#ccar for continuous variables
ccar<-mtcars[,c("mpg","disp","hp","drat","wt")]
attach(ccar)
hp2<-hp^2
wt2<-wt^2
# We have seen in our previous analysis the these two squared terms give better disgnostics.
model <- lm(mpg ~ disp + hp + wt + drat+ hp2+ wt2)
install.packages("olsrr")
library(olsrr)
allm<-ols_step_all_possible(model)
cp<-allm[["result"]]$cp-allm[["result"]]$n
mcp<-min(cp)
which(cp==mcp)
adjr<-allm[["result"]]$adjr
madjr=max(adjr)
which(adjr==madjr)
aic<-allm[["result"]]$aic
maic<-min(aic)
which(aic==maic)
sbc<-allm[["result"]]$sbc
msbc<-min(sbc)
which(sbc==msbc)
# Seems like we have obtained the the Answer to the Ultimate 
# Question of Life, the Universe, and Everything.
best<-ols_step_best_subset(model)
best[["metrics"]][,c("predictors","adjr","cp","aic","sbc")]
plot(best[["metrics"]]$n,best[["metrics"]]$cp)
abline(0,1)
forw<-ols_step_forward_aic(model)
forw$model$terms[[3]]
back<-ols_step_backward_aic(model)
back$model$terms[[3]]
plot(forw)
## Partial correlation
ols_correlations(model)
mpgr1<-lm(mpg~wt+hp+drat+hp2+wt2)$residuals
disr1<-lm(disp~wt+hp+drat+hp2+wt2)$residuals
cor(mpgr1, disr1)  #partial
cor(mpg, disr1)    #part