15.6 Calculate the adjusted for the data in Exercise 15.4.
15.7 All other things being equal, the ability of two variables to predict a third will increase
as the correlation between them decreases. Explain this fact in terms of semipartial cor-
relation.
15.8 All other things being equal, the stability of any given regression coefficient across different
samples of data is partly a function of how that variable correlates with other predictors.
Explain this fact.
15.9 What does the Tolerance column in Exhibit 15.6 contribute to the answers in Exercises 15.7
and 15.8?
15.10 Using the data in Exercise 15.4, generate and show that.
15.11 Use Yand from Exercise 15.10 to show that is.
15.12Using the following (random) data, demonstrate what happens to the multiple correlation
when you drop cases from the data set (e.g., use 15 cases, then 10, 6, 5, 4)
Y 50594 83704 71479
X 1 38158 24791 35689
X 2 76431 97531 86037
X 3 17418 86836 19777
X 4 36051 35911 74209
15.13 Calculate the adjusted for the 15 cases in Exercise 15.12.
15.14 Refer to the first three variables from Exercise 15.4.
a. Use any computer program to calculate the squared semipartial correlation and the
squared partial correlation for Satisfaction as the criterion and No. Supervised as the
predictor, partialling out Responsibility.
b. Draw a Venn diagram to illustrate these two coefficients.15.15 Refer to the first three variables in Exercise 15.4.
a. Draw a figure comparable to Figure 15.1.
b. Obtain the regression solution for these data and relate the solution to the figure.15.16 The State of Vermont is divided into 10 Health Planning Districts—they correspond roughly
to counties. The following data represent the percentage of live births of babies weighing
under 2500 grams (Y), the fertility rate for females 17 years of age or younger ( ), total
high-risk fertility rate for females younger than 17 or older than 35 years of age ( ),
percentage of mothers with fewer than 12 years of education ( ), percentage of births to
unmarried mothers ( ), and percentage of mothers not seeking medical care until the third
trimester ( ).
YX 1 X 2 X 3 X 4 X 5
6.1 22.8 43.0 23.8 9.2 6
7.1 28.7 55.3 24.8 12.0 10
7.4 29.7 48.5 23.9 10.4 5
6.3 18.3 38.8 16.6 9.8 4
6.5 21.1 46.2 19.6 9.8 5
5.7 21.2 39.9 21.4 7.7 6
6.6 22.2 43.1 20.7 10.9 7
8.1 22.3 48.5 21.8 9.5 5
6.3 21.8 40.0 20.6 11.6 7
6.9 31.2 56.7 25.2 11.6 9A stepwise regression is shown in Exhibit 15.7. (Only the first three steps are shown to con-
serve space. For purposes of this exercise, we will not let the lack of statistical significance
worry us.)X 5X 4X 3X 2X 1R^2YN MSresidual g(Y 2 YN)^2 >(N 2 p 2 1)YN R0.1234=rYYNR^2Exercises 573