Lecture 15 - Regression Correlation Background Defines...

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Regression Correlation Background Defines relationship between two variables X and Y R ranges from -1 (perfect negative correlation) 0 (No correlation) +1 (perfect positive correlation)
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Regression Correlation Background R 2 Indicates reduction in error knowing X and Predicting Y R 2 ranges from 0 (No reduction in error) 1 (complete reduction in error)
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Regression Examples Predicting height from G.P.A. R 2 = 0 (Knowing height does not help predict G.P.A – best guess is always mean G.P.A.) R 2 = 1 (Knowing height in CM completely predicts height in Inches)
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Regression Real world examples are somewhere in between Predicting height from weight R 2 = .36 (Knowing height somewhat helps predict weight)
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Regression But how do we figure out HOW to make that prediction given one of the variables?
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Regression Need background concept of slope How much does Y change for a given change in X? All lines have 0 2 4 6 8 10 12 14 16 18 20 0 1 2 3 4 5 6 7 8 9 Y=X Y=2X Y=X/2
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Regression -20 -15 -10 -5 0 5 10 15 20 0 1 2 3 4 5 6 7 8 9 Y=-X Y=-2X Y=-X/2 All lines have R=-1
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Regression Need background concept of INTERCEPT What is Y when X=0? All lines have Same Slope but different intercept -5 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 Y=2X Y=2X+5 Y=2X-3
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Regression Unique line is defined by Slope and Y- Intercept Y=bX+a b=slope a=Y-Interecpt -7 -4 -1 2 5 8 11 14 17 20 0 1 2 3 4 5 6 7 8 9 Y=?x+?
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Lecture 15 - Regression Correlation Background Defines...

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