Scenario 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 Movieii'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 Movieiiin millions of USD X2iX2i Critical review of Movieiifrom Rotten Tomatoes (range 0 100) X3iX3i Number of official trailer views on YouTube in millions of views X4iX4i Star Power of Movieii This is a relative measure that determines the overall caliber of movie stars in the cast A high number for Star Power means that Movieiihas 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 Movieii This is a dummy variable that equals 1 if Movieiiis based off of a book or is a sequel to another movie (zero otherwise) X6iX6i Is Movieiia Childrens' Movie This is a dummy variable that equals 1 if Movieiiis considered a childrens' movie (zero otherwise) 1 (10 pts) Test your independent variables (X1iX1ithroughX6iX6i) 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 (10 pts) 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 (10 pts) 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 (15 pts) Using your results from question 3, answer the following questions a What is theR2R2value 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 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 0 312 8796 24 73855 68 46289 1 415144 84 20405 0 0 630 8719 29 40774 73 3181 2 293946 136 3266 1 0 424 9993 33 48867 75 58276 2 015917 109 2396 1 0 593 5278 59 22001 83 04229 2 808389 129 7981 0 1 292 491 20 21138 94 31965 1 554791 79 07107 1 0 407 9676 39 43011 63 60983 2 035057 103 7012 0 1 618 9588 42 34858 85 03756 2 65622 136 9696 1 1 583 8917 41 50006 64 99011 2 378133 131 9271 0 1 288 9931 40 47123 75 40671 1 865025 83 21838 0 0 631 2733 46 20963 85 33139 2 570077 133 2881 1 0 186 5086 25 21318 56 94465 1 411351 66 14756 1 1 404 4439 50 82799 67 8339 2 354256 101 7672 0 1 515 63 31 29813 66 54828 1 922105 119 4541 0 0 592 8004 30 96375 106 163 2 190792 132 9852 0 0 196 2189 35 82953 77 3497 1 717876 67 74236 1 1 336 899 24 14033 68 09806 1 696605 97 20894 1 1 397 0135 20 25008 83 28359 1 790365 107 5616 1 1 319 9253 49 93507 84 78904 2 215687 86 80727 1 1 518 5073 41 89501 70 55336 2 251309 123 1387 1 0 585 3125 44 37747 86 05567 2 577017 127 3513 0 1 500 3813 57 29431 63 58791 2 659989 112 7828 0 0 448 3815 46 82611 88 12986 2 431913 111 6604 0 0 383 2273 26 07747 82 65685 1 674427 105 1347 0 1 321 6445 57 12007 90 74434 2 361478 89 06921 1 0 321 8481 45 71396 64 90399 1 815505 82 36707 0 1 368 2161 26 77037 53 68044 1 810851 99 72763 0 0 366 0264 40 50475 76 53185 2 158186 98 53531 0 0 261 7492 53 93478 64 68595 2 016782 75 17331 1 0 212 0768 42 17841 106 9836 1 791295 62 73684 0 0 252 6101 44 18628 92 96616 1 568194 66 5423 1 0 388 2548 27 01697 89 13227 1 784271 102 0219 1 1 364 6668 40 82354 63 15801 2 137231 98 57829 1 1 244 1655 59 22131 65 38442 2 101132 72 3199 0 0 597 3065 36 68726 86 29242 2 280594 129 8238 1 0 235 1016 26 43395 72 66049 1 48909 75 67027 0 0 497 2731 21 01862 78 32849 1 961873 124 1473 1 0 447 5432 55 94019 67 10247 2 4981 108 2366 1 0 524 0156 38 70334 81 22659 2 