EXAMPLE 11.16 Do Budget and Opening-Weekend Theater Count Add Predictive Ability?

movies

CASE 11.2 In the multiple regression analysis using all three explanatory variables, opening-weekend revenue (Opening) appears to be the most helpful (given the other two explanatory variables are in the model). A question we might ask is

  • Do these other two variables help predict movie revenue, given that opening-weekend revenue is included?

The same question in another form is

  • If we start with a model containing all three variables, does removing theater count and budget reduce our ability to predict revenue?

The first regression run includes explanatory variables: Opening, Budget, and Theaters. The for this model is .

Now remove the variables Budget and Theaters and redo the regression with just Opening as the explanatory variable. For this model we get .

The test statistic is

The degrees of freedom are and .

The closest entry in Table E has 2 and 30 degrees of freedom. For this distribution we would need or larger for significance at the 5% level. Thus, . Software gives . Budget and theater count do not contribute significantly to explaining U.S. box office revenue when opening weekend revenue is already in the model.