466 CHAPTER 12 MULTIPLE LINEAR REGRESSION12-69. Consider the jet engine thrust data in Exercise 12-64.
(a) Use all possible regressions to select the best regression
equation, where the model with the minimum value of
MSEis to be selected as “best.’’
(b) Repeat part (a) using the CPcriterion to identify the best
equation.
(c) Use stepwise regression to select a subset regression model.
(d) Compare the models obtained in parts (a), (b), and (c)
above.
12-70. Consider the electronic inverter data in Exercise 12-66
and 12-67. Define the response and regressors variables as in
Exercise 12-67, and delete the second observation in the sample.
(a) Use all possible regressions to find the equation that mini-
mizes Cp.
(b) Use all possible regressions to find the equation that
minimizes MSE.
(c) Use stepwise regression to select a subset regression model.
(d) Compare the models you have obtained.
12-71. Consider the three-variable regression model for the
jet engine thrust data in Exercise 12-65. Calculate the variance
inflation factors for this model. Would you conclude that mul-
ticollinearity is a problem in this model?
12-72. A multiple regression model was used to relate y
viscosity of a chemical product to x 1 temperature and x 2
reaction time. The data set consisted of n15 observations.
(a) The estimated regression coefficients were
and. Calculate an estimate of
mean viscosity when x 1 100 °F and x 2 2 hours.
(b) The sums of squares were SST1230.50 and SSE
120.30. Test for significance of regression using
0.05. What conclusion can you draw?ˆ 1 0.85, ˆ 2 10.40ˆ 0 300.00,(c) What proportion of total variability in viscosity is
accounted for by the variables in this model?
(d) Suppose that another regressor, x 3 stirring rate, is added
to the model. The new value of the error sum of squares is
SSE117.20. Has adding the new variable resulted in a
smaller value of MSE? Discuss the significance of this
result.
(e) Calculate an F-statistic to assess the contribution of x 3 to
the model. Using 0.05, what conclusions do you
reach?
12-73. An article in the Journal of the American Ceramics
Society(Vol. 75, 1992, pp. 112–116) describes a process for
immobilizing chemical or nuclear wastes in soil by dissolving
the contaminated soil into a glass block. The authors mix CaO
and Na 2 O with soil and model viscosity and electrical conduc-
tivity. The electrical conductivity model involves six regres-
sors, and the sample consists of n14 observations.
(a) For the six-regressor model, suppose that SST0.50 and
R^2 0.94. Find SSEand SSR, and use this information to
test for significance of regression with 0.05. What are
your conclusions?
(b) Suppose that one of the original regressors is deleted from
the model, resulting in R^2 0.92. What can you conclude
about the contribution of the variable that was removed?
Answer this question by calculating an F-statistic.
(c) Does deletion of the regressor variable in part (b) result in
a smaller value of MSEfor the five-variable model, in
comparison to the original six-variable model? Comment
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