To study how social media may influence the productsconsumers? buy, researchers collected the opening weekend boxoffice revenue? (in millions of? dollars) for 23 recentmovies and the social media message rate?(average number ofmessages referring to the movie per? hour). The data areavailable below. Conduct a complete simple linear regressionanalysis of the relationship between revenue? (y) and messagerate? (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?: ?1?0 against Ha?:?1=0

B.H0??0:=0 againstHa?:?0?0

C.H0?:?0?0 against Ha?:?0=0

D.H0?:?1=0 againstHa?:?1?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.)Statethe conclusion at ?=0.05.

Since the? p-value is less than ??, there is sufficientevidence to 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.)Interpretthe value 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.