# we use mtcars dataset
require(MASS)
dat = mtcars[,c(1,3:7)]
attach(dat)

plot(dat, pch=16)

# correlation plot
require(ellipse)
plotcorr(cor(dat))

# let’s fit a simple linear model via least-squares
fit = lm(mpg ~ ., data = dat)
summary(fit)

# CIs for the coefficients
confint(fit)
# (note that the _combined_ level is _not_ 95%)

# 95% confidence interval for the mean response at a given predictor vector
new = data.frame(disp=200, hp=120, drat=3.5, wt=3.1, qsec=18)
predict(fit, new, interval=’confidence’)

# Explaining the (adjusted) R-squared
fit0 = lm(mpg ~ disp)
par(mfrow=c(1,2))
plot(disp, mpg)
abline(fit0)
boxplot(mpg-mean(mpg), residuals(fit0), names=c(‘mpg (centered)’, ‘residuals’))

# comparing models with ANOVA
fit0 = lm(mpg ~ disp + wt) # a model with only disp and wt, implicitly assuming that the other variables are not in the model
anova(fit0, fit) # ANOVA F-test comparing this simpler model with the model above that includes all 6 predictor variables