EPS 625 – INTERMEDIATE STATISTICS
BLOCK ENTRY MULTIPLE REGRESSION – EXAMPLE
A researcher conducted a study to evaluate a strength-injury hypothesis. She collects data on a
group of 100 elderly women. Specifically, the study was designed with five predictor variables
divided into lower-body strength measures (QUADRICEPS, GLUTS, and ABDOMENS) and
upper-body strength measures (ARMS and GRIP). The researcher sets out to determine how
accurately can a physical INJURY index (injury, which is the number and severity of accidents)
be predicted from a linear combination of five different strength measures for elderly women?
Specifically, she wants to know:
1. How well can a physical injury index be predicted from a linear combination of
strength measures in elderly women?
2. How well do the lower-body strength measures predict the physical injury index
for elderly women?
3. How well do the upper-body strength measures predict the physical injury index
for elderly women?
4. For elderly women, how well do the upper-body strength measures predict the
physical injury index over and above the lower-body strength measures?
The dataset for this example is on the web site, labeled Injury Index (MLR) – Dataset. The
dataset contains a total of 6 variables for a sample of 100 elderly women. For this example, you
will use an a priori alpha level of .05 ( = .05) for all analyses. Your dependent measure will be
the participants’ physical injury index (INJURY), which is based on the records kept by the
participant’s physician and the independent variables are as follows:
quadriceps A measure of strength primarily associated with the quadriceps
gluts
A measure of strength of the muscles in the upper part of the back of the leg
and the buttocks
abdomens A measure of strength of the muscles of the abdomen and the lower back
arms
A measure of strength of the muscles of the arms and the shoulders
grip
An assessment of the hand-grip strength
injury
Overall injury index based on the records kept by the participant’s physician
Once you have obtained the data set, complete/answer each of the following questions. Be brief
– but be thorough in order to receive the maximum possible points for each question. Be sure to
answer all parts and sub-parts of each question.
1. First, check for multicollinearity. Conduct the appropriate diagnostic analysis and indicate
your findings below. Be sure to include what you found, the criteria in which it was judged
against, and indicate whether there is a concern or not and how you made your decision.
FOR MULTICOLLINEARITY:
Checked: VARIANCE INFLATION FACTOR (VIF)
Criteria (critical value): 10.0 (greater than)
VARIABLE
OBTAINED
(INDICATED) VALUE
CONCERN OR NOT
A CONCERN
REASON FOR
DECISION
QUADRICEPS
1.441
Not a concern
VIF < 10.0
GLUTS
1.670
Not a concern
VIF < 10.0
ABDOMENS
1.478
Not a concern
VIF < 10.0
ARMS
1.410
Not a concern
VIF < 10.0
GRIP
1.272
Not a concern
VIF < 10.0
2. Using the full dataset – run the regression analysis to answer the following questions:
1. How well can a physical injury index be predicted from a linear combination of strength
measures in elderly women?
2. How well do the lower-body strength measures predict the physical injury index for
elderly women?
3. How well do the upper-body strength measures predict the physical injury index for
elderly women?
4. For elderly women, how well do the upper-body strength measures predict the physical
injury index over and above the lower-body strength measures?
2a. In answering the first research question, indicate what proportion of the total variance in
the injury index is explained by the entire set of independent variables? Is this proportion
of explained variance significant? Indicate how you made that decision.
Approximately 32.7% (r2 = .327)
YES, this is significant (from the Model 2 section of the ANOVA table)
F(5, 94) = 9.127, p < .001
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2b. In answering the second research question, indicate what proportion of the total variance
in the injury index is explained by the set of control (lower-body strength) variables? Is
this proportion of explained variance significant? Indicate how you made that decision.
Approximately 24.5% (r2 = .245)
YES, this is significant (from the Model 1 section of the Model Summary, Change
Statistics table or the Model 1 section of the ANOVA table)
F(3, 96) = 10.363, p < .001
2c. In answering the third and fourth research questions, indicate what proportion of the total
variance in the physical injury index is explained by the second set (upper-body strength)
of variables? Is this proportion of explained variance significant? Indicate how you made
that decision.
Approximately 8.2% (r2 = .082)
YES, this is significant (from the Model 2 section of the Model Summary, Change
Statistics table)
F(2, 94) = 5.738, p < .01
(or p = .004)
3. Of the five independent variables, which ones (if any) have a significant influence on the
dependent measure? Indicate how you made your determination (account for all 5 variables).
Information can be included From Model 1:
Quadriceps, t = 1.033 (Not Significant) p = .304
Gluts, t = -1.633 (Not Significant) p = .106
(or p > .05)
(or p > .05)
Abdomens, t = -3.944, p < .001
However, the information From Model 2 is what will be used to compare all
variables individually:
Quadriceps, t = 1.536 (Not Significant) p = .128
(or p > .05)
Gluts, t = -1.245 (Not Significant) p = .216
(or p > .05)
Abdomens, t = -3.834 (Significant), p < .001
(p < .05)
Arms, t = -3.366 (Significant), p < .01
Grip, t = 1.596 (Not Significant) p = .114
(or p = .001, or p < .05)
(or p > .05)
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4. List the independent variables, from greatest to least, that are of relative importance (have a
significant influence) on the dependent measure. Indicate how you made your determination.
Careful on the selection.
