assumptions_1.R

install.packages("faraway")
library(faraway) # for data

#
# A regression that meets the assumptions
# 

plot(stat500$midterm,stat500$final)
res <- lm(stat500$final~stat500$midterm)
res <- lm(final~midterm,data=stat500)
summary(res)
plot(res$fit,res$res)
sr <- res$res/sd(res$res)
plot(res$fit,sr)
identify(res$fit,sr)
#
# Is it normal?
#
hist(res$fit)
x <- rnorm(100)
hist(x)
qqnorm(x)
qqline(x)
#
# A better plot
# 
install.packages("car")
library(car)

qqPlot(x)
qqPlot(x,id.n=3)
#
# Our regression
# 
qqnorm(res$fit)
qqline(res$fit)
qqPlot(res$fit,id.n=3)
#
# A test for normality
#
shapiro.test(res$res)
#
# A test for constant variance
#
ncvTest(res)

#
# Example 2
# 
install.packages("alr3")
library(alr3)


data(sniffer)
plot(sniffer$TankTemp,sniffer$Y)
res <- lm(sniffer$Y~sniffer$TankTemp)
abline(res)
plot(res$fit,res$res)

qqPlot(res$res)
shapiro.test(res$res)
ncvTest(res)

#
# Example 3
#
data(forbes)
plot(forbes)
res <- lm(pres~bp,data=forbes)
abline(res)
plot(res$fit,res$res)
sr <- res$res/sd(res$res)
plot(res$fit,sr)
identify(res$fit,sr)

res2 <- lm(pres~bp,data=forbes,subset=c(-12))
summary(res)
summary(res2)
plot(res2$fit,res2$res)