Question 11.79

11.79 Predicting movie revenue.

CASE 11.2 A plot of theater count versus box office revenue suggests that the relationship may be slightly curved.

movies

  1. Examine this question by running a regression to predict the box office revenue using the theater count and the square of the theater count. Report the relevant test statistic with its degrees of freedom and -value, and summarize your conclusion.
  2. Now view this analysis in the framework of testing a hypothesis about a collection of regression coefficients, which you studied in Section 11.2 (page 559). The first model includes theater count and the square of theater count, while the second includes only theater count. Run both regressions and find the value of for each. Find the statistic for comparing the models based on the difference in the values of . Carry out the test and report your conclusion.
  3. Verify that the square of the statistic that you found in part (a) for testing the coefficient of the quadratic term is equal to the statistic that you found for this exercise.

11.79

(a) . The quadratic term for theaters, , is significant and should be included in the model already containing Theaters. (b) For the first model, ; for the second model, . are 1 and should be included in a model that already contains Theaters. (c) with rounding error.