Question 11.81

11.81 Predicting movie revenue, continued.

CASE 11.2 Refer to Exercise 11.79. Although a quadratic relationship between total U.S. revenue and theater count provides a better fit than the linear model, it does not make sense that box office revenue would again increase for very low budgeted movies (unless you are the Syfy Channel). An alternative approach to describe the relationship between theater count and box office revenue is to consider a piecewise linear equation.

movies

  1. It appears the relationship between theater count and U.S. revenue changes around a count of 2800 theaters. Create a new variable that is the max . This is simply the difference between the theater count and 2800 with all negative differences rounded to 0.
  2. Fit the model with theater count and the variable you created in part (a). Report the relevant test statistic with its degrees of freedom and -value, and summarize your conclusion.
  3. Obtain the fitted values from this model, and plot them versus theater count. Use this diagram to explain why this is called a piecewise linear model.
  4. Compare the results of this model with the quadratic fit of Exercise 11.79. Which model do you prefer? Explain your answer.

11.81

(b) . The new variable is significant and should be included in the model already containing Theaters. (It should be noted that Theaters is no longer significant in this model and could be removed.) (c) As shown in the plot, it is called a piecewise linear model because we are only measuring linearity for a piece of the variable Theaters (greater than 2800). (d) The results for the quadratic model and the results for the piecewise linear model are very similar; both models required that we retain the additional variable (quadratic or new). Answers will vary for preference; both models add some complexity for interpretation.