446 CHAPTER 12 MULTIPLE LINEAR REGRESSIONEXERCISES FOR SECTION 12-5
12-36. Consider the regression model for the NFL data in
Exercise 12-4.
(a) What proportion of total variability is explained by this
model?
(b) Construct a normal probability plot of the residuals. What
conclusion can you draw from this plot?
(c) Plot the residuals versus and versus each regressor, and
comment on model adequacy.
(d) Are there any influential points in these data?
12-37. Consider the gasoline mileage data in Exercise 12-5.
(a) What proportion of total variability is explained by this
model?
(b) Construct a normal probability plot of the residuals and
comment on the normality assumption.
(c) Plot residuals versus and versus each regressor. Discuss
these residual plots.
(d) Calculate Cook’s distance for the observations in this data
set. Are any observations influential?
12-38. Consider the electric power consumption data in
Exercise 12-6.
(a) Calculate R^2 for this model. Interpret this quantity.
(b) Plot the residuals versus. Interpret this plot.
(c) Construct a normal probability plot of the residuals and
comment on the normality assumption.
12-39. Consider the wear data in Exercise 12-7.
(a) Find the value of R^2 when the model uses the regressors x 1
and x 2.
(b) What happens to the value of R^2 when an interaction term
x 1 x 2 is added to the model? Does this necessarily imply
that adding the interaction term is a good idea?yˆyˆyˆ12-40. For the regression model for the wire bond pull
strength data in Exercise 12-8.
(a) Plot the residuals versus and versus the regressors used in
the model. What information do these plots provide?
(b) Construct a normal probability plot of the residuals. Are
there reasons to doubt the normality assumption for this
model?
(c) Are there any indications of influential observations in the
data?
12-41. Consider the semiconductor HFE data in Exercise
12-9.
(a) Plot the residuals from this model versus. Comment on
the information in this plot.
(b) What is the value of R^2 for this model?
(c) Refit the model using log HFE as the response variable.
(d) Plot the residuals versus predicted log HFE for the model
in part (c). Does this give any information about which
model is preferable?
(e) Plot the residuals from the model in part (d) versus the re-
gressor x 3. Comment on this plot.
(f ) Refit the model to log HFE using x 1 , x 2 , and 1x 3 , as the re-
gressors. Comment on the effect of this change in the model.
12-42. Consider the regression model for the heat treating
data in Exercise 12-10.
(a) Calculate the percent of variability explained by this model.
(b) Construct a normal probability plot for the residuals.
Comment on the normality assumption.
(c) Plot the residuals versus and interpret the display.
(d) Calculate Cook’s distance for each observation and pro-
vide an interpretation of this statistic.yˆyˆyˆTable 12-11 Influence Diagnostics for the Wire Bond Pull Strength Data 2
Observations Cook’s Distance Measure Observations Cook’s Distance Measure
ihii Di ihii Di
1 0.1573 0.035 14 0.1129 0.003
2 0.1116 0.012 15 0.0737 0.187
3 0.1419 0.060 16 0.0879 0.001
4 0.1019 0.021 17 0.2593 0.565
5 0.0418 0.024 18 0.2929 0.155
6 0.0749 0.007 19 0.0962 0.018
7 0.1181 0.036 20 0.1473 0.000
8 0.1561 0.020 21 0.1296 0.052
9 0.1280 0.160 22 0.1358 0.028
10 0.0413 0.001 23 0.1824 0.002
11 0.0925 0.013 24 0.1091 0.040
12 0.0526 0.001 25 0.0729 0.000
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