College Textbooks
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:
Profit per Text, y
|
16.5
|
22.4
|
24.9
|
28.8
|
31.5
|
35.8
|
Sales Cost per Text x
|
5.0
|
5.6
|
6.1
|
6.8
|
7.4
|
8.6
|
Expecting profit per book to rise and then plateau, the publisher fitted the model E(y) = β0
+ β1x + β2x2
to the data.
MINITAB output for Exercise
Regression Analysis: y versus x, x-sq
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. How much of the regression sum of squares is accounted for by the quadratic term? The linear term?
e. 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?
f. Do the data indicate a significant curvature in the relationship between y and x? Test at the 5% level of significance.
g. What conclusions can you draw from the accompanying residual plots?
MINITAB plots for Exercise