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chapter14

# chapter14 - Regression Model Building Setting Possibly a...

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Regression Model Building Setting: Possibly a large set of predictor variables (including interactions). Goal: Fit a parsimonious model that explains variation in Y with a small set of predictors Automated Procedures and all possible regressions: Backward Elimination (Top down approach) Forward Selection (Bottom up approach) Stepwise Regression (Combines Forward/Backward) C p Statistic - Summarizes each possible model, where “best” model can be selected based on statistic

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Backward Elimination Select a significance level to stay in the model (e.g. SLS=0.20, generally .05 is too low, causing too many variables to be removed) Fit the full model with all possible predictors Consider the predictor with lowest t -statistic (highest P -value). If P > SLS, remove the predictor and fit model without this variable (must re-fit model here because partial regression coefficients change) If P SLS, stop and keep current model Continue until all predictors have P -values below SLS
Forward Selection Choose a significance level to enter the model (e.g. SLE=0.20, generally .05 is too low, causing too few variables to be entered) Fit all simple regression models. Consider the predictor with the highest t -statistic (lowest P -value) If P SLE, keep this variable and fit all two variable models that include this predictor If P > SLE, stop and keep previous model Continue until no new predictors have P SLE

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Stepwise Regression Select SLS and SLE (SLE<SLS) Starts like Forward Selection (Bottom up process) New variables must have P SLE to enter Re-tests all “old variables” that have already been entered, must have P SLS to stay in model Continues until no new variables can be entered and no old variables need to be removed
All Possible Regressions - C p Fits every possible model. If K potential predictor variables, there are 2 K -1 models.

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chapter14 - Regression Model Building Setting Possibly a...

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