Polynomial fitting with R using poly vs. I function

Question

I'm trying to understanding polynomial fitting with R. From my research on the internet, there apparently seems to be two methods. Assuming I want to fit a cubic curve ax^3 + bx^2 + cx + d into some dataset, I can either use:

lm(dataset, formula = y ~ poly(x, 3))

or

lm(dataset, formula = y ~ x + I(x^2) + I(x^3))

However, as I try them in R, I ended up with two different curves with complete different intercepts and coefficients. Is there anything about polynomial I'm not getting right here?

Answer 1

This comes down to what the different functions do. poly generates orthonormal polynomials. Compare the values of poly(dataset$x, 3) to I(dataset$x^3). Your coefficients will be different because the values being passed directly into the linear model (as opposed to indirectly, through either the I or poly function) are different.

As 42 pointed out, your predicted values will be fairly similar. If a is your first linear model and b is your second, b$fitted.values - a$fitted.value should be fairly close to 0 at all points.