MULTIPLE REGRESSION 2
Individual Write-up: Multiple Regression
Findings
Research Question
The research question for this study was:
RQ1: Is there a significant predictive relationship between the criterion variable (Stats
Exam Scores) and the linear combination of predictor variables (Math test, English test, English
GPA, Math GPA, and Other GPA) for college students?
The null hypothesis for the study is:
H01: There will be no significant predictive relationship between the criterion variable
(Statistics Exam Scores) and the linear combination of predictor variables (Math test, English
test, English GPA, Math GPA, and Other GPA) for college students.
MULTIPLE REGRESSION 3
Descriptive Statistics
Data obtained for the predictor variables and criterion variables relationships statistics
exam score can be found in Table 1.
Table 1
Descriptive Statistics
Mean
Std.
Deviation N
Average percentage correct
on statistics exams
60.11 19.788 100
Math aptitude test score 460.6
0
77.366 100
English aptitude test score 478.2
0
71.653 100
High school English GPA 2.818
3
.27633 100
High school math GPA 2.776
3
.30234 100
GPA in other high school
classes
3.023
6
.22220 100
Results
Data screening
A data screening was conducted on the predictor variables and criterion variables
to determine if there were any inconsistencies. A matrix scatter plot was used to determine if
there were any extreme bivariate outliers. The matrix scatter plot showed no extreme bivariate
outliers. See Figure 1 for the matrix scatter plot.
MULTIPLE REGRESSION 4
Assumptions
A MULTIPLE REGRESSION was used to assess the null hypothesis that looked at
whether there will be no significant predictive relationship between the criterion variable
(Statistics Exam Scores) and the linear combination of predictor variables (Math test, English
test, English GPA, Math GPA, and Other GPA) for college students. The MULTIPLE
REGRESSION requires an assumption of multivariate normal distribution and non-
MULTIPLE REGRESSION 5
multicollinearity to be acceptable. There was multivariate normal distribution examined by using
a matrix scatter plot. There were no violations of multivariate normal distributions found. The
“classic cigar shape” was formed. See Figure 2 for Matrix scatter plot.
Figure 2. Matrix Scatter Plot for predictor variables and criterion variable
MULTIPLE REGRESSION 6
There was an assumption of non-multicollinearity among the predictor variables that was
tested by examining the Variance Inflation Factor (VIF) for each predictor variable. Looking at
the VIF it was determined that the assumption of non-multicollinearity among the predictor
variables was tenable with the VIF values ranging from 1.17-1.42. See Table 2 for VIF values.
Table 2
Coefficients
Model
Unstandardized
Coefficients
Standardize
d
Coefficients
t Sig.
Collinearity Statistics
B Std. Error Beta Tolerance VIF
1 (Constant) 6.745 27.691 .244 .808
Math aptitude test
score .116 .025 .453 4.726 .000 .847 1.181
English aptitude test
score .049 .027 .179 1.816 .073 .801 1.249
High school English
GPA -3.365 7.446 -.047 -.452 .652 .719 1.391
High school math GPA 5.478 6.865 .084 .798 .427 .707 1.415
GPA in other high
school classes -9.702 8.500 -.109 -1.141 .257 .854 1.172
a. Dependent Variable: Average percentage correct on statistics exams
Results for Null Hypothesis One
A MULTIPLE REGRESSION was conducted to examine the predictive
relationship between the predictor variables and the criterion variable, and to test the null
hypothesis, the lack of a significant predictive relationship between the predictor variables and
the criterion variable. The null hypothesis was rejected at a 95% confidence level were R2 = .27,
MULTIPLE REGRESSION 7
adjusted R2 = .23, F(5,94) = 6.92, p < .001. See Table 3 for ANOVA and Table 4 for Model
Summary
Table 3
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression 10432.432 5 2086.486 6.922 .000b
Residual 28333.358 94 301.419
Total 38765.790 99
a. Dependent Variable: Average percentage correct on statistics exams
b. Predictors: (Constant), GPA in other high school classes, Math aptitude test
score, High school English GPA, English aptitude test score, High school math
GPA
Table 4
Model Summaryb
Model R R Square
Adjusted R
Square Std. Error of the Estimate
1 .519a.269 .230 17.361
a. Predictors: (Constant), GPA in other high school classes, Math aptitude test
score, High school English GPA, English aptitude test score, High school math
GPA
b. Dependent Variable: Average percentage correct on statistics exams
MULTIPLE REGRESSION 8
The predictive model was determined to be statistically significant. The math test scores
best predicted the criterion variable with a t-stat of 4.73 and a p-value of <.001. See Table 5
Regression Model Coefficients.
Table 5
Coefficientsa
Model
Unstandardized
Coefficients
Standar
dized
Coeffic
ients
t Sig.
95.0%
Confidence
Interval for B Correlations
Collinearity
Statistics
B
Std.
Error Beta
Lower
Bound
Upper
Bound
Zero-
order
Parti
al Part
Tolera
nce VIF
1 (Constant) 6.745 27.691 .244 .808 -48.236 61.726
Math aptitude
test score
.116 .025 .453 4.72
6
.000 .067 .164 .484 .438 .417 .847 1.181
English
aptitude test
score
.049 .027 .179 1.81
6
.073 -.005 .103 .202 .184 .160 .801 1.249
High school
English GPA
-3.365 7.446 -.047 -.45
2
.652 -18.150 11.420 .062 -.04
7
-.04
0
.719 1.391
High school
math GPA
5.478 6.865 .084 .798 .427 -8.153 19.109 .229 .082 .070 .707 1.415
GPA in other
high school
classes
-9.702 8.500 -.109 -
1.14
1
.257 -26.578 7.175 .024 -.11
7
-.10
1
.854 1.172
a. Dependent Variable: Average percentage correct on statistics exams
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