Predicting Movie Revenue 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 movies total U.S. box office revenue (USRevenue). Among the explanatory variables are the movies 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. The data file is boxoffice.csv. You can use the following R command to load the data from your local device to R. boxoffice.data = read.csv(file.choose(), head=T)

1. Preliminary analysis.

(a) (0.5 points) The response variable (USRevenue) is quantitative. How about the explanatory variables? Which of the explanatory variables are quantitative? which categorical?

(b) (1 points) Consider three (quantitative) explanatory variables: Budget, Opening and Theater. Use scatterplot to study the relationship between the response variable and each of these 3 explanatory variables. Comment.

(c) (1 points) Provide correlation matrix among four variables, Budget, Opening, Theaters, and USRevenue. Is each quantitative explanatory variable highly correlated with the response variable? are explanatory variables highly correlated with themselves?

2. (1 points) 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. Lets call this model 1. Model 1: USRevenue = 0 + 1Budget + 2Opening + 3T heaters

3. (1 points) Comment on how well your linear model fits the data in terms of R2 .

4. (2 points) 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 1, 2, and 3 significantly different from zero, at significance level 0.05? 1

5. (2 points) Print out the ANOVA tests and comment on the results.

6. (1.5 points) 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?

7. (1 points) For each additional million dollars put in the Budget, how much increase in the U.S. box office revenue you predict?

8. (1 points) A new movie just comes out. Its budget is 100 millions, openingweekend revenue is 50 millions, and it is shown in 3500 theaters over the openingweekend. What is the 90% prediction interval for this new movie?

9. (2 points) Run regression analysis on the next two models: Model 2: USRevenue = 0 + 1T heaters and Model 3: USRevenue = 0 + 1Budget + 2Opening Among Model 1-3, which do you prefer? and Why?

10. (1 point) 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, and Rating 1 = 1.

11. (2 points) Consider the following multiple regression: Model 4: USRevenue = 0 + 1Budget + 2Opening + 3Rating1 What is the predicted USRevenue for the new movie, if it has Rating 1=0? and what is the predicted USRevenue for the new movie, if it has Rating 1=1?

12. (3 points) What is your final model? Briefly explain why.

13. (Bonus 5 points, optional) How to improve your final model in 12? Document your steps and provide reasonings. You should continue to use USRevenue as response variable, however, you could expand the model to incorporate all the other variables in the data set boxoffice.csv

