Question 14.79

14.79 Regression or ANOVA?

Refer to the price promotion study that we examined in Exercise 14.63 (pages 754–755). The explanatory variable in this study is the number of price promotions in a 10-week period, with possible values of 1, 3, 5, and 7. ANOVA treats the explanatory variable as categorical—it just labels the groups to be compared. In this study, the explanatory variable is, in fact, quantitative, so we could use simple linear regression rather than one-way ANOVA if there is a linear pattern.

ppromo

758

  1. Make a scatterplot of the responses against the explanatory variable. Is the pattern roughly linear?
  2. In ANOVA, the test null hypothesis states that groups have no effect on the mean response. What test in regression tests the null hypothesis that the explanatory variable has no linear relationship with the response?
  3. Carry out the regression. Compare your results with those from the ANOVA in Exercise 14.63. Are there any reasons—perhaps from part (a)—to prefer one or the other analysis?

14.79

(a) The pattern is roughly linear. (b) Testing the slope equal to zero is the test of no linear relationship. (c) . There is a significant linear relationship between price and the number of promotions. Because the relationship is linear as shown in part (a), the regression is preferable because it not only says that the number of promotions affects price, but also describes the relationship as a linear one, in which we can quantify the relationship by interpreting the slope. In this problem, for each additional promotion read, the expected price goes down by 0.11648.