2. Practice

3. Practice

4. Practice

5. Practice r = X = 20 X2 = 120 Y = 19 Y2 = 123 XY = 72 N = 4 (4) 72

6. Practice r = X = 20 X2 = 120 Y = 19 Y2 = 123 XY = 72 N = 4 -92 20
(4)
120
(4)
123 20 19
X = 20 X2 = 120
Y = 19 Y2 = 123
XY = 72 N = 4

7. Practice r = X = 20 X2 = 120 Y = 19 Y2 = 123 XY = 72 N = 4 -92 2080
131
X = 20 X2 = 120
Y = 19 Y2 = 123
XY = 72 N = 4

8. Practice -.90 = X = 20 X2 = 120 Y = 19 Y2 = 123 XY = 72 N = 4 -92
102.37 80
131
X = 20 X2 = 120
Y = 19 Y2 = 123
XY = 72 N = 4

9. Remember this: Statistics Needed
Need to find the best place to draw the regression line on a scatter plot
Need to quantify the cluster of scores around this regression line (i.e., the correlation coefficient)

10. Regression allows us to predict!. . . . .

11. Straight Line Y = mX + b Where:
Y and X are variables representing scores
m = slope of the line (constant)
b = intercept of the line with the Y axis (constant)

12. Excel Example

13. That’s nice but
How do you figure out the best values to use for m and b ?
First lets move into the language of regression

14. Straight Line Y = mX + b Where:
Y and X are variables representing scores
m = slope of the line (constant)
b = intercept of the line with the Y axis (constant)

15. Regression Equation Y = a + bX Where:
Y = value predicted from a particular X value
a = point at which the regression line intersects the Y axis
b = slope of the regression line
X = X value for which you wish to predict a Y value

16. Practice Y = -7 + 2X What is the slope and the Y-intercept?
Determine the value of Y for each X:
X = 1, X = 3, X = 5, X = 10

17. Practice Y = -7 + 2X What is the slope and the Y-intercept?
Determine the value of Y for each X:
X = 1, X = 3, X = 5, X = 10
Y = -5, Y = -1, Y = 3, Y = 13

18. Finding a and b Uses the least squares method Minimizes Error
Error = Y - Y
 (Y - Y)2 is minimized

19. . . . . .

20. . . . . . Error = Y - Y  (Y - Y)2 is minimized Error = 1 Error = .5

21. Finding a and b Ingredients r value between the two variables
Sy and Sx
Mean of Y and X

22. b = b r = correlation between X and Y SY = standard deviation of Y
SX = standard deviation of X

23. a
a = Y - bX
Y = mean of the Y scores
b = regression coefficient computed previously
X = mean of the X scores

24. Mean Y = 4.6; SY = 2.41 r = .88 Mean X = 3.0; SX = 1.41

25. Mean Y = 4.6; SY = 2.41 r = .88 Mean X = 3.0; SX = 1.41

26. Mean Y = 4.6; SY = 2.41 r = .88 Mean X = 3.0; SX = 1.41
b =

27. Mean Y = 4.6; SY = 2.41 r = .88 Mean X = 3.0; SX = 1.41
b =
.88
1.50
1.41

28. Mean Y = 4.6; SY = 2.41 r = .88 Mean X = 3.0; SX = 1.41 b = 1.5
a = Y - bX

29. Mean Y = 4.6; SY = 2.41 r = .88 Mean X = 3.0; SX = 1.41 b = 1.5
0.1 = (1.50)3.0

30. Regression Equation
Y = a + bX
Y = (1.5)X

31. Y = (1.5)X . . . . .

32. Y = (1.5)X X = 1; Y = 1.6 . . . . . .

33. Y = (1.5)X X = 5; Y = 7.60 . . . . . . .

34. Y = (1.5)X . . . . . . .

37. Practice

38. Mean Y = 14.50; Sy = 4.43 Mean X = 6.00; Sx= 2.16 r = -.57

39. Mean Y = 14.50; Sy = 4.43 Mean X = 6.00; Sx= 2.16 r = -.57
b =

40. Mean Y = 14.50; Sy = 4.43 Mean X = 6.00; Sx= 2.16 r = -.57
b =
-.57
-1.17
2.16

41. Mean Y = 14.50; Sy = 4.43 Mean X = 6.00; Sx= 2.16 b = -1.17
a = Y - bX

42. Mean Y = 14.50; Sy = 4.43 Mean X = 6.00; Sx= 2.16 b = -1.17
21.52= (-1.17)6.0

43. Regression Equation
Y = a + bX
Y = (-1.17)X

44. Y = (-1.17)X . 22 20 . 18 16 . 14 . 12 10

45. Y = (-1.17)X . . 22 20 . 18 16 . 14 . 12 10

46. Y = (-1.17)X . . 22 20 . 18 16 . 14 . . 12 10

47. Y = (-1.17)X . . 22 20 . 18 16 . 14 . . 12 10