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Dealing with a large collection of categories complicates a regression, and software does not always provide the needed tools. The follow- ing procedure is often helpful. Rather than add State to the regression (as in the previous question), save the residuals from the model in Table 4. Then use a one-way analysis of variance (ANOVA) to discover whether the average residual in any pair of states is statistically significantly different.
(a) Does the F-statistic of the one-way ANOVA detect a statistically significant difference among the averages? Does the result differ from the partial F obtained by adding State directly to the regression? Explain.
(b) Do any pairs of states have statistically signifi- cantly different means? With so many compari- sons, be sure to use an appropriate adjustment for multiple comparisons.
(c) How could you incorporate these differences into the regression model without adding the 50 coef- ficients needed to represent State?