# poly {stats}

### 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 if
`raw = TRUE`

. - 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.

### Values

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")`

.

### 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.

### Note

This routine is intended for statistical purposes such as `contr.poly`

: it does not attempt to orthogonalize to machine accuracy.

### Examples

Documentation reproduced from R 3.0.2. License: GPL-2.