Question

A box office analyst seeks to predict opening weekend box office gross for movies. Toward this​ goal, the analyst plans to use online trailer views as a predictor. For each of the 66 ​movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross​ (in millions of​ dollars) are collected and stored in the accompanying table. A linear regression was performed on these​ data, and the result is the linear regression equation: Yi=-0.843+1.4100Xi Complete parts​ (a) through​ (d).

a. Determine the coefficient of​ determination,r squared​, and interpret its meaning.

r squared= _______​(Round to three decimal places as​ needed.)

Interpret the meaning of r squared.

The value of r squared indicates that ____% of the variation in _____ (online trailer reviews or box office gross) can be explained by the variation in______(online trailer reviews. or box office gross.) ​(Round to one decimal place as​ needed.)

b. Determine the standard error of the estimate.

Syx=_______ ​(Round to two decimal places as​ needed.)

c. How useful do you think this regression model is for predicting opening weekend box office​ gross?

A. It is not useful for predicting box office gross because the coefficient of determination is close to 0.

B. It is not useful for predicting box office gross because the coefficient of determination is close to 1.

C.It is very useful for predicting box office gross because the coefficient of determination is very close to 1.

D.It is somewhat useful for predicting box office gross 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 opening weekend box office​ gross? Select all that apply.

A.The amount spent on advertising might explain the variation in opening weekend box office​ gross, because viewers are probably more likely to watch a movie that has been advertised heavily.

B.The timing of the release of the movie might explain the variation in opening weekend box office​ gross, because a movie released at the same time as multiple other major movies may get crowded out.

C.The type of movie might explain the variation in opening weekend box office​ gross, since some genres are more heavily attended than others.

Data Table

Online Trailer Views (millions)	Opening Weekend Box Office Gross ($millions)
60.353	33.402
12.595	7.514
11.673	5.285
8.69	22.957
85.963	103.634
34.641	65.484
20.074	19.111
7.751	12.278
2.601	3.466
47.792	35.408
8.737	19.85
27.256	14.924
5.355	1.113
57.884	148.476
5.655	10.251
11.71	9.522
9.723	1.346
2.511	4.388
1.008	1.872
5.259	7.37
7.221	5.622
8.849	1.686
32.008	95.005
0.391	4.822
2.932	14.858
10	13.592
52.747	49.905
4.299	3.257
28.31	22.168
6.516	5.009
13.781	15.777
58.961	42.714
77.439	176.85
7.021	4.09
33.808	63.369
2.898	15.706
41.91	86.158
4.989	4.69
6.63	33.377
0.942	3.705
2.258	1.513
11.327	18.47
8.966	12.202
15.177	4.357
13.714	30.436
31.231	53.003
52.612	46.607
16.235	13.003
6.884	3.776
11.698	18.223
2.827	3.471
23.075	13.602
12.606	40.011
0.826	1.385
27.536	20.13
7.273	3.404
3.323	1.207
4.267	10.951
3.79	8.344
7.597	11.614
12.912	13.501
7.067	5.106
5.02	1.985
7.739	22.8
16.795	13.689
7.643	2.08

Answer 1

Solution:

We can use the excel regression data analysis tool to find the answers to the given questions. The excel output is given below:

a. Determine the coefficient of​ determination,r squared​, and interpret its meaning.

r squared= 0.663

Interpret the meaning of r squared.

The value of r squared indicates that 66.3% of the variation in box office gross can be explained by the variation in online trailer reviews.

b. Determine the standard error of the estimate.

Syx=19.66 ​(Round to two decimal places as​ needed.)

c. How useful do you think this regression model is for predicting opening weekend box office​ gross?

Answer: D. It is somewhat useful for predicting box office gross 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 opening weekend box office​ gross? Select all that apply.

Answer:

A. The amount spent on advertising might explain the variation in opening weekend box office​ gross, because viewers are probably more likely to watch a movie that has been advertised heavily.

B. The timing of the release of the movie might explain the variation in opening weekend box office​ gross, because a movie released at the same time as multiple other major movies may get crowded out.