R 《回归分析与线性统计模型》page93.6

rm(list = ls()) #数据处理
library(openxlsx)
library(car)
library(lmtest)
data = read.xlsx("xiti4.xlsx",sheet = 1)
data
attach(data)

fm1 = lm(y~x1+x2+x3+x4+x5+x6+x7) #多元回归模型
coef(fm1)

#残差图:残差分析
ei = resid(fm1)
X = cbind(1,as.matrix(data[,2:8]))
t = ti(ei,X) #外部学生化残差
r = ri(ei,X) #学生化残差
plot(fitted(fm1),t)

#判别强影响点
#cook距离
res = cooks.distance(fm1)
res[res>4/(25-7-1)]

         15          20          22          23          24 
  0.7626036   0.4177263   1.0797246 115.3547590   5.9390636 

influence.measures(fm1)

#判别异常点
calcu_F = function(p,r) #p回归参数个数，r学生化残差
{
  n = length(r)
  ans = (n-p-2)*(r**2)/(n-p-1-r**2)
  return(ans)
}
FF = calcu_F(7,r)
f_val = qf(1-0.05,1,17)
FF[FF>f_val] #F统计量

       15        20        23        24 
 6.369148  8.245486 27.667296 10.433935 

> #判别异常点
> outlierTest(fm1) #Bonferroni p<0.05此点异常
    rstudent unadjusted p-value Bonferroni p
23 -5.259971         7.7773e-05    0.0019443