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 mediamessage rate​(average number of messages referring to the movieper​ hour). The data are available below. Conduct a complete simplelinear 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 y=−0.031+l0.086x.​(Round to three decimal places as​ needed.)
Check the usefulness of the hypothesized model. What are thehypotheses to​ test?
A.H0​: β1≠0 against Ha​:β1=0
B.H0​β0:=0 againstHa​:β0≠0
C.H0​:β0≠0 against Ha​:β0=0
D.H0​:β1=0 againstHa​:β1≠0 Your answer is correct.
Determine the estimate of the standard deviation.
s=9.59 ​(Round to two decimal places as​ needed.)
What is the test statistic for the​ hypotheses?
t=15.14 ​(Round to two decimal places as​ needed.)
What is the​ p-value for the test​ statistic?
​p-value=0​(Round to three decimal places as​ needed.)State theconclusion at α=0.05.
Since the​ p-value is less than α​, there is sufficient evidenceto reject H0.
Conclude there is
a linear relationship between revenue and message rate.What isthe value for the coefficient of determination
r2​?
r2=0.92 ​(Round to two decimal places as​ needed.)Interpret thevalue of r2 in the context of this problem.
A.r2 is the proportion of the total sample variability aroundmessage rate that is explained by the linear relationship betweenthe revenue and the message rate.
B.r2 is the proportion of the sample points that do not fitwithin the​ 95% confidence interval.
C. r2 is the proportion of the sample points that fit on theestimated linear regression line.
D.r2 is the proportion of the total sample variability aroundmean revenue that is explained by the linear relationship betweenthe revenue and the message rate.
