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University of North Texas Dr. J. Kyle Roberts © 2004
Unit 8: Regression
Lesson 1: Understanding the Single Predictor Regression Equation
EDER 6010: Statistics for Educational Research
Dr. J. Kyle Roberts
University of North Texas
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GPA for Denton ISD Students
4.54.03.53.02.52.01.51.0.5
MA
TH
100
90
80
70
60
50
University of North Texas Dr. J. Kyle Roberts © 2004
Kyle’s “Mock” Data
JohnMeredithKyleAddie
X1234
Y1112
1 2 3 4
X
1 2 3 4
Y
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Data from Unit 2 Lesson 1: Reviewing the Homework
r = .78
University of North Texas Dr. J. Kyle Roberts © 2004
Remember the Pearson r?“How well does a single line represent my data?”
r = .85 r = -.25 r = 1.0
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Regression will answer the question: Where should I draw the line?
University of North Texas Dr. J. Kyle Roberts © 2004
Equation for a Line
y = a + bx
Where: “a” is the point at which the line intercepts the y-axis and “b” is the slope of the line
Slope = rise/run
y = 1 + .5(x)
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University of North Texas Dr. J. Kyle Roberts © 2004
What is the “Point” of Regression?
Regression is about prediction
If we know someone’s score on one variable, can we “predict” how well they will perform on another variable?
Using students’ gpa to “predict” how they will do on the SAT
SAT = 400 + 100(gpa)
Therefore, if someone had a gpa of 4.0, then we would
“predict” that they would score an 800 on the SAT.
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University of North Texas Dr. J. Kyle Roberts © 2004
Running a Regression in SPSSCreate a dataset utilizing our “mock” data
Analyze Regression Linear
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University of North Texas Dr. J. Kyle Roberts © 2004
SPSS Results
y = a + bxy = .50 + .30(x) Beta = Pearson r
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University of North Texas Dr. J. Kyle Roberts © 2004
Understanding Beta (β)β is the correlation between the dependent variable and the independent variable-or-β is the regression coefficient for the standardized (z-scores) variables
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University of North Texas Dr. J. Kyle Roberts © 2004
What does β tell us?
Remember that β is roughly analogous to the Pearson r.
Therefore, if we were to square the β we would have a measure of effect size which we refer to as an R2.
R2 = effect size for regression-and-η2 = effect size for ANOVA
The effect size tells us how well our regression coefficients are functioning
R2 for the present dataset = .60. Or “x” explains 60% of the variance of “y”.
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University of North Texas Dr. J. Kyle Roberts © 2004
Utilizing “Dummy” Coded Variables
Math = students scores on a math achievement variable
Gender = male – “0.00” female – “1.00”
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University of North Texas Dr. J. Kyle Roberts © 2004
SPSS Results
Predicted Math = 84.20 + 8.0(Gender)This means that the “average” male scores 8.0 points less than the “average” female
Mathmale = 84.20 + 8.0(0.0)Mathmale = 84.20
Mathfemale = 84.20 + 8.0(1.0)Mathfemale = 92.20
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)(0.820.84ˆ xy
University of North Texas Dr. J. Kyle Roberts © 2004
ANOVA and Regression
Results from an ANOVA Results from the regression
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58.2 58.2 R
University of North Texas Dr. J. Kyle Roberts © 2004
Unit 8: Regression
Lesson 1: Understanding the Single Predictor Regression Equation
EDER 6010: Statistics for Educational Research
Dr. J. Kyle Roberts
University of North Texas
GPA for Denton ISD Students
4.54.03.53.02.52.01.51.0.5
MA
TH
100
90
80
70
60
50
