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Statistics and Probability with Applications for Engineers and Scientists by Irwin Guttman, Bhisham C. Gupta

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16

Multiple 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 model 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 of multiple ...

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