495572 124 1474 0 1 283 7761 42 63141 42 4862 2 045187 95 68842 0 0 488 7331 53 74245 67 2579 2 702044 116 6644 1 1 649 8484 55 4281 77 49037 2 794329 138 573 0 0 476 0659 31 47969 73 49551 2 049281 112 0028 0 1 309 7346 46 1572 44 62968 1 986593 85 81128 0 0 165 1847 22 62617 75 14766 1 22821 63 86177 0 1 307 9281 41 99596 75 76737 2 053785 90 80408 1 1 297 6807 31 61389 60 60791 1 785641 87 82038 1 0 494 933 27 03996 46 62632 1 999756 119 0812 0 0 333 0971 29 73534 69 46538 1 675094 92 23102 1 0 249 5373 54 21599 77 97103 1 880722 66 67562 0 0 506 493 56 39212 83 86001 2 475704 115 3458 1 1 178 9668 44 03433 83 20836 1 55562 65 27251 0 0 155 2296 22 76795 59 54512 1 457576 63 39136 1 0 257 1004 45 23932 64 1052 1 830454 80 43846 1 0 467 5809 40 87805 110 8036 2 087753 109 343 1 0 402 1765 27 85569 57 5112 1 810799 105 4807 1 0 347 5609 59 76892 78 07164 2 218889 93 2821 1 0 537 9044 26 86943 81 42522 2 148125 124 202 1 0 598 7308 49 87397 61 68246 2 51337 129 4543 1 0 198 5161 34 80656 75 11279 1 509124 68 47923 1 0 602 4254 48 43961 80 08421 2 471915 130 6313 1 1 543 7283 31 28081 68 70253 2 205347 126 6506 0 0 512 7382 25 04993 81 53681 1 940611 124 6945 1 1 367 512 35 63675 45 86212 2 053844 106 7984 0 0 392 8991 55 41165 70 87069 2 241907 92 09139 1 0 209 3722 24 16936 86 98166 1 285531 66 18086 1 1 625 6458 21 20352 104 4286 2 122946 139 3542 1 0 331 9468 45 88154 55 50568 2 07171 90 08958 0 0 179 4078 25 33928 59 03871 1 393694 69 29297 1 1 193 5244 29 61735 71 88708 1 538884 63 67425 1 1 241 9113 47 51641 65 31761 2 078312 78 06898 0 0 299 3287 43 57641 100 8015 1 919191 84 55055 1 0 381 0341 39 1011 73 3042 2 239251 102 8698 1 0 479 9868 39 65092 63 07066 2 425921 117 118 0 0 656 2794 44 6423 90 00378 2 524393 135 0043 1 1 529 3601 50 47087 63 19123 2 470627 125 5566 1 1 179 2646 29 33486 50 83814 1 531872 67 85443 0 0 370 4616 30 91061 94 42696 2 009518 94 0142 1 0 574 8207 34 19605 63 36229 2 268224 135 6452 0 0 365 2465 22 074 83 50865 1 638156 100 8636 1 0 291 9405 55 07325 70 38963 2 146434 81 81834 1 0 165 3366 55 08396 78 21317 2 022616 63 27839 0 1 404 443 54 32698 67 77666 2 415155 103 8292 1 1 575 9138 58 85712 93 25957 2 623044 121 2995 1 0 524 6336 42 95142 47 32456 2 538729 121 4593 1 1 356 8129 33 30285 106 4916 1 962918 90 24719 1 0 466 665 20 83038 92 71532 1 910323 115 6548 1 1 493 8861 21 7047 82 50644 1 870623 116 7202 0 0 414 7666 50 59372 81 65408 2 302225 101 6754 1 0 557 3706 53 09529 94 67682 2 71701 124 8683 0 1 369 3499 45 39663 92 29666 2 051722 93 67032 1 0 568 5045 24 99555 53 08628 2 285904 134 9779 1 0 505 4393 50 3299 73 64689 2 347012 115 3169 1 0 588 8554 27 50526 53 62702 2 091675 132 1156 1 1 348 1642 26 12008 87 09402 1 787868 97 71425 0 1 232 9787 21 24596 76 16131 1 500369 81 14143 0 0 292 731 58 02909 61 29311 2 294198 83 83624 0 1 419 2577 50 89126 87 86008 2 166167 101 5467 1 0 506 5325 46 88018 68 25297 2 423964 119 476 0 0 546 1037 59 13013 57 10941 2 969214 132 4118 0 0 493 3211 26 01707 77 94391 2 017834 123 6177 0 1 220 5285 25 32476 41 28995 1 353339 