436 CHAPTER 12 MULTIPLE LINEAR REGRESSION12-13. Consider the regression model fit to the soil shear
strength data in Exercise 12-1.
(a) Test for significance of regression using 0.05. What
is the P-value for this test?
(b) Construct the t-test on each regression coefficient. What
are your conclusions, using 0.05?
12-14. Consider the absorption index data in Exercise 12-2.
The total sum of squares for yis SST742.00.
(a) Test for significance of regression using 0.01. What
is the P-value for this test?
(b) Test the hypothesis H 0 : 1 0 versus H 1 : 1 0 using
0.01. What is the P-value for this test?
What conclusion can you draw about the usefulness of x 1 as a
regressor in this model?
12-15. Consider the NFL data in Exercise 12-4.
(a) Test for significance of regression using 0.05. What
is the P-value for this test?
(b) Conduct the t-test for each regression coefficient 2 , 7 ,
and 8. Using 0.05, what conclusions can you draw
about the variables in this model?
12-16. Reconsider the NFL data in Exercise 12-4.
(a) Find the amount by which the regressor x 8 (opponents’
yards rushing) increases the regression sum of squares.
(b) Use the results from part (a) above and Exercise 12-14 to
conduct an F-test for H 0 : 8 0 versus H 1 : 8 0 using
0.05. What is the P-value for this test? What conclu-
sions can you draw?
12-17. Consider the gasoline mileage data in Exercise 12-5.
(a) Test for significance of regression using 0.05. What
conclusions can you draw?
(b) Find the t-test statistic for both regressors. Using
0.05, what conclusions can you draw? Do both regressors
contribute to the model?
12-18. A regression model Y 0 1 x 1 2 x 2 3 x 3
has been fit to a sample of n25 observations. The calcu-
latedt-ratios are as follows: for 1 ,
t 0 4.82, for 2 , t 0 8.21 and for 3 , t 0 0.98.
(a) Find P-values for each of the t-statistics.
(b) Using 0.05, what conclusions can you draw about
the regressor x 3? Does it seem likely that this regressor
contributes significantly to the model?
12-19. Consider the electric power consumption data in
Exercise 12-6.
(a) Test for significance of regression using 0.05. What
is the P-value for this test?
(b) Use the t-test to assess the contribution of each regressor
to the model. Using 0.05, what conclusions can you
draw?
12-20. Consider the bearing wear data in Exercise 12-7
with no interaction.ˆj (^) se 1 ˆj 2 , j1, 2, 3
(a) Test for significance of regression using 0.05. What
is the P-value for this test? What are your conclusions?
(b) Compute the t-statistics for each regression coefficient.
Using 0.05, what conclusions can you draw?
(c) Use the extra sum of squares method to investigate the
usefulness of adding x 2 load to a model that already
contains x 1 oil viscosity. Use 0.05.
12-21. Reconsider the bearing wear data from Exercises
12-7 and 12-20.
(a) Refit the model with an interaction term. Test for signifi-
cance of regression using 0.05.
(b) Use the extra sum of squares method to determine
whether the interaction term contributes significantly to
the model. Use 0.05.
(c) Estimate 2 for the interaction model. Compare this to the
estimate of 2 from the model in Exercise 12-20.
12-22. Consider the wire bond pull strength data in
Exercise 12-8.
(a) Test for significance of regression using 0.05. Find
the P-value for this test. What conclusions can you draw?
(b) Calculate the t-test statistic for each regression coeffi-
cient. Using 0.05, what conclusions can you draw?
Do all variables contribute to the model?
12-23. Reconsider the semiconductor data in Exercise
12-9.
(a) Test for significance of regression using 0.05. What
conclusions can you draw?
(b) Calcuate the t-test statistic for each regression coefficient.
Using 0.05, what conclusions can you draw?
12-24. Exercise 12-10 presents data on heat treating gears.
(a) Test the regression model for significance of regression.
Using 0.05, find the P-value for the test and draw
conclusions.
(b) Evaluate the contribution of each regressor to the model
using the t-test with 0.05.
(c) Fit a new model to the response PITCH using new
regressors x 1 SOAKTIME SOAKPCT and x 2
DIFFTIME DIFFPCT.
(d) Test the model in part (c) for significance of regression
using 0.05. Also calculate the t-test for each regres-
sor and draw conclusions.
(e) Estimate 2 for the model from part (c) and compare this
to the estimate of 2 for the model in part (a). Which
estimate is smaller? Does this offer any insight regarding
which model might be preferable?
12-25. Data on National Hockey League team performance
was presented in Exercise 12-11.
(a) Test the model from this exercise for significance of
regression using 0.05. What conclusions can you
draw?
EXERCISES FOR SECTION 12-2
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