By William N. Venables, David M. Smith

This educational handbook presents a complete creation to R, a software program package deal for statistical computing and portraits. R helps a variety of statistical ideas and is well extensible through user-defined features. one among R's strengths is the convenience with which publication-quality plots could be produced in a wide selection of codecs. it is a published version of the educational documentation from the R distribution, with extra examples, notes and corrections. it truly is in line with R model 2.9.0, published April 2009. R is unfastened software program, dispensed below the phrases of the GNU common Public License (GPL). it may be used with GNU/Linux, Unix and Microsoft home windows. the entire cash raised from the sale of this booklet helps the improvement of loose software program and documentation.

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Y~A+x Single classification analysis of covariance model of y, with classes determined by A, and with covariate x. y y y y ~ ~ ~ ~ A*B A + B + A:B B %in% A A/B Two factor non-additive model of y on A and B. The first two specify the same crossed classification and the second two specify the same nested classification. In abstract terms all four specify the same model subspace. y ~ (A + B + C)^2 y ~ A*B*C - A:B:C Three factor experiment but with a model containing main effects and two factor interactions only.

4 Singular value decomposition and determinants The function svd(M) takes an arbitrary matrix argument, M, and calculates the singular value decomposition of M. This consists of a matrix of orthonormal columns U with the same column space as M, a second matrix of orthonormal columns V whose column space is the row space of M and a diagonal matrix of positive entries D such that M = U %*% D %*% t(V). D is actually returned as a vector of the diagonal elements. The result of svd(M) is actually a list of three components named d, u and v, with evident meanings.

Suppose, for example, we choose ! for the internal character. %" <- function(X, y) { ... % y. ) The matrix multiplication operator, %*%, and the outer product matrix operator %o% are other examples of binary operators defined in this way. 3 [Generating regular sequences], page 8, if arguments to called functions are given in the “name =object ” form, they may be given in any order. Furthermore the argument sequence may begin in the unnamed, positional form, and specify named arguments after the positional arguments.