Statistical Methods for Psychology

Exercises 575

ANALYSIS OF VARIANCE
SUM OF SQUARES DF MEAN SQUARE F RATIO
REGRESSION 2.9318295 3 0.9772765 4.05
RESIDUAL 1.4481706 6 0.2413618
VARIABLES IN EQUATION VARIABLES NOT IN EQUATION
STD..
ERROR STD..
OF REG F TO. PARTIAL F TO
VARIABLE COEFFICIENT COEFF COEFF TOLERANCE REMOVE LEVEL. VARIABLE CORR. TOLERANCE ENTER LEVEL
(Y-INTERCEPT 1.830 )
X2 3 0.104 0.035 0.942 0.55484 8.93 1. X1 2 –0.14937 0.24520 0.11 1
X4 5 0.190 0.170 0.359 0.53416 1.25 1. X3 4 0.14753 0.31072 0.11 1
X5 6 –0.294 0.130 –0.799 0.44362 5.14 1

Exhibit 15.7 (continued)

a. What are the values ofR for the successive steps?

b. From the definition of a partial correlation (in terms of Venn diagrams), show that

the at step 2 is a function of at step 1 and the partial correlation listed under

step 1—“VARIABLES NOT IN EQUATION.”

15.17 In Exercise 15.16 what meaning attaches to as far as the Vermont Department of Health

is concerned?

15.18 In Exercise 15.16 the adjusted would actually be lower for five predictors than for three

predictors. Why?

15.19 In Exercise 15.16 the fifth predictor has a very low correlation with the criterion (r 5 .05)

and yet plays a significant role in the regression. Why?

15.20 For the data in Exercise 15.16, compute. How well does this equa-

tion fit compared with the optimal equation? Why should this be the case?

15.21 For the data in Exercise 15.16, would it be safe to conclude that decreasing the number of

mothers who fail to seek medical care before the third trimester is a good way to decrease

the incidence of low-birthweight infants?

15.22Create a set of data on 10 cases that illustrates leverage, distance, and influence. Use any

standard regression program to produce statistics measuring these attributes.

15.23Produce a set of data where the variance of Yvalues associated with large values of Xis

greater than the variance of Yvalues associated with small values of X. Then run the regres-

sion and plot the residuals on the ordinate against Xon the abscissa. What pattern emerges?

Computer Exercises

15.24 Use the data set Mireault.dat from Mireault (1990), described in the Appendix and found on

the Web site for this book, to examine the relationship between current levels of depression

and other variables. A reasonable model might propose that depression (DepressT) is a

function of (1) the person’s current perceived level of vulnerability to additional loss

(PVLoss), (2) the person’s level of social support (SuppTotl), and (3) the age at which the

person lost a parent during childhood (AgeAtLos). Use any statistical package to evaluate

the model outlined here. (Because only subjects in Group 1 lost a parent to death during

childhood, your analysis will be restricted to that group.)

15.25 A compulsive researcher who wants to cover all possibilities might throw in the total score

on perceived vulnerability (PVTotal) as well as PVLoss. (The total includes vulnerability to

accidents, illness, and life-style related problems.)

a. Run this analysis adding PVTotal to the variables used in Exercise 15.24.

YN= 1 X 211 X 423 X 5

R^2

R*

R^2 R^2