Exercise for the Final (not graded)

Ten sales regions of equal sales potential for a company were randomly selected. The advertising expenditures (in units of $10,000) in these 10 sales regions were purposely set during July of last year at, respectively, 5, 6, 7, 8, 9, 10, 11, 12, 13 and 14. The sales volumes (in units of $10,000) were then recorded for the 10 sales regions and found to be, respectively, 113, 116, 106, 105, 129, 114, 110, 110, 104, and 103. Assuming that the simple linear regression model is appropriate, it can be shown thatb0= 119.8667,b1= -.9333.

Coef SE Coef T P

Constant119.8678.340714.371.0000

Ad exp -.9333.8404 -1.111 .2990

Is the slope significant? Conduct a formal critical value test, and a formal P-value test.

Is the F test significant?

Can you predictwhen X is 1? If yes, what is your prediction?

Can you predictwhen X is 11? If yes, what is your prediction?

The following table is the output of multiple linear regression analysis.

ANOVA SS df MS F p-value

Regression19,762.5919119,762.5919532.31.0000

Residual 334.1354 937.1262

Total20,096.727310

(a)Use the table to report theF statistic.What is its degrees of freedom? What is the number of observations?

(b)Find thep-value related toF on the computer output and report its value. Using thep-value, test the significance of the regression model at the .10, .05, .01, and .001 levels of significance. What do you conclude?

THE FUEL CONSUMPTION CASE

Using the appropriate model, sample sizen, and output below:

Model:y = 0+ 1x1+ 2x2+ Sample size:n= 8

S = .5561R-Sq = 93.1%R-Sq(adj) = 90.3%

Analysis of Variance

Source DFSS MS F P

Regression 220.814110.407033.66.0013

Residual Error51.5459.3092

Total722.3600

(1)ReportSSE,s2, andsas shown on the output. Calculate s2fromSSEand other numbers.(Round your answersto 4 decimal places.)

(2)Report the total variation, unexplained variation, and explained variation as shown on the output.(Round your answers to 3 decimal places.)

Total variation

Unexplained variation

Explained variation

(3)Report R2andadjusted R2as shown on the output.(Round your answers to 3 decimal places.)

(4)Calculate theFstatistic .

(7)Find thep-value related toFon the output. Using thep-value, test the significance of the linear regression model by setting = .10, .05, .01, and .001.