# R-program for Supplementary Exercises 2.11, 2.48, 10.38 and 10.39 of IPS7e

foot <- read.csv("r:/Chapter 2/ex02_011.csv")
# scatterplot with fitted line
plot(foot$ma, foot$hav)
abline( lsfit(foot$ma, foot$hav))

# correlation
cor(foot)
cor.test(~ ma+hav, data=foot)

# simple linear regression
foot.reg <- lm(hav ~ ma, data=foot)
summary(foot.reg)
anova(foot.reg)

# prediction
new <- data.frame(ma=25)
foot.pred <- predict(foot.reg, new, interval="prediction"); foot.pred
foot.ci <- predict(foot.reg, new, interval="confidence"); foot.ci

# 95% CIs for regression parameters
confint(foot.reg)

# analysis without outlier (briefly)
cor.test(~ ma+hav, data=foot[foot$hav<50,])
summary (lm(hav ~ ma, data=foot[foot$hav<50,]))