Statistics and Probability with Applications for Engineers and Scientists, Preliminary Edition

Chapter 16

Multiple Linear Regression Analysis

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

• The 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
• Further discussion of inferences about the regression parameters
• The multiple linear regression model using 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 and carry out hypothesis testing to test which of these 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 of multiple ...