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Published bySavannah Callahan Modified over 3 years ago

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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 and draw the location of the regression line Hours slept (X) Happine ss (Y) Pam87 Jim99 Dwight54 Michael68 Meredith76

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..... r =.76

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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)

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Regression allows us to predict!.....

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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)

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Excel Example

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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

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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)

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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

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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

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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

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

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.....

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

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

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b b = r = correlation between X and Y S Y = standard deviation of Y S X = standard deviation of X

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

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

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.....

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

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

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

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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

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

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.....

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

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

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Y = (1.5)X

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