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4/11/11
Regression 2
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Finding Regression Coefficient
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Goal regression equation with best fit to data
Minimize error between Y and Y
hat
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Math Solution
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Matrix Algebra
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Combines Xs into matrix
Rows for subjects columns for variables
Transposes, matrix inverse, derivatives and other math fun
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Practical solution
Use a computer
R: linear model function, lm (YX1+X2+X3)
Matlab: regress (predictors, dependent)
SPSS – point and click
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Regression vs. Correlation
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One predictor and One outcome: regression = correlation
Plus commitment about which variable predicts the other
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Multiple predictors
Predictors affect each other
Each coefficient depends on what other predictors are included
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Example 3
rd
variable problem (Correlation is useless)
Math achievement and verbal achievement both depend on overall
IQ
Math helps with English?
Add IQ as a predictor math achievement  IQ predict English
achievement
b sub math will be near 0
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 Spring '11
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