A1 X Vfx Title E F 0 Rating1 A B D 1 Title USRelease Genre Rating "The Core" 28/03/2003 Adventure PG-13 3 "x2" 2/5/03 Action PG-13 4 "The Matrix | 15/05/2003 Action R "The Hollywi 13/06/2003 Action PG-13 6 "Terminator 1/7/03 Action R 7 "The League 11/7/03 Adventure PG-13 8 "The Rundov 26/09/2003 Action PG-13 9 "Looney Tun 14/11/2003 Comedy PG 10 "the Cat in th 21/11/2003 Comedy PG 11 "Lord of the 17/12/2003 Adventure PG-13 12 "Mona Lisa S 19/12/2003 Drama PG-13 13 "Cold Mount 25/12/2003 Drama R 14 "The Stepfor 11/6/04 Comedy PG-13 15 "Catwoman' 23/07/2004 Action PG-13 16 "Lemony Sni 17/12/2004 Comedy PG 17 "Robots" 11/3/05 Adventure PG 18 "Star Wars: F 19/05/2005 Adventure PG-13 19 "The Longest 27/05/2005 Comedy PG-13 20 "Madagascar 27/05/2005 Adventure PG 21 "Oliver Twist 23/09/2005 Drama PG-13 22 "Legend of Z 28/10/2005 Adventure PG 23 "Harry Potte 18/11/2005 Adventure PG-13 24 "The Pink Pa 10/2/06 Comedy PG 25 "Ice Age: The 31/03/2006 Adventure PG 26 "Mission: Im 5/5/06 Action PG-13 27 "Click" 23/06/2006 Comedy PG-13 28 "Pirates oftt 7/7/06 Adventure PG-13 29 "Miami Vice 28/07/2006 Action R 30 "Open Seaso 29/09/2006 Adventure PG 31 "dj vu" 22/11/2006 Thriller/Susp PG-13 32 "The Holiday 8/12/06 Romantic Cc PG-13 33 "Spider-Man 4/5/07 Adventure PG-13 34 "Hairspray" 20/07/2007 Musical PG 35 "The Simpso 27/07/2007 Comedy PG-13 36 "The Matrix ! 5/11/03 Action R 37 "The Invasio 17/08/2007 Thriller/Susp PG-13 38 "The Kingdo: 28/09/2007 Action R 39 "Finding Ner 30/05/2003 Adventure G 40 "Beowulf" 16/11/2007 Adventure PG-13 41 "His Dark Ma 7/12/07 Adventure PG-13 42 boxoffice Production Sequel 1 Live Action 1 Live Action 1 Animation/L / 1 Live Action 1 Animation/L 1 Live Action 1 Live Action 0 Live Action 0 Live Action 1 Animation/L 1 Live Action 1 Live Action 1 Live Action 1 Live Action O Live Action O Digital Anim 1 Animation/ 1 Live Action O Digital Anim 1 Live Action o Live Action 1 Animation/L 0 Live Action 0 Digital Anim 1 Live Action 1 Live Action 1 Live Action 1 Live Action o Digital Anim 1 Live Action 1 Live Action 1 1 Live Action 0 Live Action 1 Digital Anim 1 Live Action 1 Live Action 1 Live Action 0 Digital Anim 1 Digital Anim 1 Live Action H J L M N Budget Opening Theaters USRevenue IntRevenue World Reven Profit 0 85 12.053131 3017 31.11126 43.021371 74.132631 1 125 85.558731 3741 214.94969 191.45082 406.40051 1 127 91.774413 3603 281.55369 457.02324 738.57693 0 75 11.112632 2840 30.207785 20.9 51.107785 1 170 44.04144 3504 150.3583 282.7 433.0583 0 78 23.075892 3002 66.4626 112.8 179.2626 0 85 18.533765 3152 47.641743 33.19015 80.831893 0 80 9.317371 2903 20.95082 33.589842 54.540662 0 109 38.32916 3464 101.01828 32.8 133.81828 1 94 72.629713 3703 377.02733 756 1133.0273 0 0 65 11.528498 2677 63.8031 57.795209 121.59831 0 80 14.574213 2163 95.632614 66 161.63261 0 100 21.406781 3057 59.475623 36.746348 96.221971 0 100 16.728411 3117 40.19871 33.689193 73.887903 0 100 30.061756 3620 118.62712 83 201.62712 0 80 36.045301 3776 128.20001 132.5 260.70001 1 115 108.43584 3661 380.27058 468.72824 848.99882 0 82 47.60648 3634 