Question 1 - A simpler model. Refer to the previous exercise. In the multiple regression analysis using all four 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 opening-weekend 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 = (n-p-1/q)(R₁²-R₂²/1-R₁²) with q and n- p - 1 degrees of freedom. R₁² 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 that 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?

Question 2 - Effect of potential outliers. Consider the simpler model of Question 1 for this analysis.

(a) Two movies have much larger U.S. revenues than those predicted. Which ones are they, and how much more revenue did they obtain compared with that predicted?

(b) Remove these two movies and redo the multiple regression. Make a table giving the regression coefficients and their standard errors, t statistics, and P-values.

(c) Compare these results with those from Question 1. How does the removal of these outlying movies impact the estimated model?

(d) Obtain the residuals from this reduced data set and graphically examine their distribution. Do the residuals appear approximately Normal? Explain your answer.