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.
poly(x, …, degree = 1, coefs = NULL, raw = FALSE, simple = FALSE)
polym (…, degree = 1, coefs = NULL, raw = FALSE)# S3 method for poly
predict(object, newdata, …)
a numeric vector at which to evaluate the
polynomial. x can also be a matrix. Missing values are not
allowed in x.
the degree of the polynomial. Must be less than the
number of unique points when raw is false, as by default.
for prediction, coefficients from a previous fit.
if true, use raw and not orthogonal polynomials.
logical indicating if a simple matrix (with no further
attributes but dimnames) should be
returned. For speedup only.
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.
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=<non-NULL>),
and predict.poly(): a matrix.
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 three-term 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.
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.
# NOT RUN {
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, tol = 1e-15))
## 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, tol = 1e-15))
options(od)
# }
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