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How does social media may influence the products consumers buy?

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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)
1361.7	143
1219.1	75
680.2	63
579.3	34
459.3	33
415.7	32
309.5	22
290.2	21
249.1	21
167.8	20
154.4	19
148.6	18
143.7	18
120.3	17
117.4	17
106.9	17
100.4	17
93.5	15
85.8	15
75.5	13
54.1	8
42.2	3
4.6	2

Fit a least squares regression line using the data above

statsguru

statsguru Added an answer on Dec 13,2018

This questions can be answered by fitting a simple linear regression model in excel of performing manual calculations on the data using the simple linear regression formula.

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.942519
R Square	0.888343
Adjusted R Square	0.883026
Standard Error	10.30258
Observations	23

ANOVA
	df	SS	MS	F	Significance F
Regression	1	17733.948	17733.95	167.0756	1.82742E-11
Residual	21	2229.008	106.1432
Total	22	19962.957

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	3.883	2.843	1.366	0.186	-2.030	9.796
Message_Rate	0.079	0.006	12.926	0.000	0.067	0.092

Here, I present the calculated using the Excel data analysis Toolpak.

The estimated regression line is;- Revenue = 3.883 + 0.0793* Message_Rate

Based on this model, Questions related to the Goodness of the fitness of the model can be answered

a) Check the usefulness of the hypothesized model. What are the hypotheses to test?

H0: B1 = 0, against B1 != 0

The p value is less than 0.001, therefore the null hypothesis is rejected the model fits the data well.

b) Determine the estimate of the standard deviation.

s = 10.303 (Obtained from the summary table)

c) What is the test statistic for the hypotheses?

The test statistic is the t-test associated with the slope coefficeint;- 12.93

b) The p value and the conclusion;-

Since the p-value is less than alpha, there is sufficient evidence to reject H0. Conclude there is a linear relationship between revenue and message rate.

d) The value of the coefficient of determination is 0.89 , obtained from the summary table.

The interpretation of the coefficient of determination follows that it is the proportion of variability in the revenue that can be explained by the message rate, In this case, 89% of the variation in the revenue can be explained by the message rate.

How does social media may influence the products consumers buy?

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