72 13546 1 0 329 1835 53 94315 71 19995 1 99743 78 38761 1 0 292 0699 49 36601 68 9751 2 232828 87 41912 0 0 331 7751 55 88607 83 65862 2 104245 85 38723 0 0 624 3696 32 32964 62 58179 2 416405 134 1081 0 0 566 0518 52 64869 95 42567 2 647895 122 559 1 1 274 9195 50 48433 61 24289 2 057278 83 9625 0 0 448 3555 21 93133 62 03994 1 845 112 3548 1 0 476 2125 47 14583 89 09017 2 329126 108 0448 0 0 308 3091 26 068 85 08084 1 654366 88 71628 0 0 501 0634 59 59234 85 68015 2 69403 113 794 1 0 543 0884 42 01908 96 21034 2 51848 126 8016 1 0 536 4499 43 62872 68 71603 2 481473 128 6631 1 0 625 8049 45 38203 88 83624 2 745461 134 9409 0 0 547 0608 41 82734 59 75178 2 364295 125 7741 1 0 433 4684 20 5584 62 04274 2 096486 117 9271 0 1 287 0285 47 1579 105 4289 1 80152 76 88934 0 1 667 1671 55 74724 95 18958 2 817815 135 2412 1 1 239 8088 37 69644 56 38038 1 602634 70 54882 0 1 236 657 24 37133 111 3543 1 359098 69 75522 1 0 454 6683 36 76434 73 03022 1 947118 114 9644 1 1 224 4874 56 65882 96 19358 1 88464 65 10626 1 0 292 1963 32 12949 66 29087 1 608442 81 67877 1 0 344 4732 48 34929 74 32918 2 101488 93 35706 1 0 320 4522 55 6759 84 38209 1 995645 76 52719 1 0 631 6728 42 38255 72 53184 2 577334 139 8151 1 1 391 244 43 72943 75 88298 2 151205 98 27497 1 0 189 9304 52 68863 89 63605 2 037464 65 57128 0 0 255 8723 27 23261 56 99129 1 457824 75 99904 1 0 284 9516 41 80123 57 74424 1 823662 81 64516 0 0 298 0544 49 26957 79 71739 1 922332 85 49091 0 1 534 2016 51 03072 41 68642 2 665781 124 8142 1 0 309 7158 57 44121 87 36772 2 105406 82 88252 1 0 217 7654 59 37922 63 58024 1 980502 60 47619 0 0 219 4638 58 11021 64 78357 2 132143 67 19286 1 1 295 166 49 39755 84 69347 2 295485 82 92616 1 1 502 0453 28 00256 84 70343 1 922748 121 6603 1 0 233 2914 41 00962 75 80168 1 827142 73 41362 1 0 298 13 56 4989 75 94517 2 326792 91 54595 1 0 241 6571 27 93482 85 82057 1 485958 69 8702 0 0 322 0181 54 92884 85 61318 2 27614 85 04177 0 0 390 8702 42 24902 67 96817 2 158597 100 9467 1 0 274 5832 33 87353 99 50141 1 866896 89 63454 0 0 560 9427 29 33348 86 3461 2 214424 131 6181 1 0 489 0139 25 04946 64 71152 1 909358 117 4849 0 0 380 4266 36 08346 86 96472 1 940785 98 71828 0 1 276 783 55 36965 58 59159 1 973869 74 97718 0 0 319 1638 30 87773 53 35741 1 768048 92 91588 1 1 552 4554 44 16332 73 94527 2 435736 124 3933 1 1 505 2867 50 50117 92 75865 2 360093 113 6329 1 0 412 7224 58 08062 82 15201 2 389414 102 9681 0 0 551 2805 45 02203 94 3376 2 32254 120 6539 1 1 534 4761 50 29664 73 20758 2 566485 128 3474 0 0 199 4213 40 07386 50 57703 1 752941 76 27412 0 1 632 8139 57 25704 73 07877 2 838706 132 6244 0 0 293 1084 27 64301 99 89908 1 778004 80 43268 1 0 589 4725 52 2613 91 42251 2 758983 125 6487 1 0 466 9569 29 47288 102 8498 2 022633 115 6489 0 0 359 1742 24 88969 75 28108 1 617556 102 6264 0 1 394 3733 33 10341 80 2993 2 129657 102 9928 1 1 468 996 26 92117 65 80222 1 928263 115 0067 0 0 564 0708 43 36859 78 40882 2 397748 121 2804 0 0 286 8813 57 44794 71 63082 2 223449 74 90701 0 0 210 1656 53 55985 62 09999 1 742977 66 70797 