# Mlr

## Contents

### Purpose

Multiple Linear Regression for multivariate Y.

### Synopsis

- model = mlr(x,y,options)
- pred = mlr(x,model,options)
- valid = mlr(x,y,model,options)
- mlr % Launches analysis window with MLR as the selected method.

Please note that the recommended way to build and apply a MLR model from the command line is to use the Model Object. Please see this wiki page on building and applying models using the Model Object.

### Description

MLR identifies models of the form Xb = y + e.

#### Inputs

**y**= X-block: predictor block (2-way array or DataSet Object)

**y**= Y-block: predictor block (2-way array or DataSet Object)

#### Outputs

**model**= scalar, estimate of filtered data.

**pred**= structure array with predictions

**valid**= structure array with predictions

### Options

**options** = a structure array with the following fields.

**display**: [ {'off'} | 'on'] Governs screen display to command line.

**plots**: [ 'none' | {'final'} ] governs level of plotting.

**ridge**: [ 0 ] ridge parameter to use in regularizing the inverse.

**preprocessing**: { [] [] } preprocessing structure (see PREPROCESS).

**blockdetails**: [ 'compact' | {'standard'} | 'all' ] level of detail (predictions, raw residuals, and calibration data) included in the model.

- ‘Standard’ = the predictions and raw residuals for the X-block as well as the X-block itself are not stored in the model to reduce its size in memory. Specifically, these fields in the model object are left empty: 'model.pred{1}', 'model.detail.res{1}', 'model.detail.data{1}'.
- ‘Compact’ = for this function, 'compact' is identical to 'standard'.
- 'All' = keep predictions, raw residuals for both X- & Y-blocks as well as the X- & Y-blocks themselves.

#### Studentized Residuals

From version 8.8 onwards, the Studentized Residuals shown for MLR Scores Plot are now calculated for calibration samples as:

MSE = sum((res).^2)./(m-1); syres = res./sqrt(MSE.*(1-L));

where res = y residual, m = number of samples, and L = sample leverage. This represents a constant multiplier change from how Studentized Residuals were previously calculated. For test datasets, where pres = predicted y residual, the semi-Studentized residuals are calculated as:

MSE = sum((res).^2)./(m-1); syres = pres./sqrt(MSE);

This represents a constant multiplier change from how the semi-Studentized Residuals were previously calculated.

### See Also

analysis, crossval, ils_esterror, modelstruct, pcr, pls, preprocess, ridge, testrobustness, EVRIModel_Objects