Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP, 2nd Edition

Chapter 16Multiple Linear Regression Analysis

The focus of this chapter is the development of procedures to fit multiple linear regression models.

Topics Covered

• Multiple linear regression models
• Estimation of regression coefficients
• Estimation of regression coefficients using matrix notation
• Properties of the least‐squares estimators
• Analysis of variance approach to regression analysis
• Discussion of inferences about the regression parameters
• Multiple linear regression models that use qualitative or categorical predictor variables
• Standardized regression coefficients, and multicollinearity and its consequences
• Building regression type prediction models
• Residual analysis
• Certain criteria for model selection
• Basic concepts of logistic regression

Learning Outcomes

After studying this chapter, the reader will be able to

• Use the least‐squares method to estimate the regression coefficients in a multiple regression model and carry out hypothesis testing to determine which regression coefficients are significant.
• Fit multiple linear regression models to a given set of data when using two or more predictor variables and perform residual analysis to check the validity of the models under consideration.
• Fit multiple linear regression models to a given set of data involving qualitative or categorical predictor variables.
• Determine the presence and possible elimination of multicollinearity.
• Use various criteria, such as the coefficient of multiple determination, adjusted coefficient ...