1. Run a multiple regression with Budget (X1), Opening (X2) and Theaters (X3) as
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Question
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: USRevenue = 0 + 1Budget + 2Opening + 3T heaters
2. Comment on how well your linear model fits the data.
3. Print out the linear regression results, including the estimated regression coef- ficients, 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?
Title USRelease Genre Rating Rating1 Production Method Sequel Budget Opening Theaters USRevenue IntRevenue WorldRevenue Profit LOpening "The Core" 28/03/2003 Adventure PG-13 1 Live Action 0 85 12.05313 3017 31.11126 43.02137 74.13263 0 2.489324 "X2" 2/5/2003 Action PG-13 1 Live Action 1 125 85.55873 3741 214.9497 191.4508 406.4005 1 4.449203 "The Matrix Reloaded" 15/05/2003 Action R 1 Animation/Live Action 1 127 91.77441 3603 281.5537 457.0232 738.5769 1 4.519334 "The Hollywood Homicide" 13/06/2003 Action PG-13 1 Live Action 0 75 11.11263 2840 30.20779 20.9 51.10779 0 2.408082 "Terminator 3: Rise of the Machines" 1/7/2003 Action R 1 Animation/Live Action 1 170 44.04144 3504 150.3583 282.7 433.0583 0 3.785131 "The League of Extraordinary Gentlemen" ######## Adventure PG-13 1 Live Action 0 78 23.07589 3002 66.4626 112.8 179.2626 0 3.138788 "The Rundown" 26/09/2003 Action PG-13 1 Live Action 0 85 18.53377 3152 47.64174 33.19015 80.83189 0 2.919594 "Looney Tunes: Back in Action" 14/11/2003 Comedy PG 0 Live Action 0 80 9.317371 2903 20.95082 33.58984 54.54066 0 2.231881 "the Cat in the Hat" 21/11/2003 Comedy PG 0 Live Action 0 109 38.32916 3464 101.0183 32.8 133.8183 0 3.646211 "Lord of the Rings: The Return of the King" 17/12/2003 Adventure PG-13 1 Animation/Live Action 1 94 72.62971 3703 377.0273 756 1133.027 1 4.285374 "Mona Lisa Smile" 19/12/2003 Drama PG-13 1 Live Action 0 65 11.5285 2677 63.8031 57.79521 121.5983 0 2.444822 "Cold Mountain" 25/12/2003 Drama R 1 Live Action 0 80 14.57421 2163 95.63261 66 161.6326 1 2.679254 "The Stepford Wives" ######## Comedy PG-13 1 Live Action 0 100 21.40678 3057 59.47562 36.74635 96.22197 0 3.063708 "Catwoman" 23/07/2004 Action PG-13 1 Live Action 0 100 16.72841 3117 40.19871 33.68919 73.8879 0 2.817109 "Lemony Snicket's A Series of Unfortunate Events" 17/12/2004 Comedy PG 0 Live Action 0 100 30.06176 3620 118.6271 83 201.6271 1 3.403254 "Robots" ######## Adventure PG 0 Digital Animation 0 80 36.0453 3776 128.2 132.5 260.7 1 3.584777 "Star Wars: Revenge of the Sith" 19/05/2005 Adventure PG-13 1 Animation/Live Action 1 115 108.4358 3661 380.2706 468.7282 848.9988 1 4.686159 "The Longest Yard" 27/05/2005 Comedy PG-13 1 Live Action 0 82 47.60648 3634 158.1195 32.20111 190.3206 1 3.862969 "Madagascar" 27/05/2005 Adventure PG 0 Digital Animation 0 75 47.22459 4131 193.2029 334.8 528.0029 1 3.854915 "Oliver Twist" 23/09/2005 Drama PG-13 1 Live Action 0 65 17.45322 2689 2.07092 24.6 26.67092 0 2.859524 "Legend of Zorro" 28/10/2005 Adventure PG 0 Live Action 1 80 16.32851 3520 45.57534 95.9 141.4753 0 2.792912 "Harry Potter and the Goblet of Fire" 18/11/2005 Adventure PG-13 1 Animation/Live Action 1 150 102.3351 3858 290.013 606 896.013 1 4.628252 "The Pink Panther" ######## Comedy PG 0 Live Action 0 80 20.22041 3477 82.22647 76.7 158.9265 1 3.006693 "Ice Age: The