Читать книгу Introduction to Linear Regression Analysis - Douglas C. Montgomery - Страница 54

Suppose that x and y are jointly distributed random variables but the form of this joint distribution is unknown. It can be shown that all of our previous regression results hold if the following conditions are satisfied:

1 The conditional distribution of y given x is normal with conditional mean β0 + β1x and conditional variance σ2.

2 The x’s are independent random variables whose probability distribution does not involve β0, β1, and σ2.

While all of the regression procedures are unchanged when these conditions hold, the confidence coefficients and statistical errors have a different interpretation. When the regressor is a random variable, these quantities apply to repeated sampling of (xi, yi) values and not to repeated sampling of yi at fixed levels of xi.