ABSTRACT

Analysis of variance (ANOVA) involves comparing random samples from several populations. This chapter discusses how to use multiple regression to analyze ANOVA data. Comparing one of the reduced polynomial models against the one-way ANOVA model is often referred to as a test of lack of fit. In the tests, the degrees of freedom, sums of squares, and mean squares used in the numerator of the tests are all described as being for lack of fit. The denominator of the test is based on the error from the one-way ANOVA. For testing lack of fit in the simple linear regression model with the ASI data, the numerator sum of squares can be obtained by differencing the sums of squares for error in the simple linear regression model and the one-way ANOVA model. The chapter examines an unbalanced one-way ANOVA and compares a simple linear regression including identification of pure error and lack of fit to a weighted regression on sample means.