Chapter 13.4, Problem 13.10E

College Textbooks A publisher of college textbooks conducgted 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 raidly. These inflation-adjusted data (in thousands of dollars) were collect:

Expecting profit per book to rise and then plateau, the publisher fitted the model $E(y)={\beta }_0+{\beta }_{1}x+{\beta }_2{x}^2$ to the data.

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

$s=\sqrt{\frac{SSE}{n-k-1}}$
3. Do the data provide sufficient evidence to indicate that the model contributes information for the pred iction of? What is the p-value for this test. and what does it mean?
4. What sign would you expect the actual value of ${\beta }_2$ to have? Find the value of ${\beta }_2$ in the printout. Does this value confirm your expecLation?
5. Do the data indicate a significant curvature in the relationship between y and x? Test at the 5% level of significance.
6. What conclusions can you draw from the accompaflying residual plots?