Statistics Toolbox

Linear Models

Introduction

Linear models represent the relationship between a continuous response variable and one or more predictor variables (either continuous or categorical) in the form

where:

• y is an n-by-1 vector of observations of the response variable.
• X is the n-by-p design matrix determined by the predictors.
• is a p-by-1 vector of parameters.
• is an n-by-1 vector of random disturbances, independent of each other and usually having a normal distribution.

MATLAB uses this general form of the linear model to solve a variety of specific regression and analysis of variance (ANOVA) problems. For example, for polynomial and multiple regression problems, the columns of X are predictor variable values or powers of such values. For one-way, two-way, and higher-way ANOVA models, the columns of X are dummy (or indicator) variables that encode the predictor categories. For analysis of covariance (ANOCOVA) models, X contains values of a continuous predictor and codes for a categorical predictor.

The following sections describe a number of functions for fitting various types of linear models:

• One-Way Analysis of Variance (ANOVA)
• Two-Way Analysis of Variance (ANOVA)
• N-Way Analysis of Variance
• Multiple Linear Regression
• Quadratic Response Surface Models
• Stepwise Regression
• Generalized Linear Models
• Robust and Nonparametric Methods

See the sections below for a tour of some of the related graphical tools:

• The polytool Demo
• The aoctool Demo
• The rsmdemo Demo

Note    See Linear Models for information on fitting nonlinear models.

The Bootstrap

One-Way Analysis of Variance (ANOVA)