The following data represent a companys yearly sales volume

The following data represent a company\'s yearly sales volume and its advertising expenditure over a period of B years. Which variable is the dependent variable? Using the Excel spreadsheet, run the least squares model 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

Solution

a)

The dependent variable is the SALES IN MILLIONS OF DOLLARS.

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b)

c)

c)

If x = 40, then

y^ = -18.5 + x

y^ = -18.5 + 40 = 21.5 million dollars [ANSWER]

d)

it indicates that on the average, an increase in $10000 in advertising expenses will result in an increase of $1 million in sales.

e)

r^2 = 0.808510638

from the table. This means that 80.85% of the variation in sales can be explained by changes in the advertising expenses.

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SUMMARY OUTPUT
Regression Statistics
Multiple R	0.899172
R Square	0.808511
Adjusted R Square	0.776596
Standard Error	1.732051
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	76	76	25.33333	0.002373
Residual	6	18	3
Total	7	94
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-18.5	7.178642	-2.57709	0.041933	-36.0655	-0.9345	-36.0655	-0.9345
X Variable 1	1	0.19868	5.033223	0.002373	0.513848	1.486152	0.513848	1.486152
RESIDUAL OUTPUT
Observation	Predicted Y	Residuals
1	13.5	-2.5
2	14.5	1.5
3	16.5	1.5
4	15.5	1.5
5	17.5	-1.5
6	18.5	0.5
7	20.5	-1.5
8	23.5	0.5