R: Compute Orthogonal Polynomials

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)

[Package stats version 2.8.1 Index]