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, simple = FALSE)
polym (..., degree = 1, coefs = NULL, raw = FALSE)
## S3 method for class 'poly'
predict(object, newdata, ...)
Arguments
x , newdata 
a numeric vector or an object with 
degree 
the degree of the polynomial. Must be less than the
number of unique points when 
coefs 
for prediction, coefficients from a previous fit. 
raw 
if true, use raw and not orthogonal polynomials. 
simple 
logical indicating if a simple matrix (with no further

object 
an object inheriting from class 
... 

Details
Although formally degree
should be named (as it follows
...
), an unnamed second argument of length 1 will be
interpreted as the degree, such that poly(x, 3)
can be used in
formulas.
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. 343–4), and used in the predict
part of
the code.
poly
using ...
is just a convenience wrapper for
polym
: coef
is ignored. Conversely, if polym
is
called with a single argument in ...
it is a wrapper for
poly
.
Value
For poly
and polym()
(when simple=FALSE
and
coefs=NULL
as per default):
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 and
class c("poly", "matrix")
.
For poly(*, simple=TRUE)
, polym(*, coefs=<nonNULL>)
,
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.
Author(s)
R Core Team. Keith Jewell (Campden BRI Group, UK) contributed improvements for correct prediction on subsets.
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
cars
for an example of polynomial regression.
Examples
od < options(digits = 3) # avoid too much visual clutter
(z < poly(1:10, 3))
predict(z, seq(2, 4, 0.5))
zapsmall(poly(seq(4, 6, 0.5), 3, coefs = attr(z, "coefs")))
zm < zapsmall(polym ( 1:4, c(1, 4:6), degree = 3)) # or just poly():
(z1 < zapsmall(poly(cbind(1:4, c(1, 4:6)), degree = 3)))
## they are the same :
stopifnot(all.equal(zm, z1, tolerance = 1e15))
## poly(<matrix>, df)  used to fail till July 14 (vive la France!), 2017:
m2 < cbind(1:4, c(1, 4:6))
pm2 < zapsmall(poly(m2, 3)) # "unnamed degree = 3"
stopifnot(all.equal(pm2, zm, tolerance = 1e15))
options(od)