library(DAAG)
head(hills)


names(hills) <- c("Distance (miles)","Climb (feet)","Time (hours)")
plot(hills,pch=16)

logHills <- log(hills)
names(logHills) <- c("LogDistance (log miles)","logClimb (log feet)","logTime (log hours)")
plot(logHills ,pch=16)

plot(hills[,2],hills[,3],pch=16)
lines(lowess(hills[,2],hills[,3],f=.5))

lm.obj <- lm(hills[,3]~hills[,1]+hills[,2])
plot(lm.obj$fitted,lm.obj$residuals,xlab="Fitted",ylab="Residuals",pch=16)
lines(lowess(lm.obj$fitted,lm.obj$residuals,f=.5),col="red")
abline(h=0)

lm.obj <- lm(hills[-18,3]~hills[-18,1]*hills[-18,2])
plot(lm.obj$fitted,lm.obj$residuals,xlab="Fitted",ylab="Residuals",pch=16)
lines(lowess(lm.obj$fitted,lm.obj$residuals,f=.5),col="red")
abline(h=0)