Movie studios spend much effort trying to predict how much money their movies wi
ID: 3319371 • Letter: M
Question
Movie studios spend much effort trying to predict how much money their movies will make. One possible predictor is the amount of money spent on the production of the movie. In the Excel table “Question 2” you can see the budget and the amount of money made worldwide for the 13 movies with the highest profit up through 2007. The budget and gross are in millions of dollars.
(a) Run the simple linear regression analysis
(b) Report the correlation coefficient and the coefficient of determination. Explain what the latter means.
(c) Find and report the regression line.
(d) Find the predicted number of gross for an upcoming movie if the movie has a production budget of 500 million.
Release Date Movie Budget (in Mil) (X) Gross (in Mil) (Y) 12/19/97 Titanic 200 1848.813795 12/17/03 The Lord of the Rings: The Return of the King 94 1133.027325 6/11/93 Jurassic Park 63 920.1 5/25/77 Star Wars Ep. IV: A New Hope 11 797.9 5/19/04 Shrek 2 70 915.278586 6/11/82 ET: The Extra-Terrestrial 10.5 792.910554 7/7/06 Pirates of the Caribbean: Dead Man's Chest 150 1065.659812 12/18/02 The Lord of the Rings: The Two Towers 94 926.284377 11/16/01 Harry Potter and the Sorcerer's Stone 125 976.457891 5/19/99 Star Wars Ep. I: The Phantom Menace 115 924.288297 11/15/02 Harry Potter and the Chamber of Secrets 100 878.98788 5/30/03 Finding Nemo 94 866.592978 7/3/96 Independence Day 75 817.400878 5/25/07 Pirates of the Caribbean: At World's End 150 952.420425 12/19/01 The Lord of the Rings: The Fellowship of the Ring 109 868.621686 7/11/07 Harry Potter and the Order of the Phoenix 150 938.468864 5/23/97 The Lost World: Jurassic Park 75 786.686679 7/18/08 The Dark Knight 185 997.037655 6/15/94 The Lion King 79.3 783.839505 5/19/05 Star Wars Ep. III: Revenge of the Sith 115 848.999005Explanation / Answer
b)
r=0.6392
r^ 2 = 0.40858
this means 40.86 % of variation in y is explained by this model
c) y^ = 641.6822 + 3 *x
d)
y^ = 641.6822 + 3 *500 = 2141.6822
SUMMARY OUTPUT Regression Statistics Multiple R 0.639204151 R Square 0.408581947 Adjusted R Square 0.375725388 Standard Error 182.1259502 Observations 20 ANOVA df SS MS F Significance F Regression 1 412477.9743 412477.9743 12.43532389 0.002411257 Residual 18 597057.5115 33169.86175 Total 19 1009535.486 Coefficients Standard Error t Stat P-value Lower 95% Intercept 641.682259 96.96272436 6.617824151 3.26082E-06 437.9711343 Budget (in Mil) (X) 3.005681428 0.852342997 3.526375461 0.002411257 1.2149752Related Questions
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