# [R] Prediction when using orthogonal polynomials in regression

From: Ajay Narottam Shah <ajayshah_at_mayin.org>
Date: Fri 27 Jan 2006 - 03:40:23 EST

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.

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