# codes for mini project of simple and multiple regressions
install.packages("HistData")
library(HistData)
data(GaltonFamilies)
attach(GaltonFamilies)
head(GaltonFamilies)

# Q1
summary(lm(childHeight~father))

# Q3
40.13929 + 0.38451*70

# Q4
summary(lm(childHeight~mother))
summary(lm(childHeight~father))$r.squared
summary(lm(childHeight~mother))$r.squared

# Q5-6
summary(lm(childHeight~father))$coef
summary(lm(childHeight~father+mother))$coef
cov(father, mother)

# Q8
rhat = resid(lm(father~mother))
summary(lm(childHeight~rhat))$coef

# Q9
m = summary(lm(childHeight~father+mother))
names(m)
m$fstatistic
summary(lm(childHeight~father+mother))