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**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

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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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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

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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 = -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

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**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

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

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**Finding a and b Ingredients r value between the two variables**

Sy and Sx Mean of Y and X

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**b = b r = correlation between X and Y SY = standard deviation of Y**

SX = 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; SY = 2.41 r = .88 Mean X = 3.0; SX = 1.41**

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

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

b =

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

b = .88 1.50 1.41

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**Mean Y = 4.6; SY = 2.41 r = .88 Mean X = 3.0; SX = 1.41 b = 1.5**

a = Y - bX

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**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

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

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Y = (1.5)X . . . . .

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

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

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

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