# [R] Prediction when using orthogonal polynomials in regression

Ajay Narottam Shah ajayshah at mayin.org
Thu Jan 26 17:40:23 CET 2006

```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)
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.

```