using lm(poly) to get formula coeff [duplicate]

Question

I'm trying to using lm(poly) to get a polynomial regression for some points, but got some questions about the regression formula coefficients it returns.

sample like this:

x=seq(1,100)
y=x^2+3*x+7
fit=lm(y~poly(x,2))

Results are:

lm(formula = y ~ poly(x, 2))

Coefficients:

(Intercept)  poly(x, 2)1  poly(x, 2)2  
       3542        30021         7452  

Why are the coefficients not 7,3,2?

Thank you very much!

Answer 1

You need to set the raw argument to TRUE of you don't want to use orthogonal polynomial which is the default

set.seed(101)
N <- 100
x <- rnorm(N, 10, 3)
epsilon <- rnorm(N)
y <- 7 + 3 * x + x^2 + epsilon

coef(lm(y ~ poly(x, 2, raw = TRUE)))

##             (Intercept) poly(x, 2, raw = TRUE)1 
##                  7.8104                  2.7538 
## poly(x, 2, raw = TRUE)2 
##                  1.0150

From the help of the poly function you have

Description:

 Returns or evaluates orthogonal polynomials of degree 1 to
 ‘degree’ over the specified set of points ‘x’. These are all
 orthogonal to the constant polynomial of degree 0.  Alternatively,
 evaluate raw polynomials.

And

raw: if true, use raw and not orthogonal polynomials.

But you can also use what Ferdinand proposed, it works.

coef(lm(y ~ x + I(x^2)))
## (Intercept)           x      I(x^2) 
##      7.8104      2.7538      1.0150