以下内容并不能完全回答这个问题。不过，它可能会给你一些想法。这是我最近为了评估使用一到四个自变量（因变量在 df1 数据框的第一列中）的几个回归模型的拟合而做的事情。
# create the combinations of the 4 independent variables
library(foreach)
xcomb <- foreach(i=1:4, .combine=c) %do% {combn(names(df1)[-1], i, simplify=FALSE) }
# create formulas
formlist <- lapply(xcomb, function(l) formula(paste(names(df1)[1], paste(l, collapse="+"), sep="~")))
as.character(formlist) 的内容是
[1] "price ~ sqft" "price ~ age"
[3] "price ~ feats" "price ~ tax"
[5] "price ~ sqft + age" "price ~ sqft + feats"
[7] "price ~ sqft + tax" "price ~ age + feats"
[9] "price ~ age + tax" "price ~ feats + tax"
[11] "price ~ sqft + age + feats" "price ~ sqft + age + tax"
[13] "price ~ sqft + feats + tax" "price ~ age + feats + tax"
[15] "price ~ sqft + age + feats + tax"
然后我收集了一些有用的指标
# R squared
models.r.sq <- sapply(formlist, function(i) summary(lm(i))$r.squared)
# adjusted R squared
models.adj.r.sq <- sapply(formlist, function(i) summary(lm(i))$adj.r.squared)
# MSEp
models.MSEp <- sapply(formlist, function(i) anova(lm(i))['Mean Sq']['Residuals',])
# Full model MSE
MSE <- anova(lm(formlist[[length(formlist)]]))['Mean Sq']['Residuals',]
# Mallow's Cp
models.Cp <- sapply(formlist, function(i) {
SSEp <- anova(lm(i))['Sum Sq']['Residuals',]
mod.mat <- model.matrix(lm(i))
n <- dim(mod.mat)[1]
p <- dim(mod.mat)[2]
c(p,SSEp / MSE - (n - 2*p))
})
df.model.eval <- data.frame(model=as.character(formlist), p=models.Cp[1,],
r.sq=models.r.sq, adj.r.sq=models.adj.r.sq, MSEp=models.MSEp, Cp=models.Cp[2,])
最终的数据框是
model p r.sq adj.r.sq MSEp Cp
1 price~sqft 2 0.71390776 0.71139818 42044.46 49.260620
2 price~age 2 0.02847477 0.01352823 162541.84 292.462049
3 price~feats 2 0.17858447 0.17137907 120716.21 351.004441
4 price~tax 2 0.76641940 0.76417343 35035.94 20.591913
5 price~sqft+age 3 0.80348960 0.79734865 33391.05 10.899307
6 price~sqft+feats 3 0.72245824 0.71754599 41148.82 46.441002
7 price~sqft+tax 3 0.79837622 0.79446120 30536.19 5.819766
8 price~age+feats 3 0.16146638 0.13526220 142483.62 245.803026
9 price~age+tax 3 0.77886989 0.77173666 37884.71 20.026075
10 price~feats+tax 3 0.76941242 0.76493500 34922.80 21.021060
11 price~sqft+age+feats 4 0.80454221 0.79523470 33739.36 12.514175
12 price~sqft+age+tax 4 0.82977846 0.82140691 29640.97 3.832692
13 price~sqft+feats+tax 4 0.80068220 0.79481991 30482.90 6.609502
14 price~age+feats+tax 4 0.79186713 0.78163109 36242.54 17.381201
15 price~sqft+age+feats+tax 5 0.83210849 0.82091573 29722.50 5.000000
最后，一个 Cp 图（使用库 wle）
