11.26 A simpler model. In the multiple regression analysis using all four explanatory variables, Theaters and Budget appear to be the least helpful (given that the other two explanatory variables are in the model).

(a) Perform a new analysis using only the movie’s openingweekend revenue and IMDb rating. Give the estimated regression equation for this analysis.

(b) What percent of the variability in USRevenue is explained by this model?

(c) In this chapter we discussed the F test for a collection of regression coefficients. In most cases, this capability is provided by the software. When it is not, the test can be performed using the R2-values from the full and reduced models. The test statistic is F  a n  p  1 q

b a R21

 R22 1  R21 b

with q and n  p  1 degrees of freedom. R21 is the value for the full model and R22 is the value for the reduced model. Here n  35 movies, p  4 variables in the full model, and q  2 variables were removed to form the reduced model. Plug in the values of R2 from part

(b) of this exercise and part

(d) of the previous exercise, and compute the test statistic and P-value. Do Theaters and Budget combined add any significant predictive information beyond what is already contained in Opening and Opinion?