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
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.