

   UUnniivvaarriiaattee PPaarrttiiaall LLeeaasstt SSqquuaarreess RReeggrreessssiioonn

        svdpls1b(X, y, K=r)

   AArrgguummeennttss::

          X: Matrix of explanatory variables. Each column rep-
             resents a variable and each row an observation.
             The columns of this matrix are assumed to have
             been centred. The number of rows of `X' should
             equal the number of observations in `y'. `NA's and
             `Inf's are not allowed.

          y: Vector of responses. y is assumed to have been
             centred.  `NA's and `Inf's are not allowed.

          K: Number of PLS factors to fit in the PLS regres-
             sion. This must be less than or equal to the rank
             of `X'.

   DDeessccrriippttiioonn::

        Performs univariate partial least squares (PLS) regres-
        sion of a vector on a matrix of explanatory variables
        using the Orthogonal Loadings Algorithm.

   DDeettaaiillss::

        Univariate Partial Least Squares Regression is an exam-
        ple of a regularised regression method. It creates a
        lower dimensional representation of the original
        explanatory variables and uses this representation in
        an ordinary least squares regression of the response
        variables. (cf. Principal Components Regression).
        Unlike Principal Components Regression, PLS regression
        chooses the lower dimensional representation of the
        original explanatory variables with reference to the
        response variable `y'.

   VVaalluuee::

        a vector of regression coefficients

   RReeffeerreenncceess::

        Denham, M. C. (1994).  Implementing partial least
        squares.  Statistics and Computing (to appear)

        Helland, I. S. (1988).  On the Structure of partial
        least squares regression, Communications in Statistics,
        17, pp. 581-607

        Martens, H.  and Naes, T. (1989).  Multivariate Cali-
        bration.  Wiley, New York.

   SSeeee AAllssoo::

        pls1a,pls1b,pls1c,svdpls1a,svdpls1c

   EExxaammpplleess::

        data(crimes)
        attach(crimes)
        svdpls1b(scale(cbind(Murder, Assault, UrbanPop),scale=FALSE),
              scale(Rape,scale=FALSE), 2)

