O'Reilly logo

Introduction to Linear Regression Analysis, 5th Edition by G. Geoffrey Vining, Elizabeth A. Peck, Douglas C. Montgomery

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

CHAPTER 3

MULTIPLE LINEAR REGRESSION

A regression model that involves more than one regressor variable is called a multiple regression model. Fitting and analyzing these models is discussed in this chapter. The results are extensions of those in Chapter 2 for simple linear regression.

3.1 MULTIPLE REGRESSION MODELS

Suppose that the yield in pounds of conversion in a chemical process depends on temperature and the catalyst concentration. A multiple regression model that might describe this relationship is

images

where y denotes the yield, x1 denotes the temperature, and x2 denotes the catalyst concentration. This is a multiple linear regression model with two regressor variables. The term linear is used because Eq. (3.1) is a linear function of the unknown parameters β0, β1 and β2.

The regression model in Eq. (3.1) describes a plane in the three-dimensional space of y, x1 and x2. Figure 3.1a shows this regression plane for the model

images

where we have assumed that the expected value of the error term ε in Eq. (3.1) is zero. The parameter β0 is the intercept of the regression plane. If the range of the data includes x1 = x2 = 0, then β0 is the mean of y when x1 = x2 = 0. Otherwise β0 has no physical interpretation. The parameter β1 indicates the expected change in response(y) per unit change in ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required