correlation and regression examples

correlation and regression examples - COMPUTATION EXAMPLES...

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COMPUTATION EXAMPLES FOR CORRELATION AND REGRESSION 1
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FORMULAS FOR CORRELATION AND REGRESSION Correlation coefficient r : r = ( X - X )( Y - Y ) q ( X - X ) 2 q ( Y - Y ) 2 Slope of least squares regression line b : b = ( X - X )( Y - Y ) ( X - X ) 2 Intercept of least squares regression line a : a = Y - bX 2
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COMPARE r AND b FORMULAS Both have same numerator. Just need SS X in b denominator. 3
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VISUAL AND HEARING PERFORMANCE SCORES FOR 10 SUBJECTS A B C D E F G H I J X 15 12 10 14 10 8 6 13 16 13 Y 20 15 12 18 10 13 12 10 18 15 4
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INTERMEDIATE CALCULATIONS A B C D E F G H I X 15 12 10 14 10 8 6 13 16 Y 20 15 12 18 10 13 12 10 18 ( X - X ) 2 9.61 0.01 3.61 4.41 3.61 15.21 34.82 9.61 16.81 ( Y - Y ) 2 32.49 0.49 5.29 13.69 18.49 1.69 5.29 18.49 13.69 ( X - X ) × ( Y - Y ) 17.67 0.07 4.37 7.77 8.17 5.07 13.57 -13.33 15.17 X = 11 . 9 Y = 14 . 3 SS X = ( X - X ) 2 = 98 . 9 Y = ( Y - Y ) 2 = 110 . 1 CP XY = ( X - X )( Y - Y ) = 59 . 3 5
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ESTIMATES OF CORRELATION, REGRESSION Correlation coefficient r : r = ( X - X )( Y - Y ) q ( X - X ) 2 q ( Y - Y ) 2 = 59 . 3 98 . 9 110 . 1 = 0 . 57 Slope of least squares regression line b : b = ( X - X )( Y - Y ) ( X - X ) 2 = 59 . 3 98 . 9 = 0 . 60 Intercept of least squares regression line a : a =
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This note was uploaded on 11/30/2009 for the course HP 400m at USC.

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correlation and regression examples - COMPUTATION EXAMPLES...

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