Multiple Linear Regression

Abstract

This chapter discusses multiple linear regression, in which the outcome variable is continuous. The least squares estimation in multiple linear regression requires the minimum residual sum of squares. As in simple linear regression, it is necessary to test the regression model and each partial-regression coefficient after establishing the regression model. The F-test, that is, analysis-of-variance testing, can be used to examine the hypothesis of the multiple linear regression model. Several methods can be used to comprehensively assess the goodness of fit of multiple linear regression model. The commonly used indicators include the coefficient of determination and adjusted coefficient of determination. The coefficient of determination, adjusted coefficient of determination, and residual analysis are often used to evaluate the fit of the regression model. Some issues such as multicollinearity among independent variables, variable selection to optimize statistical estimates, and sample size have been addressed.