In: Statistics and Probability
To study how social media may influence the products consumers buy, researchers collected the opening weekend box office revenue (in millions of dollars) for 23 recent movies and the social media message rate (average number of messages referring to the movie per hour). The data are available below. Conduct a complete simple linear regression analysis of the relationship between revenue (y) and message rate (x).
Message Rate |
Revenue ($millions) |
||
---|---|---|---|
1363.2 |
146 |
||
1219.2 |
79 |
||
681.2 |
67 |
||
583.6 |
37 |
||
454.7 |
35 |
||
413.9 |
34 |
||
306.2 |
21 |
||
289.8 |
18 |
||
245.1 |
18 |
||
163.9 |
17 |
||
148.9 |
16 |
||
147.4 |
15 |
||
147.3 |
15 |
||
123.6 |
14 |
||
118.1 |
13 |
||
108.9 |
13 |
||
100.1 |
12 |
||
90.3 |
11 |
||
89.1 |
6 |
||
70.1 |
6 |
||
56.2 |
5 |
||
41.6 |
3 |
||
8.4 |
1 |
The least squares regression equation is ModifyingAbove y with caret=________+ ( _______ )x. (Round to three decimal places as needed.) |
|||
PrintDone
Message Rate (X) | Revenue ($millions) (Y) | X * Y | X^2 | |
1363.2 | 146 | 199027.2 | 1858314.24 | |
1219.2 | 79 | 96316.8 | 1486448.64 | |
681.2 | 67 | 45640.4 | 464033.44 | |
583.6 | 37 | 21593.2 | 340588.96 | |
454.7 | 35 | 15914.5 | 206752.09 | |
413.9 | 34 | 14072.6 | 171313.21 | |
306.2 | 21 | 6430.2 | 93758.44 | |
289.8 | 18 | 5216.4 | 83984.04 | |
245.1 | 18 | 4411.8 | 60074.01 | |
163.9 | 17 | 2786.3 | 26863.21 | |
148.9 | 16 | 2382.4 | 22171.21 | |
147.4 | 15 | 2211 | 21726.76 | |
147.3 | 15 | 2209.5 | 21697.29 | |
123.6 | 14 | 1730.4 | 15276.96 | |
118.1 | 13 | 1535.3 | 13947.61 | |
108.9 | 13 | 1415.7 | 11859.21 | |
100.1 | 12 | 1201.2 | 10020.01 | |
90.3 | 11 | 993.3 | 8154.09 | |
89.1 | 6 | 534.6 | 7938.81 | |
70.1 | 6 | 420.6 | 4914.01 | |
56.2 | 5 | 281 | 3158.44 | |
41.6 | 3 | 124.8 | 1730.56 | |
8.4 | 1 | 8.4 | 70.56 | |
Total | 6970.8 | 602 | 426457.6 | 4934795.8 |
Equation of regression line is
b = 0.0865
a = -0.0309
Equation of regression line becomes
Equation of regression line becomes