Introduction to Probability and Statistics for Engineers and Scientists

428 Chapter 9: Regression

in the weight of the tumor. The data were as follows:

Coded Amount of Drug Tumor Weight Reduction

1 .50

2 .90

3 1.20

4 1.35

5 1.50

6 1.60

7 1.53

8 1.38

9 1.21

10 .65

Estimate the maximum expected tumor reduction and the amount of the drug

that attains it by fitting a quadratic regression equation of the form

Y=β 0 +β 1 x+β 2 x^2 +e

39.The following data represent the relation between the number of cans damaged in

a boxcar shipment of cans and the speed of the boxcar at impact.

Speed Number of Cans Damaged

354

362

365

594

5 122

584

6 142

7 139

7 184

8 254

(a) Analyze as a simple linear regression model.

(b) Plot the standardized residuals.

(c) Do the results of part (b) indicate any flaw in the model?

(d) If the answer to part (c) is yes, suggest a better model and estimate all resulting

parameters.