Question
In: Statistics and Probability
To study how social media may influence the products consumers buy, researchers collected the opening weekend...
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)
1363.3 148
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
Solutions
Expert Solution
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.893045 | |||||||
| R Square | 0.797529 | |||||||
| Adjusted R Square | 0.787887 | |||||||
| Standard Error | 14.73495 | |||||||
| Observations | 23 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 1 | 17959.72 | 17959.72 | 82.71844 | 9.93E-09 | |||
| Residual | 21 | 4559.494 | 217.1187 | |||||
| Total | 22 | 22519.22 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 2.119965 | 4.06647 | 0.521328 | 0.607593 | -6.33672 | 10.57665 | -6.33672 | 10.57665 |
| Message_Rate | 0.079935 | 0.008789 | 9.094968 | 9.93E-09 | 0.061657 | 0.098212 | 0.061657 | 0.098212 |
-
The least square regression line is:
y' = 2.12 + 0.0799x
Calculation:
| x | y | (x-xbar)^2 | (y-ybar)^2 | (x-xbar)*(y-ybar) | |
| 1363.3 | 148 | 1124033.3 | 14799.251 | 128976.1637 | |
| 1214.8 | 74 | 831204.82 | 2270.7297 | 43444.69414 | |
| 575.9 | 64 | 74422.212 | 1417.6862 | 10271.67675 | |
| 311.3 | 36 | 67.311323 | 93.164461 | 79.18979206 | |
| 458.1 | 35 | 24026.348 | 74.860113 | 1341.124575 | |
| 293.2 | 34 | 97.923932 | 58.555766 | -75.72325142 | |
| 248.3 | 25 | 3002.5635 | 1.8166352 | 73.85500945 | |
| 679.5 | 18 | 141680.23 | 69.6862 | -3142.158034 | |
| 151.7 | 17 | 22920.643 | 87.381853 | 1415.220227 | |
| 169.6 | 17 | 17821.089 | 87.381853 | 1247.89414 | |
| 109.7 | 16 | 37401.878 | 107.0775 | 2001.224575 | |
| 144.3 | 16 | 25216.059 | 107.0775 | 1643.189792 | |
| 410.2 | 15 | 11471.341 | 128.77316 | -1215.401512 | |
| 93.4 | 15 | 43972.267 | 128.77316 | 2379.589792 | |
| 104.2 | 15 | 39559.48 | 128.77316 | 2257.03327 | |
| 121.8 | 14 | 32868.113 | 152.46881 | 2238.607183 | |
| 70.7 | 13 | 54007.739 | 178.16446 | 3101.976749 | |
| 81.3 | 12 | 49193.311 | 205.86011 | 3182.285444 | |
| 127.6 | 6 | 30798.724 | 414.03403 | 3570.955009 | |
| 52.2 | 6 | 62948.628 | 414.03403 | 5105.181096 | |
| 149.6 | 5 | 23560.915 | 455.72968 | 3276.798488 | |
| 36.3 | 3 | 71179.92 | 545.12098 | 6229.098488 | |
| 4.2 | 2 | 89338.611 | 592.81664 | 7277.459357 | |
| sum | 6971.2 | 606 | 2810793.4 | 22519.217 | 224679.9348 |
| mean | 303.0956522 | 26.34782609 | sxx | syy | sxy |
| slope=b1=sxy/sxx | 0.079934703 | |
| intercept=b0=ybar-(slope*xbar) | 2.119965151 | |
| SST | SYY | 22519.217 |
| SSR | sxy^2/sxx | 17959.724 |
| SSE | syy-sxy^2/sxx | 4559.4935 |
| r^2 | SSR/SST | 0.7975288 |
| error variance s^2 | SSE/(n-2) | 1519.8312 |
| S^2b1 | s^2/sxx | 0.0005407 |
| standard error b1=se(b1) | sqrt(s^2b1) | 0.0232532 |
| test statistics | b1/se(b1) | 3.4375748 |
__________________________________________________________________________________
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orchestra answered 2 years agoRelated Solutions
To study how social media may influence the products consumers buy, researchers collected the opening weekend...
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).
Click the icon to view the data.
Message_Rate Revenue_($millions)
1369.4 145
1217.5 76
575.9 70...
To study how social media may influence the products consumers buy, researchers collected the opening weekend...
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 ($millions)
1363.2
146
1219.2
79
681.2
67
583.6
37
454.7
35
413.9
34...
To study how social media may influence the products consumers buy, researchers collected the opening weekend...
To study how social media may influence the products consumers
buy, researchers collected the opening weekend box office revenue
(in millions of dollars) for 23 recent movies and the social media
message rate (average number of messages referring to the movie
per hour). The data are available below. Conduct a complete simple
linear regression analysis of the relationship between revenue (y)
and message rate (x).
Message Rate
Revenue ($millions)
1363.2
146
1219.2
79
681.2
67
583.6
37
454.7
35
413.9...
please!!!!!!!!!!!!!1 To study how social media may influence the products consumers buy, researchers collected the opening...
please!!!!!!!!!!!!!1
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).
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