Question

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
681.26		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 y=−0.031+0.086x.

​(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.H0​: β0=0 againstHa​: β0≠0

C.H0​:β0≠0 against Ha​: β0=0

D.H0​:β1s=0 against Ha​: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=_____(Round to three decimal places as​ needed.)

Answer 1

Given value of test statistic = 15.14

Degrees of freedom = n - 2 = 23 - 2 = 21

Hence,

P - value = 2*P(t_{​​​​​​21} > 15.14) = 2*0 = 0