What does the R function `poly` really do?
- by merlin2011
I have read through the manual page ?poly (which I admit I did not completely comphrehend) and also read the description of the function in book Introduction to Statistical Learning.
My current understanding is that a call to poly(horsepower, 2) should be equivalent to writing horsepower + I(horsepower^2). However, this seems to be contradicted by the output of the following code.
library(ISLR)
summary(lm(mpg~poly(horsepower,2), data=Auto))$coef
summary(lm(mpg~horsepower+I(horsepower^2), data=Auto))$coef
Output:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 23.44592 0.2209163 106.13030 2.752212e-289
poly(horsepower, 2)1 -120.13774 4.3739206 -27.46683 4.169400e-93
poly(horsepower, 2)2 44.08953 4.3739206 10.08009 2.196340e-21
Estimate Std. Error t value Pr(>|t|)
(Intercept) 56.900099702 1.8004268063 31.60367 1.740911e-109
horsepower -0.466189630 0.0311246171 -14.97816 2.289429e-40
I(horsepower^2) 0.001230536 0.0001220759 10.08009 2.196340e-21
My question is, why does the output not match, and what is poly really doing?
