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.

### Usage

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

## 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 `coefs` for prediction, coefficients from a previous fit. `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 `"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.

`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 2.2.1 Index]