stats (version 3.6.2)

poly: Compute Orthogonal Polynomials


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, …)


x, 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.

See Also


cars for an example of polynomial regression.


Run this code
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))

# }

Run the code above in your browser using DataLab