1 0 208 9345 25 0457 76 01222 1 212289 64 80442 1 0 307 7878 29 10571 67 94014 1 733328 87 3616 1 0 535 0786 32 65109 69 36129 2 133093 125 525 0 0 229 0324 43 35737 75 11658 1 572178 62 02926 1 0 464 7552 43 61898 49 23377 2 295031 109 639 1 0 252 3693 41 68997 65 90237 1 804782 72 24437 0 0 388 1092 28 02215 80 21753 1 770466 101 6325 1 0 196 7853 41 55839 92 13052 1 607173 60 95563 1 0 491 3214 55 19534 52 09652 2 556813 114 4049 1 1 252 0554 49 49864 88 55398 1 676453 71 07804 0 1 460 587 50 72967 81 58124 2 282453 111 6499 1 0 593 6604 59 02279 76 21709 2 695308 130 6541 1 0 556 4768 50 52798 57 47147 2 57343 124 2894 0 1 336 9124 25 88626 85 50815 1 615467 94 54729 1 1 500 6236 42 3603 50 71911 2 173553 117 9642 0 0 423 714 58 43005 50 81912 2 557327 107 7069 0 0 306 4274 28 70915 96 85395 1 607125 89 51854 0 0 584 7336 43 55936 76 02832 2 443185 133 5605 0 0 476 3781 47 00757 86 1088 2 560757 112 3667 0 1 531 4994 40 90472 61 50392 2 239187 120 5485 1 0 483 2839 37 22283 91 08298 2 059281 119 9108 0 0 660 1603 50 02741 62 9594 2 743487 137 4227 0 0 636 0155 35 44259 72 90836 2 355967 138 3222 0 1 529 2263 37 33803 75 64752 2 306099 118 8424 0 0 441 9622 58 63371 87 16416 2 386322 104 4845 1 0 617 112 30 54897 73 0444 2 276028 136 7161 0 1 577 9182 46 00961 63 1058 2 639662 129 6019 1 0 351 2292 32 41769 66 46792 1 727186 96 2167 0 1 228 9639 45 53916 26 72356 1 809436 76 65508 0 0 606 4593 27 21596 89 54506 2 053858 132 1201 1 0 179 0654 23 58786 66 74405 1 41955 61 76651 1 0 355 1715 31 73166 83 75701 1 984796 94 26724 1 0 430 2838 20 24479 101 8641 1 701505 108 76 0 1 161 811 48 73749 74 29945 1 852205 62 52731 0 1 403 1805 36 17249 106 0237 1 864338 101 3179 0 0 195 1158 27 24591 61 41455 1 351122 73 95996 0 0 259 0605 58 60392 60 67262 2 068408 78 28863 0 0 455 6533 29 51149 60 80957 1 812264 112 2923 1 1 553 3126 59 37791 76 58117 2 834613 127 8545 0 0 244 3366 54 8724 81 27455 2 170826 74 91482 1 1 196 415 24 27811 86 28602 1 287662 70 15208 0 0 586 5408 34 01485 81 96465 2 162822 132 1419 0 1 591 0909 44 14147 90 03482 2 305924 129 4057 0 1 407 052 53 85375 59 64822 2 162778 101 1273 0 0 511 127 32 40579 73 99091 2 365751 119 1785 1 1 283 6236 37 98228 67 31715 1 66653 88 28242 1 1 541 7923 30 89861 70 39931 2 020517 123 2434 1 1 473 8109 40 55591 76 78876 2 113073 115 4309 1 0 527 3107 39 53142 98 46089 2 142508 119 7032 1 0 506 2429 54 45699 61 23065 2 671862 117 7748 1 0 289 2429 49 79364 57 89325 2 112651 85 29979 0 0 306 3213 24 84174 74 4633 1 467048 86 79296 0 1 382 1313 48 65654 80 8459 2 079431 100 712 0 0 205 4382 25 52535 58 96055 1 302249 64 19477 1 1 500 6855 29 21194 57 57206 2 118836 125 3481 1 1 416 6452 57 17961 60 6369 2 46039 105 4419 0 0 444 6098 45 46083 86 11305 2 178825 107 5155 0 1 348 236 49 98941 57 05702 2 266487 100 1933 0 0 461 6987 36 14667 78 4734 1 95715 108 4495 0 0 210 5501 53 34809 54 72168 2 128045 67 67066 1 0 501 1233 28 0849 77 25717 1 961995 118 9362 1 0 321 3859 33 21637 61 16741 1 681367 94 6376 0 0 206 2646 45 88442 94 50718 1 75694 69 21032 1 0 218 