poly {stats}  R Documentation 
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.
poly(x, ..., degree = 1, coefs = NULL) polym(..., degree = 1) ## S3 method for class 'poly': predict(object, newdata, ...)
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.

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 threeterm recursion given in Kennedy & Gentle (1980, pp. 3434), and used in the “predict” part of the code.
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.
This routine is intended for statistical purposes such as
contr.poly
: it does not attempt to orthogonalize to
machine accuracy.
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.
cars
for an example of polynomial regression.
(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)