require{car}

library(car)
attitude
attach(attitude)
Y=rating
X1=complaints
X2=privileges
X3=learning
X4=raises
X5=critical
X6=advance

#attitude

#Simple linear regression

RM1=lm(Y~X1)
Yhat1=fitted(RM1)
plot(X1,Y)
abline(RM1,col="blue")
segments(X1,Yhat1,X1,Y,col="red")
anova(RM1)

RM2=lm(Y~X2)
Yhat2=fitted(RM2)
plot(X2,Y)
abline(RM2,col="blue")
segments(X2,Yhat2,X2,Y,col="red")
anova(RM2)

RM3=lm(Y~X3)
Yhat3=fitted(RM3)
plot(X3,Y)
abline(RM3,col="blue")
segments(X3,Yhat3,X3,Y,col="red")
anova(RM3)

RM4=lm(Y~X4)
Yhat4=fitted(RM4)
plot(X4,Y)
abline(RM4,col="blue")
segments(X4,Yhat4,X4,Y,col="red")
anova(RM4)

RM5=lm(Y~X5)
Yhat5=fitted(RM5)
plot(X5,Y)
abline(RM5,col="blue")
segments(X5,Yhat5,X5,Y,col="red")
anova(RM5)

RM6=lm(Y~X6)
Yhat6=fitted(RM6)
plot(X6,Y)
abline(RM6,col="blue")
segments(X6,Yhat6,X6,Y,col="red")
anova(RM6)

# Multipule regression full model
# Reduced modle marginal

FM=lm(Y~X1+X2+X3+X4+X5+X6)
summary(FM)
Anova(FM)
drop1(FM)
step(FM,direction="backward")
RM13=lm(Y~X1+X3)
anova(RM13,FM)