Meltdown" 31/03/2006 Adventure PG 0 Digital Animation 1 75 68.03354 3964 195.3306 452 647.3306 1 4.220001 "Mission: Impossible III" 5/5/2006 Action PG-13 1 Live Action 1 150 47.74327 4054 133.5013 264 397.5013 0 3.865838 "Click" 23/06/2006 Comedy PG-13 1 Live Action 0 82.5 40.01137 3749 137.3556 100.2 237.5556 1 3.689164 "Pirates of the Caribbean: Dead Man's Chest" 7/7/2006 Adventure PG-13 1 Live Action 1 150 135.6346 4133 423.3158 642.344 1065.66 1 4.909964 "Miami Vice" 28/07/2006 Action R 1 Live Action 0 135 25.72382 3021 63.47884 100.3397 163.8186 0 3.247417 "Open Season" 29/09/2006 Adventure PG 0 Digital Animation 0 85 23.62455 3833 84.30356 104.8 189.1036 0 3.162286 "dŽjˆ vu" 22/11/2006 Thriller/Suspense PG-13 1 Live Action 0 80 20.5748 3108 64.03862 117 181.0386 0 3.024067 "The Holiday" ######## Romantic Comedy PG-13 1 Live Action 0 85 12.77891 2610 63.28 141.9103 205.1903 0 2.547796 "Spider-Man 3" 4/5/2007 Adventure PG-13 1 Live Action 1 258 151.1165 4252 336.5303 555.4 891.9303 1 5.018051 "Hairspray" 20/07/2007 Musical PG 0 Live Action 0 75 27.47675 3121 118.8231 88 206.8231 1 3.31334 "The Simpsons Movie" 27/07/2007 Comedy PG-13 1 Digital Animation 0 72.5 74.03679 3922 183.135 343.7352 526.8702 1 4.304562 "The Matrix Revolutions" ######## Action R 1 Live Action 1 110 48.47515 3502 139.2598 285 424.2598 1 3.881051 "The Invasion" 17/08/2007 Thriller/Suspense PG-13 1 Live Action 0 80 5.951409 2776 15.07419 25.07285 40.14704 0 1.783628 "The Kingdom" 28/09/2007 Action R 1 Live Action 0 72.5 17.13506 2793 47.46725 39.04235 86.5096 0 2.841126 "Finding Nemo" 30/05/2003 Adventure G 0 Digital Animation 0 94 70.25171 3374 339.715 526.878 866.593 1 4.252085 "Beowulf" 16/11/2007 Adventure PG-13 1 Digital Animation 0 150 27.51587 3153 82.19522 112.8 194.9952 0 3.314763 "His Dark Materials: The Golden Compass" ######## Adventure PG-13 1 Live Action 0 205 25.78323 3528 70.10773 295.5938 365.7015 0 3.249724Explanation / Answer
1.
US revenue = 53.70 -0.4988 Budget +3.2417 Opening - 0.0012 Theatres
2.
R square is 87.18 which is a good measure to see how much of the variation in the predictor variables can be explained to predict the response variables.
3.
Standard error, t-stat and p-value for each of the 3 variables.
the intercept's p-value is 0.37 which is greater than 0.05 and hence we cannot reject null hypothesis. The intercept is not significant.
the budget's p-value is 0.018 which is less than .0.05 and hence we can say that the budget is a significant predictor.
the opening's p-value is closer to 0 and hence it is a significant predictor
the theaters' p-value is 0.95 and hence it is not a significant predictor at all.
4.
Teh anova test checks the null hypothesis if the intercept only model is equal to the model with predictors against the alternate hypothesis if the intercept model is inferior to the model with predictors.
since the significance of F is less than 0.05, we can reject the null hypothesis and say that the model with predictors is significant.
Coefficients Standard Error t Stat P-value Intercept 53.70203 60.19528 0.89213 0.378248 Budget -0.49882 0.201816 -2.47164 0.018313 Opening 3.241728 0.296468 10.93451 5.42E-13 Theaters -0.00124 0.019572 -0.06338 0.949812Related Questions
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