A publisher of college textbooks conducted a study to relate profit per text y to cost of sales x over a 6-year period when its sales force (and sales costs) were growing rapidly. These inflation-adjusted data (in thousands of dollars) were collected:

Expecting profit per book to rise and then plateau, the publisher fitted the model E(y) = β0 + β1x + β2x2 to the data.
Excel output for Exercise 13.10

a. Plot the data points. Does it look as though the quadratic model is necessary?
b. Find s on the printout. Confirm that

c. Do the data provide sufficient evidence to indicate that the model contributes information for the prediction of y? What is the p-value for this test, and what does it mean?
d. What sign would you expect the actual value of β2 to have? Find the value of β2 in the printout. Does this value confirm your expectation?
e. Do the data indicate a significant curvature in the relationship between y and x? Test at the 5% level of significance.
f. What conclusions can you draw from the accompanying residual plots?
Diagnostic plots for Exercise 13.10

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Profit per Text, y 16.5 22.4 24.9 28.8 31.5 358 Sales Cost per Text, x 5.0 5.6 6. 6.8 7.4 8.6 SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square 0.9925 Standard Error 0.5944 Observations 0.9978 0.9955 ANOVA df MS F Significance F Regression 2 Residual 3 Total 234.995 117.478 332.528 0.000 1·060 236.015 0.353 standard Coefficients -44.192 16.334 -0.820 Error t Stat P-value 0.013 0.007 0.021 8.287 -5.333 6.560 0.182 494 Intercept 2.490 x-sa SSE Vn -k-1 Normal Probability Plot of the Residuals (response is y) 95 10 0.0 Residual 0.5 1.0 Residuals versus the Fitted Values (response is y) 1.00 0.75- 0.50 0.25 0.00 -0.25 -0.50 15 20 25 30 35 Fitted Value