5516 35 38214 60 33813 1 586905 70 80552 0 0 266 3235 33 26248 62 82006 1 628279 77 50425 1 1 615 3389 58 03576 71 34403 2 713828 133 8127 1 1 426 2699 23 20238 68 68999 2 023627 111 6282 1 0 429 5478 23 59285 96 976 1 829281 109 1348 1 1 580 9579 37 89965 86 47272 2 406997 136 2811 0 0 397 6201 43 42886 79 20433 2 265065 105 2022 1 0 310 8039 25 64296 73 65162 1 737095 90 85758 0 1 328 0694 27 50237 92 65594 1 759227 97 70664 1 0 285 8687 27 24757 65 0358 1 639357 87 93344 1 0 185 0607 21 74266 77 44758 1 285652 66 11863 0 1 310 4224 45 64268 76 37798 1 898889 83 74436 0 0 507 8814 22 8473 84 97452 1 96599 116 4184 0 0 208 4838 21 19874 58 05136 1 416822 73 76289 1 1 227 1435 53 09154 81 70973 1 704266 60 63386 1 1 361 7541 20 1069 75 51409 1 681876 103 3546 0 0 582 0037 51 06864 89 02653 2 650948 128 1896 0 1 219 7925 29 81042 60 47251 1 56642 71 32321 1 0 312 9875 30 92498 69 93878 2 068853 98 62289 1 0 518 408 23 41632 72 59208 1 968423 123 9345 1 0 234 9582 29 068 58 25728 1 783553 80 63122 0 0 268 161 31 57237 63 75457 1 803817 86 99655 0 0 388 3586 21 8503 64 65763 1 599579 101 9453 0 0 522 5552 52 46093 71 46373 2 637381 121 3868 0 1 324 9303 26 26068 70 39762 1 578867 95 10808 0 0 184 636 56 50091 77 01239 1 893765 60 63245 1 0 475 1977 28 41243 82 92783 2 100222 120 0434 0 0 559 4499 49 5636 85 33636 2 568979 129 2784 0 0 165 3874 28 90638 85 03352 1 270085 61 94216 1 0 293 3897 36 36736 84 83061 1 921391 89 00872 0 0 220 886 39 84732 77 21089 1 767483 69 54077 1 1 532 9997 58 60824 66 48482 2 647844 117 2519 0 0 431 6794 45 5169 72 24543 2 319988 112 5714 0 0 197 0353 29 36777 71 39719 1 665667 70 19841 1 0 288 1646 20 03438 73 0777 1 532208 85 63898 1 0 218 2584 59 13752 91 55954 2 055203 63 36869 0 0 491 629 57 19681 76 52688 2 536017 115 4544 0 0 182 3493 21 39202 99 41507 1 25372 66 11747 0 0 291 2987 21 5705 84 67517 1 327713 93 54406 0 0 361 8111 50 8728 52 06964 2 339177 96 87536 0 0 517 5342 34 05929 87 1915 2 298217 120 3481 0 0 660 9858 39 62982 68 40171 2 620943 137 7167 0 0 464 0012 42 62695 81 9339 2 171427 111 9036 0 0 359 24 47 36837 78 75923 1 903016 89 0606 1 0 399 0763 33 80593 90 31385 1 976622 104 8778 0 0 429 2734 38 07047 51 69825 2 093028 114 7099 0 0 389 1214 45 00967 74 40711 2 139641 101 676 0 1 624 7511 23 17284 93 1864 2 284726 139 6047 1 0 480 9438 31 02142 79 0845 2 117702 118 8172 1 0 253 4368 49 87186 72 5475 1 809776 69 98782 1 0 261 4111 29 8043 55 31855 1 696152 76 68969 1 0 437 7035 34 62776 85 01678 2 083511 110 8894 0 1 529 8553 55 28129 66 95429 2 67181 125 6919 0 1 492 9104 48 26889 76 69677 2 436927 119 7593 0 1 332 2737 42 93988 76 26456 2 146108 96 72382 0 0 371 2736 24 79353 78 38744 1 557319 100 238 0 1 471 4423 25 54782 62 14132 2 014851 118 2827 1 1 527 2012 58 53492 66 09829 2 526183 122 2692 1 1 365 1867 52 1929 82 21154 2 196802 87 9998 1 1 275 6179 57 25207 64 51741 2 106946 78 89881 1 0 549 1918 45 65072 84 91999 2 413902 121 735 0 1 538 5858 32 28737 86 53835 2 272425 122 7882 0 0 389 973 31 70262 60 90279 1 879275 104 8817 1 0 191 0296 32 14406 79 27273 1 439133 61 80583 1 0 666 7354 51 31503 95 96992 2 831633 136 268 0 1 245 8142 57 27381 78 71473 1 85213 64 18749 0 0 487 2492 59 87893 86 48493 2 747523 112 7676 0 0 209 1078 42 56389 65 62478 1 641932 63 14791 1 0 165 6623 53 36048 42 10191 1 925056 61 20929 1 1 205 4556 50 18043 76 34813 1 831794 63 84372 1 1 223 8348 33 82007 80 78402 1 514662 67 46084 0 0 344 1339 51 80942 64 99921 2 346656 101 0105 0 0 184 3317 22 27861 67 09809 1 340122 62 34922 1 1 179 5256 44 45223 63 22006 1 690371 61 95455 1 1 251 5145 29 30738 70 96587 1 722182 81 90554 0 0 440 8954 40 87769 90 71594 2 147177 110 7865 1 0 317 4412 29 23896 58 11178 1 621534 87 57102 0 0 582 6655 32 55089 83 43363 2 487411 129 0668 1 0 573 1016 23 47974 84 10264 1 969159 128 618 1 0 607 6528 48 92747 63 22687 2 66418 131 2805 1 1 229 3135 52 45533 53 47124 1 959785 69 10699 0 1 592 5425 45 58952 98 21143 2 507087 126 2507 0 0 253 3675 28 18321 80 86156 1 390422 80 4744 1 0 181 9846 35 2269 68 78146 1 487334 62 70713 1 0 278 7405 41 4927 79 62673 1 774036 79 46657 1 1 363 6706 48 65561 79 90144 2 194706 95 26139 0 1 331 3413 46 35835 77 27916 2 20618 89 99275 1 1 220 8557 40 24681 94 12591 1 535213 72 99001 1 0 473 4872 57 35914 80 27113 2 543815 110 2131 1 1 518 6406 24 03086 80 57395 2 203409 126 1484 0 1 583 897 32 85749 68 77476 2 269697 132 1637 1 1 234 7411 38 95168 37 38252 1 558871 67 24637 0 0 598 0175 30 5867 53 19726 2 163892 136 39 0 0 436 4142 27 195 78 76108 1 840947 113 0916 1 1 264 484 49 73812 91 57204 1 816692 78 27503 0 0 615 5818 59 39518 79 7373 2 88119 129 7225 0 0 245 4083 38 65984 79 97406 1 591461 71 35863 0 1 461 0068 24 69294 83 13028 2 032626 115 4113 0 0 248 1183 37 88904 82 09892 1 756328 76 45301 1 1 234 0091 55 7126 64 88368 2 054027 71 30016 0 0 435 0718 40 02861 54 04895 2 034365 115 2513 0 1 260 1993 40 67604 102 4094 1 504665 66 56483 0 0 179 4788 38 3964 59 32694 1 735793 69 05236 0 0 612 2389 28 16768 60 88727 2 202583 135 3833 1 1 491 3588 42 4481 73 94136 2 528974 115 9934 1 0 213 8919 39 3233 94 28168 1 541986 63 13004 1 1 465 0181 37 08161 103 6084 1 993014 110 2772 0 0 333 8973 59 49344 95 46326 2 33048 83 85258 1 1 261 3698 51 88995 66 273 1 895414 74 78976 1 0 356 3648 24 50568 87 77092 1 744938 98 68967 1 0 185 0759 38 02919 117 1195 1 652796 60 73452 1 0 239 4622 49 85679 71 03027 2 103604 78 15257 1 0 652 2735 54 90536 95 18815 2 770149 134 7834 0 0 438 915 43 58 94 84549 2 338175 112 432 0 0 513 4344 48 53048 57 25838 2 439085 121 0132 1 1 347 3175 42 03997 68 39409 1 984102 97 58232 0 1 394 3844 21 05748 87 22212 1 870224 103 7914 1 1 207 227 59 31734 61 57788 1 945332 68 89716 1 0 236 1314 44 73466 52 64309 2 003203 82 73987 0 0 158 2175 38 34493 64 33476 1 495205 60 09789 0 0 456 7144 30 18209 61 26228 1 983187 113 2534 1 0 568 2868 35 36879 54 36055 2 256211 131 8307 1 0 263 8031 40 51623 41 9355 1 793952 83 40897 0 0 412 2253 29 05118 79 61919 1 848358 99 79704 1 0 242 3248 58 21371 60 8438 1 92209 71 50413 1 0 375 5499 38 98746 63 25902 2 078432 100 1136 0 0 294 6168 20 55936 58 00449 