This question already has an answer here:
A post "Fitting Polynomial Regression in R" used two ways to model the polynomial regression: (a)
poly(..., ...); (b)
I(...). Below is the example:
set.seed(20) q <- seq(from=0, to=20, by=0.1) y <- 500 + 0.4 * (q-10)^3 noise <- rnorm(length(q), mean=10, sd=80) noisy.y <- y + noise # fitting polynomials # two methods model_a <- lm(noisy.y ~ poly(q,3)) model_b <- lm(noisy.y ~ q + I(q^2) + I(q^3)) # their summary are all the same except the coefficients summary(model_a) summary(model_b)
The post said that:
I(q^3)will be correlated and correlated variables can cause problems. The use of
poly()lets you avoid this by producing orthogonal polynomials, therefore I’m going to use the first option (i.e.,
I am confused that:
(1) Why does the
q, I(q^2) and I(q^3) cause problems?
(2) According to
summary(), these two models are all the same, except the
Coefficients . Why the coefficients are different, while others are the same? Shouldn't they all different, or all the same?