To study how social media may influence the products consumersbuy, 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

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 the hypotheses to test?

A. H0: β1≠0 against Ha:β1=0

B. H0β0:=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 the conclusion at α=0.05.

Since the p-value is less than α, there is sufficient evidence to reject H0.

Conclude there is

a linear relationship between revenue and message rate. What is the value for the coefficient of determination

r2?

r2=0.92 (Round to two decimal places as needed.)Interpret the value of r2 in the context of this problem.

A. r2 is the proportion of the total sample variability around message rate that is explained by the linear relationship between the revenue and the message rate.

B. r2 is the proportion of the sample points that do not fit within the 95% confidence interval.

C. r2 is the proportion of the sample points that fit on the estimated linear regression line.

D. r2 is the proportion of the total sample variability around mean revenue that is explained by the linear relationship between the revenue and the message rate.