158.11946 32.201108 190.32057 0 75 47.224594 4131 193.20293 334.8 528.00293 0 65 17.453216 2689 2.07092 24.6 26.67092 1 80 16.328506 3520 45.575336 95.9 141.47534 1 150 102.33507 3858 290.01304 606 896.01304 0 80 20.220412 3477 82.226474 76.7 158.92647 1 75 68.033544 3964 195.33062 452 647.33062 1 150 47.743273 4054 133.50135 264 397.50135 0 82.5 40.011365 3749 137.35563 100.2 237.55563 1 150 135.63455 4133 423.31581 642.344 1065.6598 0 0 135 25.723815 3021 63.478838 100.33972 163.81856 0 85 23.624548 3833 84.303558 104.8 189.10356 0 80 20.574802 3108 64.038616 117 181.03862 0 85 12.778913 2610 63.28 141.91032 205.19032 1 258 151.11652 4252 336.5303 555.4 891.9303 0 75 27.476745 3121 118.82309 88 206.82309 0 72.5 74.036787 3922 183.13501 343.73518 526.87019 1 110 48.475154 3502 139.25976 285 424.25976 0 80 5.951409 2776 15.074191 25.072851 40.147042 0 72.5 17.135055 2793 47.46725 39.042352 86.509602 0 94 70.25171 3374 339.71498 526.878 866.59298 0 150 27.515871 3153 82.195215 112.8 194.99522 0 205 25.783232 3528 70.107728 295.59377 365.70149 LOpening 0 2.4893245 1 4.4492031 1 4.5193335 0 2.4080825 0 3.785131 0 3.1387884 0 2.9195942 0 2.2318805 0 3.646211 1 4.2853741 0 2.4448221 1 2.6792537 03.0637077 0 2.8171085 1 3.4032538 1 3.5847765 1 4.6861587 1 3.8629689 1 3.8549148 0 2.8595239 0 2.7929124 1 4.6282524 1 3.0066926 1 4.2200009 0 3.8658382 1 3.6891635 1 4.9099642 0 3.2474172 03.1622863 03.0240671 0 2.5477964 1 5.0180512 1 3.31334 1 4.3045621 1 3.8810514 0 1.783628 0 2.8411264 1 4.2520847 0 3.314763 0 3.2497244 A1 X Vfx Title E F 0 Rating1 A B D 1 Title USRelease Genre Rating "The Core" 28/03/2003 Adventure PG-13 3 "x2" 2/5/03 Action PG-13 4 "The Matrix | 15/05/2003 Action R "The Hollywi 13/06/2003 Action PG-13 6 "Terminator 1/7/03 Action R 7 "The League 11/7/03 Adventure PG-13 8 "The Rundov 26/09/2003 Action PG-13 9 "Looney Tun 14/11/2003 Comedy PG 10 "the Cat in th 21/11/2003 Comedy PG 11 "Lord of the 17/12/2003 Adventure PG-13 12 "Mona Lisa S 19/12/2003 Drama PG-13 13 "Cold Mount 25/12/2003 Drama R 14 "The Stepfor 11/6/04 Comedy PG-13 15 "Catwoman' 23/07/2004 Action PG-13 16 "Lemony Sni 17/12/2004 Comedy PG 17 "Robots" 11/3/05 Adventure PG 18 "Star Wars: F 19/05/2005 Adventure PG-13 19 "The Longest 27/05/2005 Comedy PG-13 20 "Madagascar 27/05/2005 Adventure PG 21 "Oliver Twist 23/09/2005 Drama PG-13 22 "Legend of Z 28/10/2005 Adventure PG 23 "Harry Potte 18/11/2005 Adventure PG-13 24 "The Pink Pa 10/2/06 Comedy PG 25 "Ice Age: The 31/03/2006 Adventure PG 26 "Mission: Im 5/5/06 Action PG-13 27 "Click" 23/06/2006 Comedy PG-13 28 "Pirates oftt 7/7/06 Adventure PG-13 29 "Miami Vice 28/07/2006 Action R 30 "Open Seaso 29/09/2006 Adventure PG 31 "dj vu" 22/11/2006 Thriller/Susp PG-13 32 "The Holiday 8/12/06 Romantic Cc PG-13 33 "Spider-Man 4/5/07 Adventure PG-13 34 "Hairspray" 20/07/2007 Musical PG 35 "The Simpso 27/07/2007 Comedy PG-13 36 "The Matrix ! 