2. Sleeping and Happiness
Hours slept
(X)
Happiness
(Y)
Pam 8 7
Jim 9
Dwight 5 4
Michael 6
Meredith
You are interested in the relationship between hours slept and happiness.
1) Make a scatter plot
2) Guess the correlation
3) Guess and draw the location of the regression line

3. . . . . .
r = .76

4. 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)

5. Regression allows us to predict!. . . . .

6. 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)

7. Excel Example

8. 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

9. 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)

10. 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

11. 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

12. 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

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

14. . . . . .

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

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

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

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

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

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

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

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

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

24. 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

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

26. Y = (1.5)X . . . . .

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

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

29. Y = (1.5)X . . . . . . .