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 YiYi Movie ii'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 X1iX1i Production Budget of Movie ii in millions of USD X2iX2i Critical review of Movie ii from Rotten Tomatoes (range 0 100) X3iX3i Number of official trailer views on YouTube in millions of views X4iX4i Star Power of Movie ii 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 ii 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 X5iX5i Established Audience of Movie ii This is a dummy variable that equals 1 if Movie ii is based off of a book or is a sequel to another movie (zero otherwise) X6iX6i Is Movie ii a Childrens' Movie This is a dummy variable that equals 1 if Movie ii is considered a childrens' movie (zero otherwise) 1 Test your independent variables (X1iX1i through X6iX6i) 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)(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 R2R2 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 Y X1 X2 X3 X4 X5 X6 540 7856 53 51886 83 85497 2 721772 119 1037 1 1 392 3442 25 19889 85 01798 1 610502 96 42906 1 0 226 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69 13787 0 1 533 0247 32 66987 103 0233 2 287354 119 1056 1 0 293 4639 30 87937 94 99378 1 575533 80 74919 1 1 231 5349 46 17957 76 49933 1 891578 65 82458 0 0 561 7889 43 56388 58 97052 2 436283 131 7163 1 0 545 8953 49 53339 84 76451 2 545712 123 6408 1 0 610 8006 58 71334 70 86375 2 735795 127 0656 0 0 533 2432 29 93278 61 85974 2 110431 127 6834 0 1 633 9746 51 33008 85 85228 2 540169 132 4893 0 0 186 6928 39 16867 71 46082 1 593284 60 06853 1 0 623 1665 57 74796 56 57585 2 755203 138 3028 0 0 627 3691 33 36437 90 07587 2 551689 137 034 1 1 468 4013 35 04119 74 26588 2 13473 112 1482 0 0 485 8693 41 94833 58 02658 2 009015 114 5848 1 0 448 3085 26 94161 78 53541 1 919219 115 3719 0 0 437 0189 55 19624 89 24015 2 455488 101 5463 1 0 333 1731 31 46556 86 48331 1 789596 92 97323 0 0 249 2775 40 43778 79 46498 1 89296 76 81016 1 1 201 6423 45 88609 62 66379 1 740939 63 83318 1 0 177 3456 33 59826 59 53667 1 577602 65 54984 0 0 371 5421 48 53457 73 37842 2 158328 92 88223 1 1 220 42 51 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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

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:

YiYi: Movie ii'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.

X1iX1i: Production Budget of Movie ii in millions of USD.

X2iX2i: Critical review of Movie ii from Rotten Tomatoes (range: 0-100).

X3iX3i: Number of official trailer views on YouTube in millions of views.

X4iX4i: Star Power of Movie ii. 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 ii 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.

X5iX5i: Established Audience of Movie ii. This is a dummy variable that equals 1 if Movie ii is based off of a book or is a sequel to another movie (zero otherwise).

X6iX6i: Is Movie ii a Childrens' Movie? This is a dummy variable that equals 1 if Movie ii is considered a childrens' movie (zero otherwise).

1. Test your independent variables (X1iX1i through X6iX6i) 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)(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 R2R2 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.

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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

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Y	X1	X2	X3	X4	X5	X6
540.7856	53.51886	83.85497	2.721772	119.1037	1	1
392.3442	25.19889	85.01798	1.610502	96.42906	1	0
226.7938	42.78069	87.96866	1.854956	71.00689	0	0
526.6946	45.02286	45.47119	2.320636	117.9093	0	1
215.5599	48.84927	71.89038	1.920509	76.53418	0	0
473.5454	42.89191	83.63071	2.211431	111.1492	0	1
183.7129	21.52862	69.78666	1.463664	72.11916	1	0
599.6974	22.07576	73.99766	2.251224	137.2786	1	0
307.7759	40.86636	51.82205	2.113057	94.87179	1	0
252.37	20.63405	74.99032	1.539588	80.96145	0	1
536.5079	59.07689	85.00274	2.715145	113.7103	0	1
412.8236	30.8982	80.15956	2.04186	111.425	1	0
490.2613	40.57568	68.53492	2.28285	114.4791	1	0
442.5426	24.59089	66.27036	1.897249	117.8929	1	0
348.112	26.38638	63.16486	1.697997	96.93911	1	0
348.9371	52.36039	77.00161	2.21493	92.18938	0	0
290.7769	49.4291	82.03832	1.99479	77.51856	1	1
500.6202	54.13279	72.275	2.432953	115.5353	0	0
256.0326	29.6194	77.19635	1.572667	81.05383	1	1
205.6868	48.18068	82.93163	1.841025	60.79235	0	0
407.8683	27.81048	67.0616	1.93969	109.3091	0	0
182.8955	57.79349	81.15615	2.058269	61.67037	1	0
421.969	33.52534	85.71593	2.001556	102.2919	1	0
638.3547	49.06613	55.09065	2.574485	138.4261	1	0
649.3245	47.64005	83.29414	2.575809	137.7048	0	0
510.2344	28.59743	82.08734	2.162174	125.2682	1	0
414.4618	36.70335	104.0404	2.014923	106.7802	1	0
153.1549	28.7506	79.8755	1.466296	65.51371	0	1
615.6946	39.46992	86.29775	2.584345	137.1338	0	0
428.1185	33.73081	74.61746	1.92795	112.8751	0	0
570.477	28.67806	92.98658	2.288639	127.107	0	0
512.3813	35.23154	69.14946	2.306401	123.0436	1	0
265.6639	37.71565	91.61004	1.549362	71.80907	1	0
167.1419	33.74354	92.67376	1.434214	60.26743	1	0
351.8053	42.67087	97.0184	1.760332	91.73536	0	1
230.7783	57.97101	89.55655	1.762049	64.88435	1	0
494.6093	27.10083	76.94782	1.915295	118.0387	1	0
470.1411	25.71383	75.98228	2.231832	120.3745	1	1
335.4125	22.78311	72.02658	1.744068	95.04096	0	0