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).o 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
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+ 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 againstHa​:β1=0

B.H0​:β0=0 against Ha​: β0 ≠0

C.H0​: β≠0 against Ha​:β0=0

D.H0​:β1=0 against Ha​:β1≠0 The answer is correct.

Determine the estimate of the standard deviation.

s=____________ (Round to two decimal places as​ needed.)

Answer 1

Following table shows the output of regression analysis generated by excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.957130968
R Square	0.916099691
Adjusted R Square	0.912104438
Standard Error	9.592074495
Observations	23
ANOVA
	df	SS	MS	F	Significance F
Regression	1	21097.13859	21097.13859	229.2970513	8.96384E-13
Residual	21	1932.165756	92.00789312
Total	22	23029.30435
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-0.03086767	2.644826475	-0.011670962	0.990798298	-5.531085404	5.469350063
Message Rate(x)	0.086462093	0.005709874	15.14255762	8.96384E-13	0.07458776	0.098336425

The least square regression line is:

y' = -0.031 + 0.086x

The hypotheses are:

D.H0​:β1=0 against Ha​:β1≠0

The estimate of the standard deviation is

s = 9.59