solution

PSYCH 302
Dr. Graham
Spring 2013
Problem Set 3
1. Go back to #1 from the last problem set. This question used data from 10 participants to examine the relationship
between self esteem and social support. Recall that the correlation between social support and self-esteem was .565
a. Calculate the regression equation predicting self-esteem (y) from social support (x). (Hint: some numbers
that will save you a lot of time are still available on the problem set 2 solutions)
b=r * (Sy/Sx) = .567 * (4.03/5.45) = .42 [1 point]
a = Y – X (b) = 10-11.8*.42 = 5.04 [1 point]
Y = 5.04 + .42 (X) [1 point]
b. In words, interpret what the slope and intercept of the regression equation you computed mean
[1 point] Intercept: the expected self esteem of someone with no social support is 5.04.
[1 point] Slope: for every point of social support someone receives, we expect their self esteem to go
up .42 points.
c. If the correlation between X and Y was zero, what value would you use to predict an individual’s level of
self-esteem?
[1 point] The mean of self-esteem, or 10, or a, or the intercept
d. What is the proportion of variance self-esteem that is explained (though not necessarily caused) by social
support.
[1 point] .567 2 = 32% or .32
2. Use the data from problem #1 to answer the following questions using SPSS. Hand in your SPSS output and
clearly indicate the following (circle the values and label them):
a. What is the value of the unstandardized slope and intercept predicting self-esteem from social support?
[1 point]
b. What is the value of the standardized slope predicting self-esteem from social support?
[1 point]
c. What is the proportion of variance in self-esteem predicted by social support?
[1 point]
d. What is the relationship between the standardized slope and the percentage of variance in self esteem
predicted by social support? The percentage of variance predicted is the squared standardized
slope
[1 point]

Regression
[DataSet1] U:\correlationSPSS.sav
SelfEsteem
SocialSupport
Pearson Correlation
Sig. (1-tailed)
N
Model
1
Descriptive Statistics
Mean Std. Deviation N
10.00 4.028 10
12.00 5.416 10
Correlations
SelfEsteem
SocialSupport
SelfEsteem
SocialSupport
SelfEsteem
SocialSupport
Variables Entered/Removed b
Social
Support a Variables Variables
Entered Removed Method
. Enter
a. All requested variables entered.
b. Dependent Variable: SelfEsteem
Model
1
Model Summary
SelfEsteem SocialSupport
1.000 .565
.565 1.000
. .044
.044 .
10 10
10 10
.565 a Adjusted Std. Error of
R R Square R Square the Estim ate
.320 .235 3.524
a. Predictors: (Constant), SocialSupport
Model
1
Regression
Residual
Total
ANOVA b
46.670 1 46.670 3.759 .089 a
Sum of
Squares df Mean Square F Sig.
99.330 8 12.416
146.000 9
a. Predictors: (Constant), SocialSupport
b. Dependent Variable: SelfEsteem
Proportion of variance predicted

Model
1
[1 point]
(Constant)
SocialSupport
Unstandardized
Coefficients
a. Dependent Variable: SelfEsteem
3a.
Coefficients a
Standardized
Coefficients
B Std. Error Beta
t Sig.
4.955 2.831 1.750 .118
.420 .217 .565 1.939 .089
2d. The percentage of variance explained (R 2 ) is the squared standardized slope (β)
[1 point] Correctly Running Analysis
Regression
[DataSet2] U:\myweb\PS3Data.sav
pain
severity
eeg
gsr
epinephe
physfit
Unstandardized Intercept
Unstandardized Slope
Descriptive Statistics
Mean Std. Deviation N
50.00 10.000 330
21.9605 19.10513 330
25.7288 18.03886 330
70.0933 15.87248 330
11.7758 8.01128 330
50.0001 9.99999 330
Standardized Slope

