# linregEst: Linear regression estimation In ffmanova: Fifty-Fifty MANOVA

 linregEst R Documentation

## Linear regression estimation

### Description

Function that performs multivariate multiple linear regression modelling (`Y = XB + E`) according to a principal component regression (PCR) approach where the number of components equals the number of nonzero eigenvalues (generalised inverse).

### Usage

``````linregEnd(Umodel, Y)

linregEst(X, Y)

linregStart(X, rank_lim = 1e-09)
``````

### Arguments

 `Umodel` this matrix is returned by `linregStart` `Y` response matrix `X` regressor matrix `rank_lim` tuning parameter for the rank. The default value corresponds to the rank function in Matlab.

### Details

The function `linregEst` performs the calculations in two steps by calling `linregStart` and `linregEnd`. The former functions function makes all calculations that can be done without knowing `Y`. The singular value decomposition (SVD) is an essential part of the calculations and some of the output variables are named according to SVD (‘⁠U⁠’, ‘⁠S⁠’ and ‘⁠V⁠’).

### Value

`linregEst` returns a list with seven components. The first three components is returned by `linregStart` - the rest by `linregEnd`.

 `Umodel` Matrix of score values according to the PCR model. `VmodelDivS` Matrix that can be used to calculate `Umodel` from `X`. That is, `Umodel` equals `X %*% VmodelDivS`. `VextraDivS1` Matrix that can be used to check estimability. That is, predictions for a new X cannot be made if `Xnew %*% VextraDivS1` is (close to) zero. `BetaU` Matrix of regression parameters according to the PCR model. `msError` Mean square error of each response `errorObs` Error observations that can be used in multivariate testing `Yhat` Fitted values. Equals `Umodel %*% BetaU`

### Note

When the number of error degrees of freedom exceeds the number of linearly independent responses, then the matrix of error observations is made so that several rows are zero. In this case the zero rows are omitted and a list with components `errorObs` and `df_error` is returned.

### Author(s)

Øyvind Langsrud and Bjørn-Helge Mevik

`ffmanova`