In: Statistics and Probability
Message_Rate Revenue_($millions)
1363.3 148
1214.8 74
575.9 64
311.3 36
458.1 35
293.2 34
248.3 25
679.5 18
151.7 17
169.6 17
109.7 16
144.3 16
410.2 15
93.4 15
104.2 15
121.8 14
70.7 13
81.3 12
127.6 6
52.2 6
149.6 5
36.3 3
4.2 2
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).
Determine the estimate of the standard deviation.?
The independent variable is Message Rate, and the dependent variable is Revenue. In order to compute the regression coefficients, the following table needs to be used:
Message_Rate |
Revenue |
Message_Rate*Revenue |
Message_Rate2 |
Revenue2 |
|
1363.3 |
148 |
201768.4 |
1858586.89 |
21904 |
|
1214.8 |
74 |
89895.2 |
1475739.04 |
5476 |
|
575.9 |
64 |
36857.6 |
331660.81 |
4096 |
|
311.3 |
36 |
11206.8 |
96907.69 |
1296 |
|
458.1 |
35 |
16033.5 |
209855.61 |
1225 |
|
293.2 |
34 |
9968.8 |
85966.24 |
1156 |
|
248.3 |
25 |
6207.5 |
61652.89 |
625 |
|
679.5 |
18 |
12231 |
461720.25 |
324 |
|
151.7 |
17 |
2578.9 |
23012.89 |
289 |
|
169.6 |
17 |
2883.2 |
28764.16 |
289 |
|
109.7 |
16 |
1755.2 |
12034.09 |
256 |
|
144.3 |
16 |
2308.8 |
20822.49 |
256 |
|
410.2 |
15 |
6153 |
168264.04 |
225 |
|
93.4 |
15 |
1401 |
8723.56 |
225 |
|
104.2 |
15 |
1563 |
10857.64 |
225 |
|
121.8 |
14 |
1705.2 |
14835.24 |
196 |
|
70.7 |
13 |
919.1 |
4998.49 |
169 |
|
81.3 |
12 |
975.6 |
6609.69 |
144 |
|
127.6 |
6 |
765.6 |
16281.76 |
36 |
|
52.2 |
6 |
313.2 |
2724.84 |
36 |
|
149.6 |
5 |
748 |
22380.16 |
25 |
|
36.3 |
3 |
108.9 |
1317.69 |
9 |
|
4.2 |
2 |
8.4 |
17.64 |
4 |
|
Sum = |
6971.2 |
606 |
408355.9 |
4923733.8 |
38486 |
Based on the above table, the following is calculated:
Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:
Therefore, we find that the regression equation is:
the estimate of the standard deviation=
= 0.01953
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