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).

Click the icon to view the data.

Message_Rate   Revenue_($millions)
1369.4 145
1217.5 76
575.9 70
308.1 36
453.2 35
292.7 34
245.8 21
675.6 19
150.8 19
162.2 19
111.1 18
146.2 17
417.2 16
95.5 16
103.6 15
119.8 15
73.8 15
84.8 14
122.3 9
58.9 8
146.4 7
37.5 2
3.9 1

a.The least squares regression equation is y equals=nothing+ (nothing) x

​(Round to three decimal places as​ needed.)

b. Determine the estimate of the standard deviation.

s=nothing

​(Round to two decimal places as​ needed.)

c. Identify the test statistic for the​ hypotheses, rounding to two decimal places.

t= nothing

d.Identify the p-value.

e.Compute fro r2

f.Use technology to create a​ 95% confidence interval for the slope β1​, rounding to three decimal places

Answer 1

using excel data analysis tool for regression o/p obtained is

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.8955
R Square	0.8018
Adjusted R Square	0.7924
Standard Error	14.4098
Observations	23
ANOVA
	df	SS	MS	F	Significance F
Regression	1	17643.9742	17643.9742	84.9735	0.0000
Residual	21	4360.4606	207.6410
Total	22	22004.4348
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	3.2974	3.9731	0.8299	0.4159	-4.9651	11.5600	-4.965148788	11.56002995
X	0.0791	0.0086	9.2181	0.0000	0.0612	0.0969	0.061216958	0.096884894

a)

Y=3.297 + 0.079x

b)

s=14.41

c)

t-stat=9.22

d)

p-value=0.0000

e)

R²=0.8018

f)

95% confidence interval for slope ß1 is (0.061,0.097 )