12 CHAPTER OUTLINE 12-1 MULTIPLE LINEAR REGRESSION MODEL 12-1.1 Introduction 12-1.2 Least Squares Estimation of the Parameters © David Lewis/ iStockphoto Multiple Linear Regression This chapter generalizes the simple linear regression to a situation where there is more than one predictor or regressor variable. This situation occurs frequently in science and engineering; for example, in Chapter 1 we provided data on the pull strength of a wire bond on a semiconductor package and illustrated its relationship to the wire length and the die height. Understanding the relationship between strength and the other two vari- ables may provide important insight to the engineer when the package is designed, or to the manufacturing personnel who assemble the die into the package. We used a multiple linear regression model to relate strength to wire length and die height. There are many examples of such relationships: The life of a cutting tool is related to the cutting speed and the tool angle; patient satisfaction in a hospital is related to patient age, type of procedure performed, and length of stay; and the fuel economy of a vehicle is related to the type of vehicle (car versus truck), engine displacement, horsepower, type of transmission, and vehicle weight. Multiple regression models give insight into the relationships between these variables that can have important practical implications. This chapter shows how to fit multiple linear regression models, perform the statis- tical tests and confidence procedures that are analogous to those for simple linear regression, and check for model adequacy. We also show how models that have polyno- mial terms in the regressor variables are just multiple linear regression models. We also discuss some aspects of building a good regression model from a collection of candidate regressors. 12-1.3 Matrix Approach to Multiple Linear Regression 12-1.4 Properties of the Least Squares Estimators 449