Your fearless instructor used linear regression to analyze a sample of 85 action movies (with the category "action" broadly defined) from the years 2014-2016. The goal was to predict the gross earnings of an action movie based on the movie's characteristics available prior to its release. For each movie, he had the following information: OBS The observation number of the movie in the dataset. Movies are listed in alphabetical order GROSS The gross earnings generated by the movie, in millions of dollars YEAR The year of the movie's release. Possible values are 2014, 2015, and 2016. PG13_RATING 1 if the movie is rated PG-13; 0 otherwise. All movies in the sample are rated PG, PG-13, or R. R_RATING 1 if the movie is rated R; 0 otherwise. All movies in the sample are rated PG, PG-13, or R. DURATION The running time of the movie, in minutes. BUDGET The production budget for the movie, in millions of dollars. FACES The number of faces on the movie's promotional poster. CASTLIKES The total number of likes for the movie's cast members on the social media site Facebook, prior to the movie's release. Base your answers to the following questions on the linear regression model below, which uses GROSS as its dependent variable.REGRESSION MODEL FOR MOVIE GROSS EARNINGS SUMMARY OUTPUT Regression Statistics Multiple R 0.6346 R Square 0.4027 Adjusted R Square 0.3484 Standard Error 97.4460 Observations 85 ANOVA of SS MS F Significance F Regression 7 493004 70429 7.417 0.000 Residual 77 731171 9496 Total 84 1224175 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 20135.3745 25832.7169 0.7795 0.4381 -31304.1366 71574.8856 YEAR -9.9893 12.8246 -0.7789 0.4384 -35.5264 15.5478 PG13_RATING -44.4127 40.7468 -1.0900 0.2791 -125.5501 36.7246 R RATING -19.7600 51.0718 0.3869 0.6999 -121.4570 81.9369 DURATION 0.3191 0.8530 0.3740 0.7094 -1.3795 2.0177 BUDGET 1.0460 0.2594 4.0328 0.0001 0.5295 1.5624 FACES -9.1013 4.7263 -1.9257 0.0578 -18.5125 0.3100 CASTLIKES 0.0009 0.0007 1.3714 0.1742 -0.0004 0.0022OBS TITLE GROSS YEAR PG13_RATING R RATING DURATION BUDGET FACES CASTLIKES 13 Hours 52.8 2016 144 50 3580 2 22 Jump Street 191.6 2014 112 50 19428 3 OONO 3 Days to Kill 30.7 2014 123 28 1286 4 300: Rise of an Empire 106.4 2014 102 110 10583 5 A Most Violent Year 5.7 2014 . -0 -00 - OC 125 20 0 3979 6 Allegiant 66.0 2016 120 110 12452 American Sniper 350.1 2014 133 58.8 DOW 16277 8 Ant-Man 180.2 2015 ooo. . . 0 - 0 - -0- 117 130 5730 . . 83 Warcraft 47.0 2016 123 160 5505 84 X-Men: Apocalypse NOO. 155.0 2016 144 178 49684 85 X-Men: Days of Future Past 233.9 2014 149 200 91434a. Remove an independent variable with a high pvalue, and see how this changes the pvalues for the remaining independent variables. b. Generate a correlation matrix ofthe independent variables and check for correlations close to +1 and 1. c. Add an interaction variable to the model. d. Measure the model's predictive performance using a validation set