EPS 625 – INTERMEDIATE STATISTICS
BLOCK ENTRY MULTIPLE LINEAR REGRESSION – EXAMPLE II
Researchers continue to be interested in understanding college students’ success. A researcher
has collected data from 500 randomly selected college students, using their Academic Major
Grade Point Average as a measure of academic success. The researcher has also collected
demographic variables (Socio Economic Status and Age) and ability/aptitude variables (High
School Grade Point Average and ACT Composite Score) for each of the students.
The dataset contains 5 variables for a sample of 500 students, and as such an alpha level of .01 is
used for all analyses. For this analysis, your dependent measure (academic success) will be the
students’ academic major grade point average (MAJOR_GPA). You will use two sets of
independent variables. The first set of independent variables will serve as a control and are the
students’ personal (demographic) variables (socio economic status when entering college, SES –
and their age when entering college, AGE). The second set of independent variables is the
students’ ability/aptitude variables (high school grade point average, HS_GPA – and their ACT
composite score, ACT_COMP). Using the set of data, the researcher wants to answer the
following two research questions:
1. To what degree is a students’ academic success predicted by their socio economic status,
age, and academic ability/aptitude?
2. To what degree does a students’ academic ability/aptitude significantly predict their
academic success over and above their socio economic status and age?
1. First, check for multicollinearity. Conduct the appropriate diagnostic analysis and indicate
your findings below based on the Tolerance Value, the Variance Inflation Factor (VIF), and
the Condition Index. Be sure to include what you found, the criteria in which it was judged
against, and indicate whether there is a concern or not for each of the independent variables.
This summary information will assist you in writing your results section.
2. Using the full dataset – run the regression analysis to answer the following questions:
2a. What is the total variance of academic success explained by the entire set of
independent variables (RQ 1)? Is this proportion significant?
2b. What is the total variance of academic success explained by the set of control
variables? Is this proportion significant?
2c. What is the total variance of academic success explained by the set of ability/aptitude
variables (RQ 2)? Is this proportion significant?
3. Of the four independent variables, which ones (if any) have a significant influence on the
dependent measure? Indicate how you made your determination.
4. List the independent variables based on their relative importance from greatest to least
influence. Indicate how you made your determination. Be careful on the selection.
5. Choose any one of the significant independent variables from the full model (Model 2) and
briefly explain its relationship with the dependent measure. Don’t forget – you will want to
be looking at its beta coefficient.
6. Using the multiple regression straight line equation, predict a student’s performance on the
statistics exam, given the following information:
SES
3.50
Age
19
High School GPA
3.50
Act Composite
24
7. Write a results section for this analysis. Your result section should be similar to the in-class
example (using APA guidelines), including the two tables and the complete narrative. Be
sure to use the example as a guide so as to not loose points. Complete Table 1 and Table 2,
using two (2) decimal places. Don’t forget to put asterisks where applicable on Table 2
(showing significance).
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Results
Ordinary least squares multiple regression was used to determine to what degree
students’ socio economic status, age, high school grade point average, and ACT composite score
were significant predictors (measures of influence) on students’ academic success. Additionally,
the analysis investigated whether students’ high school grade point average and ACT composite
score contribute significantly over and above their socio economic status and age on their
academic success? The first set of independent variables included 1) SES – the students’ socio
economic status when entering college and 2) Age – the students’ age when entering college.
This first set of variables served as the control variables. The second set of independent variables
included 1) Students’ high school grade point average and 2) Students’ ACT composite score.
The dependent variable was the students’ academic success, as measured by their academic
major grade point average.
The sample for this study consisted of 500 randomly selected students who attended and
subsequently graduated from a mid-sized regional university. With a sample size of 500 students,
an alpha level of .01 was used for all analyses. Preliminary examination of the results indicated
that there was no extreme multicollinearity in the data. 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. The means, standard deviations, and correlations among all
of the variables are given in Table 1.
To answer the first research question (To what degree is a students’ academic success
predicted by their socio economic status, age, and academic ability/aptitude?) we found that the
entire set of variables (socio economic status, age, high school grade point average, and ACT
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composite score) accounted for approximately 67%, R2 = .67, F(4, 495) = 253.32, p < .001, of
the total variance in students’ academic success. Based on the results from this sample of
students, the set of four predictor variables appear to provide a significant degree of influence on
students’ academic success.
To investigate the second research question (To what degree does a students’ academic
ability/aptitude significantly predict their academic success over and above their socio economic
status and age?), the first set of independent variables (socio economic status and age) were
entered into the analysis as the first block and served as the control variables – then the second
set of independent variables (high school grade point average and ACT composite score) were
entered into the analysis as the second block to investigate any significant influence over and
above the control variables. The set of ability/aptitude measures did predict significantly over
and above the control variables, R2 = .65, F Change(2, 495) = 489.34, p < .001. Based on the
results from this sample of students, the two measures of students’ ability/aptitude appear to
offer significant additional predictive power beyond that contributed by the students’ socio
economic status and age.
The set of control variables accounted for approximately 2%, R2 = .02, F(2, 497) = 5.84,
p < .01, of the total variance in students’ academic success. Of the two sets of variables used in
this study, three of the predictor variables were significant (important) contributors to the
explanation of the students’ academic success (see Table 2). In order of importance, the students’
high school grade point average ( = .78, p < .001) had the strongest influence. This was
followed by the students’ ACT composite score ( = .11, p < .01) then the students’ age ( =
-.10, p < .001). As can be seen, the ability/aptitude measures were both positive, indicating that
the greater the students’ high school grade point average and ACT composite score – the greater
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the students’ academic success (academic majors’ grade point average). The students’ age was
inversely related, indicating that the younger the student – the greater their academic success.
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Table 1
Means, Standard Deviations, and Correlations for Regression of Academic Success (N = ______)
1
1. Academic Success
2. Socio Economic Status
3. Age
4. High School Grade Point Average
5. ACT Composite Score
2
3
4
5
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Means
Standard Deviations
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Table 2
Results of Regression of Academic Success on Personal and Ability/Aptitude Variables
Independent Variables
B

t
Model 1
Socio Economic Status
Age
Model 2
Socio Economic Status
Age
High School GPA
ACT Composite Score
Note. R2 = ______ for Model 1 (p ______); R2 = ______ for Model 2 (p ______); Total R2 = ______ (p ______).
**p < .01, ***p < .001