# [R] Prediction when using orthogonal polynomials in regression

Gabor Grothendieck ggrothendieck at gmail.com
Fri Jan 27 15:46:46 CET 2006

```On 1/26/06, Ajay Narottam Shah <ajayshah at mayin.org> wrote:
> Folks,
>
> I'm doing fine with using orthogonal polynomials in a regression context:
>
>  # We will deal with noisy data from the d.g.p. y = sin(x) + e
>  x <- seq(0, 3.141592654, length.out=20)

This has already been answered but note that pi is a built in variable
in R.

>  y <- sin(x) + 0.1*rnorm(10)
>  d <- lm(y ~ poly(x, 4))
>  plot(x, y, type="l"); lines(x, d\$fitted.values, col="blue") # Fits great!
>  all.equal(as.numeric(d\$coefficients[1] + m %*% d\$coefficients[2:5]),
>            as.numeric(d\$fitted.values))
>
> What I would like to do now is to apply the estimated model to do
> prediction for a new set of x points e.g.
>  xnew <- seq(0,5,.5)
>
> We know that the predicted values should be roughly sin(xnew). What I
> don't know is: how do I use the object `d' to make predictions for
> xnew?
>
> --
> Ajay Shah                                      http://www.mayin.org/ajayshah
> ajayshah at mayin.org                             http://ajayshahblog.blogspot.com
> <*(:-? - wizard who doesn't know the answer.
>
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>

```