Question

The following data represent a company's yearly sales and its advertising expenditure over a period of 8 years.

Sales in Millions of Dollars (y)                                       Advertising Expenditure (in $10,000) (x)

15                                                                                            32

16                                                                                            33

18                                                                                            35

17                                                                                            34

16                                                                                            36

19                                                                                            37

19                                                                                            39

24                                                                                            42

a. Use the method of least squares to compute an estimated regression equation between sales and advertising

b. If the company's advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars.

c. What does the slope of the estimated regression line indicate?

d. Compute the coefficient of determination and fully interpret its meaning

e. Compute the correlation coefficient.

f. Use the F test to determine whether or not the regression model is significant at α = .05.

g. Use the t test to determine whether the slope of the regression model is significant at α = .05.

h. Develop a 95% confidence interval for predicting the average sales for the years when $400,000 was spent on advertising. Give your answer in dollars.

Answer 1

using excel>Addin>phstat>Regression

we have

Regression Analysis
Regression Statistics
Multiple R	0.919709009
R Square	0.845864662
Adjusted R Square	0.820175439
Standard Error	1.199415062
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	47.36842105	47.36842105	32.92682927	0.001217346
Residual	6	8.631578947	1.438596491
Total	7	56
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-10.42105263	4.971084441	-2.096333859	0.080886676	-22.58485806	1.7427528
Advertising	0.789473684	0.137582343	5.738190418	0.001217346	0.452821818	1.126125551

Confidence Interval Estimate
Data
X Value	40
Confidence Level	95%
Intermediate Calculations
Sample Size	8
Degrees of Freedom	6
t Value	2.446912
XBar, Sample Mean of X	36
Sum of Squared Differences from XBar	76
Standard Error of the Estimate	1.199415
h Statistic	0.335526
Predicted Y (YHat)	21.15789
For Average Y
Interval Half Width	1.700009
Confidence Interval Lower Limit	19.45789
Confidence Interval Upper Limit	22.8579
For Individual Response Y
Interval Half Width	3.391674
Prediction Interval Lower Limit	17.76622
Prediction Interval Upper Limit	24.54957

a.an estimated regression equation between sales and advertising is

estimated sales = -10.42 +0.7895*Advertisement

b. If the company's advertising expenditure is $400,000, the predicted sales = -10.42 +0.7895*40 = $ 21.15789 million

c. the slope of the estimated regression line indicat that for every one $ increase in advettisment increase the sales by $0.7895 million

d. the coefficient of determination = 0.8459 , about 84.59% variation in sales can be explained by advertisemet throgh the given model Compute the correlation coefficient.

f. the value of F test = 32.927 , and p value is 0.0012 , since p value is less than 0.05 so can say that  the regression model is significant .

g. the value of t test = 5.738 ,and p value is  0.0012 , since p value is less than 0.05 so can say that  the regression model is significant .

h. a 95% confidence interval for predicting the average sales for the years when $400,000 was spent on advertising is ($17.766 to $24.550)