12-5 MODEL ADEQUACY CHECKING 441EXERCISES FOR SECTIONS 12-3 AND 12-4
12-26. Consider the soil absorption data in Exercise 12-2.
(a) Find a 95% confidence interval on the regression coeffi-
cient 1.
(b) Find a 95% confidence interval on mean soil absorption
index when x 1 200 and x 2 50.
(c) Find a 95% prediction interval on the soil absorption in-
dex when x 1 200 and x 2 50.
12-27. Consider the NFL data in Exercise 12-4.
(a) Find a 95% confidence interval on 8.
(b) What is the estimated standard error of when x 2
2000 yards, x 7 60%, and x 8 1800 yards?
(c) Find a 95% confidence interval on the mean number of
games won when x 2 2000, x 7 60, and x 8 1800.
12-28. Consider the gasoline mileage data in Exercise 12-5.
(a) Find 99% confidence intervals on 1 and 6.
(b) Find a 99% confidence interval on the mean of Ywhen
x 1 300 and x 6 4.
(c) Fit a new regression model to these data using x 1 , x 2 , x 6 ,
and x 10 as the regressors. Find 99% confidence intervals
on the regression coefficients in this new model.
(d) Compare the lengths of the confidence intervals on 1 and
6 from part (c) with those found in part (a). Which inter-
vals are longer? Does this offer any insight about adding
the variables x 2 and x 10 to the model?
12-29. Consider the electric power consumption data in
Exercise 12-6.
(a) Find 95% confidence intervals on 1 , 2 , 3 , and 4.
(b) Find a 95% confidence interval on the mean of Ywhen
x 1 75, x 2 24, x 3 90, and x 4 98.
(c) Find a 95% prediction interval on the power consumption
when x 1 75, x 2 24, x 3 90, and x 4 98.
12-30. Consider the bearing wear data in Exercise 12-7.
(a) Find 99% confidence intervals on 1 and 2.
(b) Recompute the confidence intervals in part (a) after the in-
teraction term x 1 x 2 is added to the model. Compare the
lengths of these confidence intervals with those computed
in part (a). Do the lengths of these intervals provide any
information about the contribution of the interaction term
in the model?
12-31. Consider the wire bond pull strength data in Exercise
12-8.
(a) Find 95% confidence interval on the regression coeffi-
cients.ˆY|x 0(b) Find a 95% confidence interval on mean pull strength
when x 2 20, x 3 30, x 4 90 and x 5 2.0.
(c) Find a 95% prediction interval on pull strength when x 2
20, x 3 30, x 4 90, and x 5 2.0.
12-32. Consider the semiconductor data in Exercise 12-9.
(a) Find 99% confidence intervals on the regression coeffi-
cients.
(b) Find a 99% prediction interval on HFE when x 1 14.5,
x 2 220, and x 3 5.0.
(c) Find a 99% confidence interval on mean HFE when x 1
14.5, x 2 220, and x 3 5.0.
12-33. Consider the heat treating data from Exercise 12-10.
(a) Find 95% confidence intervals on the regression coeffi-
cients.
(b) Find a 95% confidence interval on mean PITCH when
TEMP1650, SOAKTIME1.00, SOAKPCT
1.10, DIFFTIME1.00, and DIFFPCT0.80.
12-34. Reconsider the heat treating data in Exercises
12-10 and 12-24, where we fit a model to PITCH using
regressors x 1 SOAKTIME SOAKPCT and x 2
DIFFTIME DIFFPCT.
(a) Using the model with regressors x 1 and x 2 , find a 95%
confidence interval on mean PITCH when SOAK-
TIME1.00, SOAKPCT1.10, DIFFTIME1.00,
and DIFFPCT0.80.
(b) Compare the length of this confidence interval with the
length of the confidence interval on mean PITCH at
the same point from Exercise 12-33 part (b), where an
additive model in SOAKTIME, SOAKPCT, DIFFTIME,
and DIFFPCT was used. Which confidence interval is
shorter? Does this tell you anything about which model
is preferable?
12-35. Consider the NHL data in Exercise 12-11.
(a) Find a 95% confidence interval on the regression coeffi-
cient for the variable “Pts.”
(b) Fit a simple linear regression model relating the response
variable “wins” to the regressor “Pts.”
(c) Find a 95% confidence interval on the slope for the simple
linear regression model from part (b).
(d) Compare the lengths of the two confidence intervals com-
puted in parts (a) and (c). Which interval is shorter? Does
this tell you anything about which model is preferable?12-5 MODEL ADEQUACY CHECKING12-5.1 Residual AnalysisThe residualsfrom the multiple regression model, defined by , play an important
role in judging model adequacy just as they do in simple linear regression. As noted in Section
11-7.1, several residual plots are often useful; these are illustrated in Example 12-9. It is alsoeiyiyˆic 12 .qxd 5/20/02 9:33 M Page 441 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH114 FIN L:Quark Files: