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In: Statistics and Probability

11.30  A simpler model. In the multiple regression analysis using all four explanatory variables, Theaters and...

11.30  A simpler model. In the multiple regression analysis using all four explanatory variables, Theaters and Budget appear to be the least helpful (given that the other two explanatory variables are in the model).

  1. (a) Perform a new analysis using only the movie’s opening-weekend revenue and IMDb rating. Give the estimated regression equation for this analysis.

  2. (b) What percent of the variability in USRevenue is explained by this model?

  3. (c) Test the null hypothesis that Theaters and Budget combined add no additional predictive information beyond what is already contained in Opening and Opinion?

All Data required is BELOW:

Title USRelease Genre Rating Sequel Budget Opening Theaters USRevenue IntRevenue WorldRevenue Ratings Hype Minutes
Inception ######### Action/Adventure PG-13 0 160 62.79 3792 292.6 524.5 817.1 8.8 33 148
Easy A ######### Comedy/Romance PG-13 0 8 17.73 2856 58.4 13.1 71.5 7.2 23 92
The Last Airbender ######### Action/Adventure PG 0 150 16.35 3169 131.6 185.5 317.1 4.4 15 103
Scott Pilgrim vs. the World ######### Comedy/Romance PG-13 0 60 10.61 2818 31.5 15.3 46.8 7.5 96 112
Step Up 3D ######### Drama/Romance PG-13 1 30 15.81 2435 42.4 119.0 161.4 6.6 110 107
Prince of Persia: The Sands of Time ######### Action/Adventure PG-13 0 200 37.81 3646 90.8 236.4 327.2 6.6 92 116
2012 ######### Action/Adventure PG-13 0 200 65.24 3404 166.1 600.7 766.8 5.8 6 158
Star Trek ######### Action/Adventure PG-13 1 140 75.20 3849 257.7 125.0 382.7 8.0 23 127
Despicable Me ######### Animation PG 0 69 56.40 3476 251.5 292.0 543.5 7.7 157 95
Wall Street: Money Never Sleeps ######### Drama PG-13 1 70 19.01 3565 52.5 83.6 136.1 6.3 68 133
Invictus ######### Drama PG-13 0 60 8.61 2125 37.5 87.0 124.5 7.4 30 134
The Twilight Saga: New Moon ######### Adventure/Drama PG-13 1 50 142.84 4024 296.6 413.2 709.8 4.6 3 130
Tooth Fairy ######### Comedy PG 0 48 14.01 3344 60.0 52.6 112.6 5.0 643 101
Charlie St. Cloud ######### Drama/Romance PG-13 0 44 12.38 2718 31.1 16.5 47.6 6.4 64 99
Bruno ######### Comedy R 0 42 30.62 2756 60.0 77.8 137.8 6.0 36 81
Tangled ######### Animation PG 0 260 48.77 3603 200.8 391.0 591.8 7.9 320 100
Cats and Dogs: The Revenge of Kitty Galore ######### Comedy PG 1 85 12.28 3705 43.6 60.3 103.9 4.7 561 82
He's Just Not That Into You ######### Comedy/Romance PG-13 0 40 27.80 3175 94.0 72.4 166.4 6.4 21 129
The Karate Kid ######### Action/Drama PG 1 40 55.67 3663 176.6 166.6 343.2 6.2 95 140
The Ugly Truth ######### Comedy/Romance R 0 38 27.61 2882 88.9 114.2 203.1 6.7 39 96
Underworld:Rise of the Lycans ######### Action/Adventure R 1 35 20.83 2942 45.8 43.3 89.1 6.6 52 92
The Hangover ######### Comedy R 0 35 44.98 3269 277.3 184.3 461.6 7.8 38 100
Paul Blart: Mall Cop ######### Comedy PG 0 26 31.83 3144 146.3 32.5 178.8 5.2 370 91
My Soul to Take ######### Horror R 0 25 6.84 2572 14.6 0.0 14.6 4.7 286 107
Up in the Air ######### Drama/Romance R 0 25 26.30 1895 83.8 76.7 160.5 7.5 15 109
Men Who Stare at Goats ######### Comedy R 0 25 12.71 2443 32.4 34.5 66.9 6.3 103 94
Dear John ######### Drama PG-13 0 25 30.47 2969 80.0 14.7 94.7 6.3 20 108
Jackass 3D ######### Comedy R 1 20 50.35 3081 117.2 47.3 164.5 7.1 106 95
17 Again ######### Comedy PG-13 0 20 23.72 3255 64.1 64.5 128.6 6.4 49 102
Vampires Suck ######### Comedy PG-13 0 20 18.57 3233 36.7 43.3 80.0 3.5 6 82
Saw 3D: The Final Chapter ######### Horror R 1 20 24.23 2808 45.7 85.0 130.7 5.6 75 90
Fame ######### Drama PG 1 18 10.01 3096 22.5 4.3 26.8 4.9 145 107
The Expendables ######### Action/Adventure R 0 80 34.83 3270 103.0 171.4 274.4 6.5 12 103
Inglourious Bastards ######### Adventure/Drama R 0 75 38.05 3165 120.5 200.1 320.6 8.3 13 153
Watchmen ######### Action R 0 130 55.21 3611 107.5 73.5 181.0 7.6 2 162
X-Men Origins: Wolverine ######### Action/Adventure PG-13 1 150 85.06 4099 179.9 195.0 374.9 6.7 17 107
Jennifer's Body ######### Comedy/Horror R 0 16 6.87 2702 16.2 16.5 32.7 5.1 8 102
Zombieland ######### Comedy/Horror R 0 24 24.73 3036 75.6 24.3 99.9 7.7 63 88
(500) Days of Summer ######### Comedy/Romance PG-13 0 7.5 12.36 1195 32.4 27.2 59.6 7.8 20 95
Friday the 13th ######### Horror R 1 19 43.59 3105 65.0 23.8 88.8 5.6 39 97
How To Train Your Dragon ######### Animation PG 0 165 43.73 4055 217.4 277.5 494.9 8.2 135 98
Hot Tub Time Machine ######### Comedy R 0 36 14.02 2754 50.2 8.0 58.2 6.5 198 101
Red ######### Action/Comedy PG-13 0 58 21.76 3255 90.4 74.6 165.0 7.1 50 111

Solutions

Expert Solution

(a) Perform a new analysis using only the movie’s opening-weekend revenue and IMDb rating. Give the estimated regression equation for this analysis.

Opening Ratings
6279 88
1773 72
1635 44
1061 75
1581 66
3781 66
6524 58
7520 80
5640 77
1901 63
r² 0.194
r   0.440
Std. Error   11.839
n   10
k   1
Dep. Var. Ratings
ANOVA table
Source SS   df   MS F p-value
Regression 269.70 1   269.6969 1.92 .2028
Residual 1,121.20 8   140.1504
Total 1,390.90 9  
Regression output confidence interval
variables coefficients std. error    t (df=8) p-value 95% lower 95% upper
Intercept 60.5986
Opening 0.0022 0.0016 1.387 .2028 -0.0015 0.0059

The estimated regression equation is:

Ratings = 60.5986 + 0.0022*Opening

(b) What percent of the variability in USRevenue is explained by this model?

19.4%

(c) Test the null hypothesis that Theaters and Budget combined add no additional predictive information beyond what is already contained in Opening and Opinion?

The p-value is 0.2222.

Therefore, we can conclude that Theaters and Budget combined add no additional predictive information beyond what is already contained in Opening and Opinion.

Title USRelease Genre Rating Sequel Budget Opening Theaters USRevenue IntRevenue WorldRevenue Ratings Hype Minutes
Inception ######## Action/Adventure PG-13 0 160 6279 3792 2926 5245 8171 88 33 148
Easy A ######## Comedy/Romance PG-13 0 8 1773 2856 584 131 715 72 23 92
The Last Airbender ######## Action/Adventure PG 0 150 1635 3169 1316 1855 3171 44 15 103
Scott Pilgrim vs. the World ######## Comedy/Romance PG-13 0 60 1061 2818 315 153 468 75 96 112
Step Up 3D ######## Drama/Romance PG-13 1 30 1581 2435 424 1190 1614 66 110 107
Prince of Persia: The Sands of Time ######## Action/Adventure PG-13 0 200 3781 3646 908 2364 3272 66 92 116
2012 ######## Action/Adventure PG-13 0 200 6524 3404 1661 6007 7668 58 6 158
Star Trek ######## Action/Adventure PG-13 1 140 7520 3849 2577 1250 3827 80 23 127
Despicable Me ######## Animation PG 0 69 5640 3476 2515 2920 5435 77 157 95
Wall Street: Money Never Sleeps ######## Drama PG-13 1 70 1901 3565 525 836 1361 63 68 133

orchestra answered 1 year ago
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