A company that holds the DVD distribution rights to movies previously released o
ID: 3219788 • Letter: A
Question
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, r2, and interpret its meaning.
r2=
(Round to four decimal places as needed.)
Interpret the meaning of r2. Choose the correct answer below.
(Round to two decimal places as needed.)
The value of r2 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.
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
Explanation / Answer
From the formula for r2,
R2 is calculated as
r = sqrt(0.5640)= 0.75
The value of r2 indicates that _56.4___% of the variation in ____ DVD revenues can be explained by the variation in box office gross)
b)
C) The correct answer is D. It is somewhat useful for predicting DVD revenue because the coefficient of determination is closer to 1 than it is to 0.
D) A,B,C,D could be possible answers to this question.
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