# How does social media may influence the products consumers​ buy?

1856 Views

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

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.