, 0.942)
>data <- data.frame(z, x)

**直線回帰
>result.1 <- lm(x ~ z, data=data)
>result.1

Call:
lm(formula = x ~ z, data = data)

Coefficients:
 (Intercept)            z  
    -0.02777      0.06574  

**共変量の平均値周りの回帰
>result.2 <- lm(x ~ I(z - mean(z)), data=data)
>result.2

Call:
lm(formula = x ~ I(z - mean(z)), data = data)

Coefficients:
   (Intercept)  I(z - mean(z))  
       0.40775         0.06574

**計算値のチェック
>sum(data$x - predict(result.1))
[1] 6.938894e-17
>data$z %*% (data$x - predict(result.1))
              [,1]
 [1,] 1.831868e-15

**残差分散
>sum(result.1$res ^2)/result.1$df
[1] 0.000644371

**パラメータの SE，信頼区間
>summary(result.1)

Call:
lm(formula = x ~ z, data = data)

Residuals:
       Min        1Q    Median        3Q       Max 
 -0.022402 -0.020304 -0.004642  0.013185  0.040380 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
 Intercept) -0.027773   0.016647  -1.668    0.146    
             0.065739   0.002116  31.063 7.39e-08 ***

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.02538 on 6 degrees of freedom
Multiple R-Squared: 0.9938,     Adjusted R-squared: 0.9928 
F-statistic: 964.9 on 1 and 6 DF,  p-value: 7.392e-08 

>confint(result.1)
                  2.5 %     97.5 %
 (Intercept) -0.06850670 0.01296021
 z            0.06056098 0.07091773

**原点を通る直線
>result.3 <- lm(x ~ z - 1, data=data)
>summary(result.3)

Call:
lm(formula = x ~ z - 1, data = data)

Residuals:
       Min        1Q    Median        3Q       Max 
 -0.036063 -0.029668 -0.014648  0.004855  0.042343 

Coefficients:
   Estimate Std. Error t value Pr(>|t|)    
 z 0.062766   0.001278   49.11  3.8e-10 ***

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.02843 on 7 degrees of freedom
Multiple R-Squared: 0.9971,     Adjusted R-squared: 0.9967 
F-statistic:  2412 on 1 and 7 DF,  p-value: 3.799e-10 

>confint(result.3)
        2.5 %     97.5 %
 z 0.05974354 0.06578778

**予測区間
>pred.1 <- predict(result.1, interval="prediction")
>matplot(data$z, pred.1, type="l", xlab="z", ylab="x")
>points(data$z, data$x)

#ref(Fig1.png)

*参照
-[[直線回帰の逆予測]]
----
-[[Fleiss]]
-[[R]]

#contents

----
Ch.2, "Simple Linear Regression Analysis" より (pp.34-36)

*プログラムと結果
**データ
>z <- c(1,2,4,6,7,8,10,15)
>x <- c(0.045, 0.114, 0.215, 0.346, 0.410, 0.520, 0.670, 0.942)
>data <- data.frame(z, x)

**直線回帰
>result.1 <- lm(x ~ z, data=data)
>result.1

Call:
lm(formula = x ~ z, data = data)

Coefficients:
 (Intercept)            z  
    -0.02777      0.06574  

**共変量の平均値周りの回帰
>result.2 <- lm(x ~ I(z - mean(z)), data=data)
>result.2

Call:
lm(formula = x ~ I(z - mean(z)), data = data)

Coefficients:
   (Intercept)  I(z - mean(z))  
       0.40775         0.06574

**計算値のチェック
>sum(data$x - predict(result.1))
[1] 6.938894e-17
>data$z %*% (data$x - predict(result.1))
              [,1]
 [1,] 1.831868e-15

**残差分散
>sum(result.1$res ^2)/result.1$df
[1] 0.000644371

**パラメータの SE，信頼区間
>summary(result.1)

Call:
lm(formula = x ~ z, data = data)

Residuals:
       Min        1Q    Median        3Q       Max 
 -0.022402 -0.020304 -0.004642  0.013185  0.040380 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
 Intercept) -0.027773   0.016647  -1.668    0.146    
             0.065739   0.002116  31.063 7.39e-08 ***

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.02538 on 6 degrees of freedom
Multiple R-Squared: 0.9938,     Adjusted R-squared: 0.9928 
F-statistic: 964.9 on 1 and 6 DF,  p-value: 7.392e-08 

>confint(result.1)
                  2.5 %     97.5 %
 (Intercept) -0.06850670 0.01296021
 z            0.06056098 0.07091773

**原点を通る直線
>result.3 <- lm(x ~ z - 1, data=data)
>summary(result.3)

Call:
lm(formula = x ~ z - 1, data = data)

Residuals:
       Min        1Q    Median        3Q       Max 
 -0.036063 -0.029668 -0.014648  0.004855  0.042343 

Coefficients:
   Estimate Std. Error t value Pr(>|t|)    
 z 0.062766   0.001278   49.11  3.8e-10 ***

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.02843 on 7 degrees of freedom
Multiple R-Squared: 0.9971,     Adjusted R-squared: 0.9967 
F-statistic:  2412 on 1 and 7 DF,  p-value: 3.799e-10 

>confint(result.3)
        2.5 %     97.5 %
 z 0.05974354 0.06578778

**予測区間
>pred.1 <- predict(result.1, interval="prediction")
>matplot(data$z, pred.1, type="l", xlab="z", ylab="x")
>points(data$z, data$x)

#ref(Fig1.png)

*参照
-[[直線回帰の逆予測]]

----

-[[Fleiss]]
-[[R]]