Читать книгу Introduction to Linear Regression Analysis - Douglas C. Montgomery - Страница 53

The linear regression model that we have presented in this chapter assumes that the values of the regressor variable x are known constants. This assumption makes the confidence coefficients and type I (or type II) errors refer to repeated sampling on y at the same x levels. There are many situations in which assuming that the x’s are fixed constants is inappropriate. For example, consider the soft drink delivery time data from Chapter 1 (Figure 1.1). Since the outlets visited by the delivery person are selected at random, it is unrealistic to believe that we can control the delivery volume x. It is more reasonable to assume that both y and x are random variables.

Fortunately, under certain circumstances, all of our earlier results on parameter estimation, testing, and prediction are valid. We now discuss these situations.