R 《回归分析与线性统计模型》page120,4.3

#P120习题4.3
rm(list = ls())
A = read.xlsx("xiti_4.xlsx",sheet = 3)
names(A) = c("ord","Y","K","L")
attach(A)
fm = lm(Y~log(K)+log(L))#线性回归模型
ei = resid(fm)
X = cbind(1,as.matrix(A[,3:4]))
t = ti(ei,X)   #外部学生化残差
plot(fitted(fm),t) #绘制残差图

　　

 

 从残差图中看出来，方差不齐

a1 = boxcox(fm,lambda = seq(0,1,by=0.1))

　　

 

 从图像中看出，λ可取0，即进行对数变换

#进行对数变换
lm.log = lm(log(Y)~log(L)+log(K))
coef(lm.log)

summary(lm.log)
detach(A)

　　

> summary(lm.log)

Call:
lm(formula = log(Y) ~ log(L) + log(K))

Residuals:
    Min      1Q  Median      3Q     Max 
-1.7251 -0.1764 -0.0059  0.1707  1.3035 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.38004    0.26873   1.414    0.166    
log(L)       0.05699    0.04471   1.275    0.211    
log(K)       0.93065    0.04131  22.526   <2e-16 ***
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.441 on 35 degrees of freedom
Multiple R-squared:  0.944,	Adjusted R-squared:  0.9408 
F-statistic:   295 on 2 and 35 DF,  p-value: < 2.2e-16