poly {stats}

R Documentation

Compute Orthogonal Polynomials

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.

Usage

poly(x, ..., degree = 1, coefs = NULL, raw = FALSE)
polym(..., degree = 1, raw = FALSE)

## S3 method for class 'poly'
predict(object, newdata, ...)

Arguments

x, newdata	a numeric vector at which to evaluate the polynomial. x can also be a matrix. Missing values are not allowed in x.
degree	the degree of the polynomial. Must be less than the number of unique points.
coefs	for prediction, coefficients from a previous fit.
raw	if true, use raw and not orthogonal polynomials.
object	an object inheriting from class "poly", normally the result of a call to poly with a single vector argument.
...	poly, polym: further vectors. predict.poly: arguments to be passed to or from other methods.

Details

Although formally degree should be named (as it follows ...), an unnamed second argument of length 1 will be interpreted as the degree.

The orthogonal polynomial is summarized by the coefficients, which can be used to evaluate it via the three-term recursion given in Kennedy & Gentle (1980, pp. 343–4), and used in the predict part of the code.

Value

For poly with a single vector argument:
A matrix with rows corresponding to points in x and columns corresponding to the degree, with attributes "degree" specifying the degrees of the columns and (unless raw = TRUE) "coefs" which contains the centering and normalization constants used in constructing the orthogonal polynomials. The matrix has given class c("poly", "matrix").

Other cases of poly and polym, and predict.poly: a matrix.

Note

This routine is intended for statistical purposes such as contr.poly: it does not attempt to orthogonalize to machine accuracy.

References

Chambers, J. M. and Hastie, T. J. (1992) Statistical Models in S. Wadsworth & Brooks/Cole.

Kennedy, W. J. Jr and Gentle, J. E. (1980) Statistical Computing Marcel Dekker.

See Also

contr.poly.

cars for an example of polynomial regression.

Examples

(z <- poly(1:10, 3))
predict(z, seq(2, 4, 0.5))
poly(seq(4, 6, 0.5), 3, coefs = attr(z, "coefs"))

polym(1:4, c(1, 4:6), degree=3) # or just poly()
poly(cbind(1:4, c(1, 4:6)), degree=3)

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