Why do some movies make more money at the box office than others? Hollywood is a multi-billion dollar industry which releases more than a hundred films a year, with large variations in the budgets and box office grosses of the movies. Identifying which factors are important to a movie’s profitability and subsequently predicting the success of a movie given its relevant parameters could save movie studios hundreds of millions of dollars a year. Using a dataset containing information on 500 movies, your job is to construct a multiple regression to determine the characteristics of a movie that help predict success at the box office. The variables are as follows:

Yi: Movie i’s box office revenue in millions of U.S. dollars (USD). This is only the domestic revenue received at U.S. theaters during the first run of the movie (i.e., no DVD sales, international revenue, etc.). The variable is in inflation adjusted terms so we can compare movie revenue without having to worry about changes in the price level.

X1i: Production Budget of Movie i in millions of USD.

X2i: Critical review of Movie i from Rotten Tomatoes (range: 0-100).

X3i: Number of official trailer views on You Tube in millions of views.

X4i: Star Power of Movie i. This is a relative measure that determines the overall caliber of movie stars in the cast. A high number for Star Power means that Movie i has a cast containing a high number of famous actors. The average of this variable is 100, so if a movie has a star power rating of 120, then that means it is 20% above average.

X5i: Established Audience of Movie i. This is a dummy variable that equals 1 if Movie i is based off of a book or is a sequel to another movie (zero otherwise).

X6i: Is Movie i a Childrens’ Movie? This is a dummy variable that equals 1 if Movie i is considered a childrens’ movie (zero otherwise).

1. Test your independent variables (X1i through X6i) for potential multicollinearity. Report the variance inflation factor (VIF) for each independent variable, and state your conclusion. If your test suggests that you should remove an independent variable from your analysis, then remove it and test the remaining independent variables for multicollinearity again. This process is to be continued until you can show evidence that all remaining independent variables pass a multicollinearity test.

2. Run a regression with box office revenue (Yi) as your dependent variable and the remaining X variables as your independent variables. Check if any of the regression coefficients are insignificantly different from zero. If so, remove the corresponding independent variables (one at a time) from your analysis and arrive at a model where all regression coefficients are statistically significant. Only state your final regression results.

3. Using your results from question 2, perform a partial residual analysis by testing the linearity assumption of your regression. Does there appear to be a pattern in any of the relationships between the residuals and your independent variables? If so, then attempt to resolve the issue by adding a squared-term (i.e., a quadratic transformation). State your final regression results which successfully pass a residual analysis.

4. Using your results from question 3, answer the following questions.

a. What is the R2 value? What does this say in the context of the scenario?

b. Interpret each of the relationships between box office revenue and the independent variables. In the occurrence of a linear and quadratic term, be sure to interpret both terms jointly and not separately.

c. Test the following hypothesis: For every $1 increase in production budget on average, a movie will increase box office revenue by MORE THAN $1. Be sure to state the null and alternative hypotheses, the p-value of the test, and your conclusion. Note: your conclusion should be made with 95% confidence or more.