Question

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...

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.?

Solutions

Expert Solution

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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