1 65418 96 85131 1 0 236 0651 35 09992 99 64692 1 349612 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 65834 69 25527 1 88588 66 30579 1 1 387 7892 41 38327 58 73126 2 021661 98 702 1 0 352 242 41 33201 60 5049 2 023383 92 09153 1 0 629 8697 49 53641 57 62319 2 579526 130 8883 1 0 211 9255 42 78193 79 43967 1 616273 72 9272 1 0 444 2875 24 72788 81 77662 1 956267 111 5442 0 0 247 7235 45 13333 71 75541 1 91779 74 3812 0 0 604 129 20 85539 101 1258 2 145581 135 5026 1 0 329 84 32 05598 66 53894 1 835762 91 09491 1 1 616 6393 29 4357 99 96769 2 21021 137 2119 0 1 234 319 33 98433 88 14674 1 715358 69 55148 0 0 383 904 23 29275 45 51246 1 656955 102 7298 1 0 495 8805 52 1379 88 31458 2 554168 116 4937 1 0 218 154 44 63422 70 16248 1 695179 69 63535 1 0 612 1445 47 31166 67 43719 2 70138 133 7826 1 0 336 5079 49 57329 75 33655 2 023782 85 05387 1 1 635 2739 38 22507 74 83942 2 458702 136 2588 0 0 331 4335 42 41811 70 64607 2 015592 91 60645 1 0 383 7525 32 1493 93 198 2 032728 100 6352 1 1 251 3554 58 1917 70 09807 2 024557 72 01982 1 0 341 2051 43 41333 89 12121 1 905565 93 87471 0 1 275 0494 52 75969 52 17289 2 09037 82 88004 1 0 535 565 52 70178 81 0757 2 644317 120 399 0 0 391 1913 34 489 69 6521 2 217542 108 0581 1 1 549 9505 48 60402 68 94334 2 53828 122 4178 1 0 606 6333 29 15903 79 05621 2 279036 134 7553 1 1 601 9474 20 25368 44 52381 1 983521 136 8536 0 1 260 1661 31 376 90 01012 1 655521 76 64219 0 1 323 5212 40 5702 79 92162 2 051327 93 10634 0 1 462 5386 39 50515 56 60424 2 245858 115 5482 1 0 228 3234 39 10223 79 10409 1 71121 71 44215 0 0 332 2975 43 39788 53 27683 2 163755 91 65652 1 0 340 469 43 62495 92 91031 2 093735 90 73667 1 0 607 9529 24 70909 67 43448 2 259047 133 0913 1 0 569 3044 37 48834 78 24693 2 335484 124 6204 1 0 460 7661 50 78744 86 78591 2 375415 112 6548 0 0 549 62 30 99006 73 75456 2 35057 130 9412 0 1 261 5383 47 2924 67 7223 1 93131 80 79171 1 0 375 0613 49 99353 64 52515 2 386245 94 61713 1 0 650 6216 58 71063 89 54144 2 707012 135 6512 0 1 560 1854 53 79121 66 5163 2 624556 126 2947 1 1 481 2924 31 20407 73 36034 2 159348 119 1123 0 0 272 1115 25 0694 68 16841 1 469429 77 49483 1 0 541 5704 40 17361 80 81219 2 252332 118 0459 1 0 430 4141 22 71805 81 75524 1 90897 111 0819 1 1 363 1709 30 22041 98 38933 1 854813 98 73354 1 0 401 4356 25 32973 63 86533 1 803943 107 6612 0 0 567 0531 28 41285 82 00659 2 053016 124 8068 0 0 294 1176 41 82287 69 10052 1 757079 82 11218 1 0 422 8166 34 86614 68 91631 2 154816 106 817 0 1 272 5332 39 34002 70 85822 2 026042 81 51708 1 1 583 0293 41 61404 51 94482 2 445242 134 3968 0 0 231 1914 47 6334 78 53961 1 907242 65 3344 0 1 267 5091 50 97471 71 61985 1 993963 81 41038 0 0 640 9397 48 19837 103 3804 2 771806 137 4277 1 1 629 0547 28 12662 73 17316 2 292549 139 7309 1 0 445 3906 48 68474 75 76429 2 334505 103 3762 1 1 236 1816 41 80267 73 98476 1 80446 76 92672 1 1 276 6943 39 13435 46 97722 1 794128 84 00911 0 0 563 7312 37 65048 78 89276 2 388105 132 3322 1 0 154 0053 29 60864 53 55719 1 579685 62 06738 0 0 242 9147 53 84503 81 