Looking at only those that were found significant (p < α)… (in order of importance –
from highest to lowest):
Abdomens, β = -.395
Arms, β = -.338
The information should be obtained from Model 2 (the full Model) in that it is where
we can compare all five variables to each other…
5. Choose any one of the significant independent variables (listed above in question 4) from the
full model (Model 2) and briefly explain its relationship with the dependent measure.
For Abdomens:
β = -.395 – indicating that as the elderly women increase their abdominal
strength (controlling for the effect of the other indexes), they decrease their
physical injury index. That is, with increased abdominal strength there should be
fewer and less severe physical injuries.
For Arms:
β = -.338 – indicating that as the elderly women increase their arm strength
(controlling for the effect of the other indexes), they decrease their physical injury
index. That is, with increased arm strength there should be fewer and less severe
physical injuries.
6. Complete Tables 1 and 2 based on your SPSS output from the Full (no data points removed)
Regression Analysis. Use three decimal places.
See below…
7. Write a brief results section for this analysis.
See below…
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Table 1
Means, Standard Deviations, and Correlations for Regression of Physical Injury Index (N = 100)
1. Injury Index
1
2
3
4
5
6
1.000
-.163
-.349
-.471
-.397
-.100
1.000
.505
.426
.329
.190
1.000
.525
.375
.278
1.000
.319
.239
1.000
.443
2. Quadriceps Measure
3. Gluts Measure
4. Abdomens Measure
5. Arms Measure
6. Grip Measure
Means
Standard Deviations
1.000
145.840
47.060
30.980
30.260
31.180
9.060
52.089
9.646
5.749
9.566
9.104
5.224
Table 2
Results of Regression of Physical Injury Index on Lower- and Upper-body Strength Measures
B

.588
.109
1.033
Gluts Measure
-1.657
-.183
-1.633
Abdomens Measure
-2.295
-.421
-3.944***
.843
.156
1.536
Gluts Measure
-1.234
-.136
-1.245
Abdomens Measure
-2.148
-.395
-3.834***
Arms Measure
-1.935
-.338
-3.366**
Grip Measure
1.519
.152
1.596
Independent Variables
t
Model 1
Quadriceps Measure
Model 2
Quadriceps Measure
Note. R2 = .245 for Model 1, (p < .001);
R2 = .082 for Model 2, (p < .01;
Total R2 = .327, (p < .001).
**p < .01
***p < .001
Results
Ordinary least squares multiple regression was used to investigate potential influences on
physical injuries for a sample of elderly women. Specifically, a block entry (hierarchical)
multiple regression design was used to answer the following research questions: (a) How well
can a physical injury index be predicted from a linear combination of strength measures in
elderly women?, (b) How well do the lower-body strength measures predict the physical injury
index for elderly women?, (c) How well do the upper-body strength measures predict the
physical injury index for elderly women?, and (d) For elderly women, how well do the upperbody strength measures predict the physical injury index over and above the lower-body strength
measures? The first set of independent (predictor) variables for this study included lower-body
strength measures: (a) a measure of strength primarily associated with the quadriceps; (b) a
measure of strength of the muscles in the upper part of the back of the leg and the buttocks; and
(c) a measure of strength of the muscles of the abdomen and the lower back. This first set of
variables served as the control variables. The second set of independent variables included
upper-body strength measures: (a) a measure of strength of the muscles of the arms and the
shoulders; and (b) an assessment of the hand-grip strength. The dependent variable for this study
was an overall physical injury index based on the records kept by the participant’s physician.
The sample for this study consisted of 100 randomly selected elderly women. As such, an
alpha level of .05 was used for all analyses. Preliminary examination of the results indicated that
there was no extreme multicollinearity in the data (all variance inflation factors were less than
2.0). Using Stevens’ (2002) established criteria for determination, exploratory data analyses were
conducted to test the assumptions of regression and to determine if there were any outliers and/or
potentially influential data points for which, none were found for this set of data.
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The means, standard deviations, and correlations among all of the variables are given in
Table 1. To investigate the four research questions, the first set of independent variables (lowerbody strength measures) were entered into the analysis as the first block and served as the control
variables – then the second set of independent variables (upper-body strength measures) were
entered into the analysis as the second block. The entire set of strength measures accounted for
approximately 33% [R2 = .327, F(5, 94) = 9.127, p < .001] of the total variance in the women’s
overall physical injury index. The set of control variables (lower-body strength measures)
accounted for approximately 25% [R2 = .245, F(3, 96) = 10.363, p < .001] of the total variance in
the women’s overall physical injury index. The set of upper-body strength measures accounted
for approximately 8% [R2 Change = .083, F Change (2, 94) = 5.738, p = .004] of the total
variance in the women’s overall physical injury index. Based on the results from this sample of
elderly women, the upper-body measures did offer significant additional predictive power for the
overall physical injury index beyond that contributed by the lower-body strength measures as
shown through the significant R2 Change = .083.
Of the two sets of variables used in this study, only the abdominal strength measure from
the lower-body measures, and the arms strength measure from the upper-body measures were
significant (important) contributors to the explanation of the elderly women’s overall physical
injury index – both were significant at the .01 alpha level (see Table 2). Of the two strength
measures (in order of importance), the abdominal strength measure ( = -.395) had the strongest
influence. This was followed by the arms strength measure ( = -.338). As can be seen, these
measures were both negative, indicating that the greater the abdominal and arm strength – the
lower the women’s overall physical injury index.
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