A company that holds the DVD distribution rights to movies previously released only in theaters wants to estimate sales revenue of DVDs based on box office success. The box office gross (in $millions) for each of 22 movies in the year that they were released and the DVD revenue (in $millions) in the following year are shown in the accompanying table, along with the summary statistics. A linear regression was performed on this data, and the result is the linear regression equation Yi = 11.361 + 0.3737X.
Movie Gross (X) DVD Revenue (Y) X^2 Y^2 XY
1 113.36 79.09 12850.4896 6255.2281 8965.6424
2 178.11 105.61 31723.1721 11153.4721 18810.1971
3 165.77 49.54 27479.6929 2454.2116 8212.2458
4 92.56 60.24 8567.3536 3628.8576 5575.8144
5 107.39 61.64 11532.6121 3799.4896 6619.5196
6 87.25 55.29 7612.5625 3056.9841 4824.0525
7 84.79 49.51 7189.3441 2451.2401 4197.9529
8 69.93 39.58 4890.2049 1566.5764 2767.8294
9 85.44 46.19 7299.9936 2133.5161 3946.4736
10 102.94 36.55 10596.6436 1335.9025 3762.457
11 33.19 30.43 1101.5761 925.9849 1009.9717
12 148.38 30.53 22016.6244 932.0809 4530.0414
13 58.96 26.85 3476.2816 720.9225 1583.076
14 49.84 28.75 2484.0256 826.5625 1432.9
15 58.95 25.71 3475.1025 661.0041 1515.6045
16 52.39 29.59 2744.7121 875.5681 1550.2201
17 78.92 40.91 6228.3664 1673.6281 3228.6172
18 42.45 29.44 1802.0025 866.7136 1249.728
19 41.08 16.77 1687.5664 281.2329 688.9116
20 35.49 18.82 1259.5401 354.1924 667.9218
21 44.08 23.02 1943.0464 529.9204 1014.7216
22 15.23 18.59 231.9529 345.5881 283.1257
Totals 1746.5 902.65 178192.866 46828.8767 86437.0243
a. Determine the coefficient of determination, r^2, and interpret its meaning.
r^2 =
(Round to four decimal places as needed.)
Interpret the meaning of r^2. Choose the correct answer below.
(Round to two decimal places as needed.)
The value of r^2 indicates that ____% of the variation in ____
(DVD revenues OR box office gross) can be explained by the
variation in ___(DVD revenues OR box office gross)
b. Determine the standard error of the estimate.
SYX =
(Round to four decimal places as needed.)
c. How useful do you think this regression model is for predicting DVD revenue?
A. It is not useful for predicting DVD revenue because the coefficient of determination is close to 0.
B. It is very useful for predicting DVD revenue because the coefficient of determination is very close to 1.
C. It is not useful for predicting DVD revenue because the coefficient of determination is close to 1.
D. It is somewhat useful for predicting DVD revenue because the coefficient of determination is closer to 1 than it is to 0.
d. Can you think of other variables that might explain the variation in DVD revenue? (multiple choice)
A. Another variable could be the time of year when the movie was released in theaters.
B. Another variable could be the amount of money spent on marketing the DVD release.
C. Another variable could be the time of year when the DVD was released.
D. Another variable could be the genre of movie.
E. Another variable could be the amount of money spent on marketing the theater release.