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11 - Regression 2 Finding Regression Coefficient o Goal...

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4/11/11 Regression 2 Finding Regression Coefficient o Goal- regression equation with best fit to data Minimize error between Y and Y hat Math Solution o Matrix Algebra o Combines Xs into matrix Rows for subjects columns for variables Transposes, matrix inverse, derivatives and other math fun o Practical solution Use a computer R: linear model function, lm (Y-X1+X2+X3) Matlab: regress (predictors, dependent) SPSS – point and click Regression vs. Correlation o One predictor and One outcome: regression = correlation Plus commitment about which variable predicts the other o Multiple predictors Predictors affect each other Each coefficient depends on what other predictors are included o 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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