FIN330 Fall 2017 Assignment # 6 Predicting Movie Revenue [C.f. PSBE]. Nash Information Services provides information and analytical services to the movie industry, including statistical models for predicting movie revenue. Consider a random sample of 40 movies released over a five-year period. This sample was collected to see if information available soon after the theatrical release can successfully predict total box office revenue. The population of interest is much larger and consists of all movies released over this five-year period. Consider that the response variable is a movie's total U.S. box office revenue (USRevenue). Among the explanatory variables are the movie's budget (Budget), opening-weekend revenue (Opening), how many theaters the movie was in for the opening weekend (Theaters), and Ratings (e.g. Rating 1). All dollar amounts are measured in millions of U.S. dollars. 1. Run a multiple regression with Budget (X1 ), Opening (X2 ) and Theaters (X3 ) as explanatory variables, and USRevenue as response variable. Write down your fitted model. Let's call this model 1. Model 1: U SRevenue = 0 + 1 Budget + 2 Opening + 3 T heaters 2. Comment on how well your linear model fits the data. 3. Print out the linear regression results, including the estimated regression coefficients, its standard error, t statistic, and P-value. Comment on the t-tests on model 1. For example, are 0 , 1 , 2 , and 3 significantly different from zero, at significance level 0.05? 4. Print out the ANOVA tests and comment on the results. 5. At significance level = 0.05, test the hypothesis of whether the coefficient associated with opening-weekend revenue is greater than 2 (i.e. the impact of opening-weekend revenue is more than double). In other words: H0 : 2 2 Ha : 2 > 2 What is your conclusion on the above hypothesis? 6. For each additional million dollars put in the Budget, how much increase in the U.S. box office revenue you predict? 7. A new movie just comes out. Its budget is 100 millions, opening-weekend revenue is 50 millions, and it is shown in 3500 theaters over the opening-weekend. What is the 90% prediction interval for this new movie? 8. Run regression analysis on the next two models: Model 2: U SRevenue = 0 + 1 T heaters and Model 3: U SRevenue = 0 + 1 Budget + 2 Opening Among Model 1-3, which do you prefer? and Why? 1 9. In the dataset boxoffice.csv, there is a variable called \"Rating 1\". Is this a categorical variable or quantitative variable? Explain the meaning of \"Rating 1 = 0\