576 Chapter 15 Multiple Regression
b. What effect did the inclusion of PVTotal have on? What effect did it have on the
standard error of the regression coefficient for PVLoss? If your program will also give
you tolerance and VIF, what effect does the inclusion of PVTotal have on them?
c. What would you conclude about the addition of PVTotal to our model?
15.26 In Exercise 15.24 we posited a model in which depression was a function of perceived vul-
nerability, social support, and age at loss. An alternative, or additional, view might be that
vulnerability itself is a function of social support and age at loss. (If you lost a parent when
you were very young and you have little social support, then you might feel particularly
vulnerable to future loss.)
a. Set up the regression problem for this question and run the appropriate analysis. (Use
PVLoss, SuppTotl, and AgeAtLos.)
b. Interpret your results.
15.27 Draw one diagram to illustrate the relationships examined in Exercises 15.24 and 15.26.
Use arrows to show predicted relationships, and write the standardized regression coeffi-
cients next to the arrows. (You have just run a simple path analysis.)
15.28Notice that in the diagram in Exercise 15.27 SuppTotl has both a direct and an indirect ef-
fect on Depression. Its direct effect is the arrow that goes from SuppTotl to DepressT. The
indirect effect (which here is not significant) comes from the fact that SuppTotl influences
PVLoss, which in turn affects DepressT. Explain these direct and indirect effects in terms of
semipartial regression coefficients.
15.29 Repeat the analysis of Exercise 15.24, requesting statistics on regression diagnostics.
a. What, if anything, do these statistics tell you about the data set?
b. Delete the subject with the largest measure of influence (usually indexed by Cook’s D).
What effect does that have for this particular data set?
15.30 It is useful to examine the effects of measurement reliability on the outcome of a regression
problem. In Exercise 15.24 the variable PVLoss was actually a reasonably reliable variable.
However, for purposes of illustration we can manufacture a new, and less reliable, measure
from it by adding a bit of random error to PVLoss.
a. Create a new variable called UnrelLos with a statement of the formUnrelLos 5
PVLoss 1 7.5 3 “random.” [Here “random” is a random-number function available
with most statistical programs. You will need to check the manual to determine the ex-
act form of the statement. I used a multiplier of 7.5 on the assumption that the random-
number function will sample from an N(0, 1) population. Multiplying by 7.5 will
increase the standard deviation of UnrelLos by 50% (see the variance sum law). You
may want to play with other constants.]
b. Now repeat Exercise 15.24 using UnrelLos in place of PVLoss.
c. What effect does this new variable have on the contribution of the perceived vulnerabil-
ity of loss to the prediction of DepressT? How has the regression coefficient changed?
How has its standard error changed? How does a test on its statistical significance
change? What changes occurred for the other variables in the equation?
15.31 The data set Harass.dat contains slightly modified data on 343 cases created to replicate the
results of a study of sexual harassment by Brooke and Perot (1991). The dependent variable
is whether or not the subjects reported incidents of sexual harassment, and the independent
variables are, in order, Age, Marital Status (1 5 married, 2 5 single), Feminist Ideology,
Frequency of the behavior, Offensiveness of the behavior, and whether or not it was reported
(0 5 no, 1 5 yes). (For each variable, higher numbers represent more of the property.
Using any logistic regression program, examine the likelihood that a subject will report sex-
ual harassment on the basis of the independent variables.
15.32 Repeat Exercise 15.31 but this time use just the dichotomous predictor Marital Status. Cre-
ate a contingency table of Married/Unmarried by Report/No Report, calculate odds ratios,
and compare those ratios to the results of the logistic regression. (The result will not be sig-
nificant, but that is not important.)R^2