# Nippls

## Contents

### Purpose

NIPALS Partial Least Squares computational engine.

### Synopsis

[reg,ssq,xlds,ylds,wts,xscrs,yscrs,bin,nipwts] = nippls(x,y,ncomp,options)

### Description

Performs PLS regression using NIPALS algorithm.

#### Inputs

• x = X-block (M by Nx).
• y = Y-block (M by Ny).

#### Optional Inputs

• ncomp = number of components {default = rank of X-block}.
• options = discussed below.

The default options can be retrieved using: options = nippls('options');.

#### Outputs

• reg = matrix of regression vectors where each row corresponds to a regression vector for a given number of latent variables. If the Y-block contains multiple columns, the rows of reg will be in groups of latent variables (so that the regression vectors for all columns of Y at 1 latent variable will come first, followed by the regression vectors for all columns of Y at 2 latent variables, etc.)
${\begin{bmatrix}{b_{y1,1}}\\{b_{y2,1}}\\{b_{y1,2}}\\{b_{y2,2}}\\{b_{y1,3}}\\{b_{y2,3}}\end{bmatrix}}$ where byn,k is the regression vector for column "n" of the Y-block calculated from "k" latent variables.
• ssq = the sum of squares captured (ncomp by 5) with the columns defined as follows:
Column 1 = Number of latent variables (LVs),
Column 2 = Variance captured (%) in the X-block by this LV,
Column 3 = Total variance captured (%) by all LVs up to this row,
Column 4 = Variance captured (%) in the X-block by this LV, and
Column 5 = Total variance captured (%) by all LVs up to this row.