The following data represent a company\'s yearly sales volume and its advertisin

Question

The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years. Which variable is the dependent variable? Using the Excel spreadsheet, run the least squares model and write and write the summary output here. If the company's advertising expenditure is $400,000. What are the predicted sales? Give the answer in dollars What does the slope of the estimated regression line indicate? Compute the coefficient of determination and fully interpret its meaning. Use the F test to determine whether or not the regression model is significant at alpha=0.05. Use the t test to determine the slope of the regression model is significant at alpha=0.05. Develop a 95% confidence interval for predicting the average sales for the years when $400,000 was spent on advertising Compute the correlation coefficient.

Explanation / Answer

a) Sales is the dependent variable as in this model it depends upon advertisment expenditure which is independent variable.

b)

So Y(sales) = -16.4803 + 0.947368*X (Advertising expenditure)

c) if X=40

Y = -16.4803 + 0.947368*40 = $21.41 millions

d) The slope i.e. 0.947368 represents the increase in sales in millions of dollars with respect to per unit (tens of thousands) increase of advertisement cost

SUMMARY OUTPUT Regression Statistics Multiple R 0.912746 R Square 0.833106 Adjusted R Square 0.80529 Standard Error 1.50911 Observations 8 ANOVA df SS MS F Significance F Regression 1 68.21053 68.21053 29.95089 0.001554 Residual 6 13.66447 2.277412 Total 7 81.875 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -16.4803 6.254642 -2.63489 0.038805 -31.7848 -1.17571 -31.7848 -1.17571 X Variable 1 0.947368 0.173107 5.472741 0.001554 0.523791 1.370945 0.523791 1.370945

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