07044 1 864951 76 03538 0 0 151 5343 32 49192 60 17273 1 331783 62 63677 0 1 288 6217 47 04877 84 55572 1 92288 80 19149 0 1 597 7821 44 49163 48 70433 2 539036 133 2377 1 1 228 7271 38 13719 72 15491 1 579662 73 83631 1 0 234 1121 51 89688 65 31121 1 89458 69 75752 0 1 486 3386 34 47597 92 82831 2 115087 114 8437 0 0 396 684 32 46323 95 77665 1 71428 100 3631 1 1 291 6509 53 77924 87 15206 2 107563 76 92565 1 1 235 2675 44 73898 69 62036 1 709571 78 67671 1 0 663 8794 59 27984 112 5189 2 80998 133 322 0 1 322 928 32 79061 102 333 1 80477 91 14359 0 1 466 8221 26 30663 76 67884 2 282608 118 5557 0 1 429 6588 46 36326 83 16863 2 34067 106 038 1 0 271 3378 53 74383 73 40252 1 928805 71 98858 1 1 490 3084 44 49828 91 2119 2 390269 110 9431 0 0 258 0186 58 98215 97 85954 2 087859 67 4771 1 0 376 4131 39 27695 97 09071 1 885295 96 79437 0 1 429 8774 29 98202 70 17959 1 985514 109 4631 1 1 407 6626 35 34453 78 0786 2 079128 104 9825 1 0 265 0717 38 15159 60 98077 1 814037 84 08111 1 0 487 3352 42 92333 75 08095 2 132557 112 4944 1 1 291 3229 38 6926 86 61328 1 941424 82 75345 0 0 623 4842 32 25954 60 00927 2 303092 131 9513 0 0 254 0748 21 34624 93 28283 1 440

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Jun 20, 2024

Scenario: 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

Scenario: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: Movieii'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 ininflation adjusted termsso we can compare movie revenue without having to worry about changes in the price level.

X1iX1i: Production Budget of Movieiiin millions of USD.

X2iX2i: Critical review of Movieiifrom Rotten Tomatoes (range: 0-100).

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

X4iX4i:Star Powerof Movieii. This is a relative measure that determines the overall caliber of movie stars in the cast. A high number forStar Powermeans that Movieiihas 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 Audienceof Movieii. This is a dummy variable that equals 1 if Movieiiis based off of a book or is a sequel to another movie (zero otherwise).

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

1.(10 pts) Test your independent variables (X1iX1ithroughX6iX6i) 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.(10 pts) 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.(10 pts) 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.(15 pts) Using your results from question 3, answer the following questions.

a.What is theR2R2value? 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.

Question

Scenario: 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

Step by Step Solution

Step: 1

Get Instant Access to Expert-Tailored Solutions

Step: 2

Step: 3

Ace Your Homework with AI

Recommended Textbook for

Introductory Real Analysis

Students also viewed these Mathematics questions

Question

Question

Question

Question

Question

Question

Question

Question

Question

Question

Question

Question

Question

Question

Question

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