5/11/03 Action R 37 "The Invasio 17/08/2007 Thriller/Susp PG-13 38 "The Kingdo: 28/09/2007 Action R 39 "Finding Ner 30/05/2003 Adventure G 40 "Beowulf" 16/11/2007 Adventure PG-13 41 "His Dark Ma 7/12/07 Adventure PG-13 42 boxoffice Production Sequel 1 Live Action 1 Live Action 1 Animation/L / 1 Live Action 1 Animation/L 1 Live Action 1 Live Action 0 Live Action 0 Live Action 1 Animation/L 1 Live Action 1 Live Action 1 Live Action 1 Live Action O Live Action O Digital Anim 1 Animation/ 1 Live Action O Digital Anim 1 Live Action o Live Action 1 Animation/L 0 Live Action 0 Digital Anim 1 Live Action 1 Live Action 1 Live Action 1 Live Action o Digital Anim 1 Live Action 1 Live Action 1 1 Live Action 0 Live Action 1 Digital Anim 1 Live Action 1 Live Action 1 Live Action 0 Digital Anim 1 Digital Anim 1 Live Action H J L M N Budget Opening Theaters USRevenue IntRevenue World Reven Profit 0 85 12.053131 3017 31.11126 43.021371 74.132631 1 125 85.558731 3741 214.94969 191.45082 406.40051 1 127 91.774413 3603 281.55369 457.02324 738.57693 0 75 11.112632 2840 30.207785 20.9 51.107785 1 170 44.04144 3504 150.3583 282.7 433.0583 0 78 23.075892 3002 66.4626 112.8 179.2626 0 85 18.533765 3152 47.641743 33.19015 80.831893 0 80 9.317371 2903 20.95082 33.589842 54.540662 0 109 38.32916 3464 101.01828 32.8 133.81828 1 94 72.629713 3703 377.02733 756 1133.0273 0 0 65 11.528498 2677 63.8031 57.795209 121.59831 0 80 14.574213 2163 95.632614 66 161.63261 0 100 21.406781 3057 59.475623 36.746348 96.221971 0 100 16.728411 3117 40.19871 33.689193 73.887903 0 100 30.061756 3620 118.62712 83 201.62712 0 80 36.045301 3776 128.20001 132.5 260.70001 1 115 108.43584 3661 380.27058 468.72824 848.99882 0 82 47.60648 3634 158.11946 32.201108 190.32057 0 75 47.224594 4131 193.20293 334.8 528.00293 0 65 17.453216 2689 2.07092 24.6 26.67092 1 80 16.328506 3520 45.575336 95.9 141.47534 1 150 102.33507 3858 290.01304 606 896.01304 0 80 20.220412 3477 82.226474 76.7 158.92647 1 75 68.033544 3964 195.33062 452 647.33062 1 150 47.743273 4054 133.50135 264 397.50135 0 82.5 40.011365 3749 137.35563 100.2 237.55563 1 150 135.63455 4133 423.31581 642.344 1065.6598 0 0 135 25.723815 3021 63.478838 100.33972 163.81856 0 85 23.624548 3833 84.303558 104.8 189.10356 0 80 20.574802 3108 64.038616 117 181.03862 0 85 12.778913 2610 63.28 141.91032 205.19032 1 258 151.11652 4252 336.5303 555.4 891.9303 0 75 27.476745 3121 118.82309 88 206.82309 0 72.5 74.036787 3922 183.13501 343.73518 526.87019 1 110 48.475154 3502 139.25976 285 424.25976 0 80 5.951409 2776 15.074191 25.072851 40.147042 0 72.5 17.135055 2793 47.46725 39.042352 86.509602 0 94 70.25171 3374 339.71498 526.878 866.59298 0 150 27.515871 3153 82.195215 112.8 194.99522 0 205 25.783232 3528 70.107728 295.59377 365.70149 LOpening 0 2.4893245 1 4.4492031 1 4.5193335 0 2.4080825 0 3.785131 0 3.1387884 0 2.9195942 0 2.2318805 0 3.646211 1 4.2853741 0 2.4448221 1 2.6792537 03.0637077 0 2.8171085 1 3.4032538 1 3.5847765 1 4.6861587 1 3.8629689 1 3.8549148 0 2.8595239 0 2.7929124 1 4.6282524 1 3.0066926 1 4.2200009 0 3.8658382 1 3.6891635 1 4.9099642 0 3.2474172 03.1622863 03.0240671 0 2.5477964 1 5.0180512 1 3.31334 1 4.3045621 1 3.8810514 0 1.783628 0 2.8411264 1 4.2520847 0 3.314763 0 3.2497244