1. 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 Next Slide

2. Kyle’s “Mock” Data Next Slide Data from Unit 2 Lesson 1: Reviewing the Homework r = .78 John Meredith Kyle Addie X 1 2 3 4 Y 1 1 1 2 1 2 3 4 X 1 2 3 4 Y

3. Remember the Pearson r? “ How well does a single line represent my data?” Next Slide Regression will answer the question: Where should I draw the line? r = .85 r = -.25 r = 1.0

4. Equation for a Line Slope = rise/run y = 1 + .5(x) Next Slide y = a + bx Where: “a” is the point at which the line intercepts the y-axis and “b” is the slope of the line

5. 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. Next Slide

6. Running a Regression in SPSS Create a dataset utilizing our “mock” data Analyze  Regression  Linear Next Slide

7. SPSS Results y = a + bx Next Slide y = .50 + .30(x) Beta = Pearson r

8. 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 Next Slide

9. 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 R 2 . R 2 = effect size for regression -and- η 2 = effect size for ANOVA The effect size tells us how well our regression coefficients are functioning R 2 for the present dataset = .60. Or “x” explains 60% of the variance of “y”. Next Slide

10. Utilizing “Dummy” Coded Variables Next Slide Math = students scores on a math achievement variable Gender = male – “0.00” female – “1.00”

11. SPSS Results Predicted Math = 84.20 + 8.0(Gender) This means that the “average” male scores 8.0 points less than the “average” female Math male = 84.20 + 8.0(0.0) Math male = 84.20 Math female = 84.20 + 8.0(1.0) Math female = 92.20 Next Slide

12. ANOVA and Regression Next Slide Results from an ANOVA Results from the regression

13. 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