Pearson Correlation
Sig. (1-tailed)
N
Model
1
pain
severity
eeg
gsr
epinephe
physfit
pain
severity
eeg
gsr
epinephe
physfit
pain
severity
eeg
gsr
epinephe
physfit
Variables Entered/Removed b
physfit,
eeg, gsr,
severity,
epinephe a
Variables
Entered
Variables
Removed Method
Correlations
pain severity eeg gsr epinephe physfit
1.000 .644 -.505 .360 .607 -.148
. Enter
a. All requested variables entered.
b. Dependent Variable: pain
Model
1
Model Summary
.719 a Adjusted Std. Error of
R R Square R Square the Estim ate
.518 .510 6.999
a.
Predictors: (Constant), physfit, eeg, gsr, severity,
epinephe
.644 1.000 -.450 .460 .856 .110
-.505 -.450 1.000 -.387 -.590 .037
.360 .460 -.387 1.000 .441 .126
.607 .856 -.590 .441 1.000 .214
-.148 .110 .037 .126 .214 1.000
. .000 .000 .000 .000 .004
.000 . .000 .000 .000 .023
.000 .000 . .000 .000 .251
.000 .000 .000 . .000 .011
.000 .000 .000 .000 . .000
.004 .023 .251 .011 .000 .
330 330 330 330 330 330
330 330 330 330 330 330
330 330 330 330 330 330
330 330 330 330 330 330
330 330 330 330 330 330
330 330 330 330 330 330

Model
1
ANOVA b
17028.965 5 3405.793 69.528 .000 a
Sum of
Squares df Mean Square F Sig.
Regression
Residual 15871.035 324 48.985
Total 32900.000 329
a. Predictors: (Constant), physfit, eeg, gsr, severity, epinephe
b. Dependent Variable: pain
Model
1
(Constant)
severity
eeg
gsr
epinephe
physfit
a.
Dependent Variable: pain
Unstandardized
Coefficients
Coefficients a
Standardized
Coefficients
B Std. Error Beta
t Sig.
54.754 2.736 20.011 .000
.222 .041 .425 5.412 .000
-.108 .028 -.194 -3.818 .000
.031 .028 .050 1.106 .270
.195 .109 .156 1.783 .076
-.227 .041 -.227 -5.499 .000

3b. SPI = 54.754 + .031 (GSR) - .108 (eeg) + .195 (Epinepherine) + .222 (Severity) - .227 (PFI)
[1 point] Intercept
[2.5 points] Each unstandardized slope with each predictor (1/2 point each)
3c. 51.8% of the variance in SPI scores is accounted for by all of the independent variables considered
together.
[1 point]
3d.
[5 points, -1 per error]
Table 1
Summary of Multiple Regression Analysis for Variables Predicting Subjective Pain
____________________________________
Zero-order Beta-
Predictor correlation weight
GSR .360 .050
EEG -.505 -.194
Epinepherine .607 .156
Burn Severity .644 .425
Physical Fitness Index -.148 -.227
Note. R 2 = .518. Dependent Variable = Subjective Pain Index. EEG = Electroencephalogram, GSR
= Galvanic Skin Response.
3e. Burn severity level is the best predictor of pain, in the context of the other variables.
[1 point]
3f. GSR is the worst predictor of pain, in the context of the other variables.
[1 point]
3g. Considered alone, Burn severity level is the best predictor of pain.
[1 point]
3h. Considered alone, Physical Fitness is the worst predictor of pain.
[1 point]

3i. Physical fitness appears to be acting as a suppressor variable. The PFI directly contributes relatively
little to the prediction of pain by itself, but gets a relatively large amount of credit in the context of the
other variables. This suggests that considering physicial fitness makes the other measures better
predictors of pain. The other predictors may be partly influenced by how physically fit an individual is;
however, it is not this part of the other variables that predicts pain. The inclusion of PFI scores acts to
suppress the noise (or error) in the other variables.
[1 point] Identify correct suppressor
[1 point] Explain appropriately
3j. Without PFI, the other variables explain 47.3% of the variance in subjective pain. This suggests that
the inclusion of PFI scores explains an additional 4.5% (.518 - .473) of the variance in subjective pain.
[1 point]