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Sleeping and Happiness You are interested in the relationship between hours slept and happiness. 1) Make a scatter plot 2) Guess the correlation 3) Guess.

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Presentation on theme: "Sleeping and Happiness You are interested in the relationship between hours slept and happiness. 1) Make a scatter plot 2) Guess the correlation 3) Guess."— Presentation transcript:

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2 Sleeping and Happiness 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 Hours slept (X) Happine ss (Y) Pam87 Jim99 Dwight54 Michael68 Meredith76

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 Thats 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 = X 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 = X 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 = 1 Error = -1 Error =.5 Error = -.5Error = 0 Error = Y - Y (Y - Y) 2 is minimized

16 Finding a and b Ingredients r value between the two variables S y and S x Mean of Y and X

17 b b = r = correlation between X and Y S Y = standard deviation of Y S X = 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; S Y = 2.41 r =.88 Mean X = 3.0; S X = 1.41

20 .....

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

22 b = Mean Y = 4.6; S Y = 2.41 r =.88 Mean X = 3.0; S X = 1.41

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

24 0.1 = (1.50)3.0 Mean Y = 4.6; S Y = 2.41 r =.88 Mean X = 3.0; S X = 1.41 b = 1.5

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

26 .....

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

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

29 Y = (1.5)X


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