General Linear Regression

 

General Linear Regression

The term general linear regression is the extension of ordinary linear regression for continuous response variables given continuous and/or categorical predictors. It includes multiple linear regression as well as ANOVA and ANCOVA and is expressed in matrix form.

Simple Linear Regression Model

(Matrix Approach)

Consider the simple linear regression model:

The estimated regression model:

Estimation of Parameters by OLS

Consider the model

Y_=Xβ_+ϵ_

The estimated model is given by:

The OLS estimate is obtained as:

The residual matrix is given by:

Properties of OLS Estimate

Coefficient of determination:

SSTotal can be obtained as:

Example: Consider the data on advertisement (X) and sale revenue (Y) for an athletic sports ware store for five months. The observations are as follows:

Find the regression equation of sale on advertisement and estimate the variance, covariance of slope and intercept, and coefficient of determination.

Solution:

Note: The given above example can be solved in a much more convenient manner.

 

• Read More: Multiple Linear Regression Matrix approach