Statistics 350 Lecture 11

Today Last Day: Start Chapter 3 Today: Section 3.8 Mid-Term Friday…..Sections ; ; (READ)

Lack of Fit for Simple Linear Regression

Goal of lack of fit test is to break down the total variability around the regression line into two part: For this to work, at least one level of X must have

Lack of Fit for Simple Linear Regression If the regression line does not fit well, how will the two variabilities compare?

Lack of Fit for Simple Linear Regression NOTATION: Suppose that there are c unique levels of X, labelled X 1, X 2,… X c Suppose have n 1, n 2,… n c observations at each level The mean response at each X i is

Lack of Fit for Simple Linear Regression The variability of points around their respective means is: The variability of the means around the regression line is:

Lack of Fit for Simple Linear Regression The test for lack of fit: