data(women)
w = women$w
h = women$h
plot(h,w)
lm1 = lm(w~h)              # simple regression
lm0 = lm(w ~ h-1)          # through 0.
lm2 = lm(w ~ h + I(h*h))   # a parabola

slm0 = summary(lm0)
slm1 = summary(lm1)
slm2 = summary(lm2)

aRs0 = slm0$adj
aRs1 = slm1$adj
aRs2 = slm2$adj

library(MASS)
boxcox(lm1)               # suggests lambda = -1

bc = function(y,lambda) {
 if (lambda != 0) ret = (y^lambda - 1)/lambda else ret = log(y)
 ret
}

cb = function(x,lambda,a,b) (lambda*(a+b*x) + 1)^(1/lambda)
lm3 = lm(bc(w,-1)~h)
f3 = function(x) cb(x,-1,lm3$co[1],lm3$co[2])
plot(h,w)
curve(f3,col="red",add=TRUE)

b2 = lm2$co
curve(b2[1]+b2[2]*x+b2[3]*x^2,col="green",add=TRUE)

abline(lm1)
abline(lm0,col="blue")