plot(cars)
reg0=lm(dist~speed,data=cars)
reg1=lm(dist~speed,data=cars,
        weights=1/sqrt(speed))
summary(reg0)
summary(reg1)
reg2=lm(dist~speed,data=cars,
        weights=1/speed)
summary(reg2)

plot(ecdf(residuals(reg0)/sd(residuals(reg0))))
curve(pnorm(x),col="red",add=TRUE)

plot(cars)

u=seq(.5,2,by=.01)
a=1; plot(u,(u^a-1)/a,type="l")
a=2; lines(u,(u^a-1)/a,type="l",col="blue")
a=-1; lines(u,(u^a-1)/a,type="l",col="red")
a=.01; lines(u,(u^a-1)/a,type="l",col="purple")

library(MASS)
reg=lm(dist~I(speed^.5),data=cars)
boxcox(reg)

base=cars
base$sp=cut(base$speed,c(0,10,13,17,20,50))
summary(lm(dist~sp,data=base))

base=cars
base$sp=cut(base$speed,c(0,13,17,20,50))
summary(lm(dist~sp,data=base))