1. Regression Chapter 6 I Introduction to Regression
Figure 1. Girl’s basketball team (Data from Ch. 5, Table 1)

2. II Criterion for the Line of Best Fit
A. Predicting Y from X
2. Line of best fit minimizes the sum of the squared
prediction errors

3. 3. Errors in predicting Y from X

4.  

5. 5. Illustration of Y intercept, aY.X, and slope of
the best fitting line, bY.X

6. Table 1. Height and Weight of Girl’s Basketball Team
–0.9
–1.4

7. B. Computation of Line of Best Fit: Predicting Y from X 

8. 1. Predicted weight for girl whose height is Xi = 6.5
C. Predicting X from Y  

9. 1. Error in predicting X from Y

10. 2. Predicted height for girl whose weight is Yi = 130
D. Comparison of Two Regression Equations

11. E. Two Regression Lines

12. F. Relationships Between r and the Two Regression Slopes

13. G. Predicted Value of Yi When r = 0
1. Alternative form of the regression equation

14. A. Comparison of SY.X & Standard Deviation (S)
III Standard Error of Estimate (SY.X)
A. Comparison of SY.X & Standard Deviation (S)

15. B. Alternative Formula for SY.X
1. Maximum value of SY.X occurs when r = 0
2. Minimum value of SY.X occurs when r = 1

16. 2. Descriptive Application of SY.X
Figure 2. Approximately 68.27% of the Y scores fall within
Yi ± SY.X

17. IV. Assumptions Associated with Regression
IV Assumptions Associated with Regression and the Standard Error of Estimate
A. Regression
1. Relationship between X and Y is linear
2. X and Y are quantitative variables
B. Standard Error of Estimate
1. Relationship between X and Y is linear
3. Homoscedasticity

18. V Multiple Regression
A. Regression Equation for k Predictors
B. Example with n = 5 Subjects and k = Predictors

19. Observed Predictor Predictor Predicted Prediction
Table 2. Multiple Regression Example with Two Predictors
Observed Predictor Predictor Predicted Prediction
Subject Score One Two Score Error
__________________________________________________
___________________________________________________

20. C. Multiple regression equation
D. Simple Regression Equations

21. Table 3. Correlation Matrix for Data in Table 1
______________________________________
Variable
Variable Y X1 X2
Y –.797
X –.338 X

22. E. Regression Plane for Data in Table 2
Figure 3. (a) Predicted scores fall on the surface of the plane
(b) Prediction errors fall above or below the surface of the plane

23. VI Multiple Correlation (R)
A. Multiple Correlation for Data in Table 2

24. 1. R2 for the multiple correlation data with two
B. Coefficient of Multiple Determination (R2)
1. R2 for the multiple correlation data with two
predictors is R2 = (.962)2 = .93
2. Coefficient of determination for the best
predictor, X2, is r2 = (–.797)2 = .64
3. Coefficient of determination for the worst
predictor, X1, is r2 = (.777)2 = .60
C. The problem of multicollinearity