Stepwise Regression SAS

Download the Data atData.htmhttp://core.ecu.edu/psyc/wuenschk/StatData/St atData.htm and so on

Download the SAS Code Programs.htmhttp://core.ecu.edu/psyc/wuenschk/SAS/SAS- Programs.htm data grades; infile 'C:\Users\Vati\Documents\StatData\MultReg.dat'; input GPA GRE_Q GRE_V MAT AR; PROC REG; a: MODEL GPA = GRE_Q GRE_V MAT AR / STB SCORR2 selection=forward slentry =.05 details; run;

Forward Selection, Step 1 Statistics for Entry DF = 1,28 VariableToleranceModel R-Square F ValuePr > F GRE_Q GRE_V MAT AR All predictors have p < the slentry value of.05. AR has the lowest p. AR enters first.

Step 2 Statistics for Entry DF = 1,27 VariableToleranceModel R-Square F ValuePr > F GRE_Q GRE_V MAT All predictors have p < the slentry value of.05. GRE-V has the lowest p. GRE-V enters second.

Step 3 Statistics for Entry DF = 1,26 VariableToleranceModel R-Square F ValuePr > F GRE_Q MAT No predictor has p <.05, forward selection terminates.

The Final Model Parameter Estimates VariableDFParameter Estimate Standard Error t ValuePr > |t|Standard ized Estimate Squared Semi- partial Corr Type II Intercept GRE_V AR R 2 =.516, F(2, 27) = 14.36, p <.001

Backward Selection b: MODEL GPA = GRE_Q GRE_V MAT AR / STB SCORR2 selection=backward slstay =.05 details; run; We start out with a simultaneous multiple regression, including all predictors. Then we trim that model.

Step 1 VariableParameter Estimate Standard Error Type II SSF ValuePr > F Intercept GRE_Q GRE_V MAT AR GRE-V and AR have p values that exceed the slstay value of.05. AR has the larger p, it is dropped from the model.

Step 2 Statistics for Removal DF = 1,26 VariablePartial R-Square Model R-Square F ValuePr > F GRE_Q GRE_V MAT Only GRE_V has p >.05, it is dropped from the model.

Step 3 Statistics for Removal DF = 1,27 VariablePartial R-Square Model R-Square F ValuePr > F GRE_Q MAT No predictor has p <.05, backwards elimination halts.

The Final Model Parameter Estimates VariableDFParameter Estimate Standard Error t ValuePr > |t|Standard ized Estimate Squared Semi- partial Corr Type II Intercept GRE_Q MAT R 2 =.5183, F(2, 27) = 18.87, p <.001

What the F Test? Forward selection led to a model with AR and GRE_V Backward selection led to a model with MAT and GRE_Q. I am getting suspicious about the utility of procedures like this.

Fully Stepwise Selection c: MODEL GPA = GRE_Q GRE_V MAT AR / STB SCORR2 selection=stepwise slentry=.08 slstay =.08 details; run; Like forward selection, but, once added to the model, a predictor is considered for elimination in subsequent steps.

Step 3 Steps 1 and 2 are identical to those of forward selection, but with slentry set to.08, MAT enters the model. Statistics for Entry DF = 1,26 VariableToleranceModel R-Square F ValuePr > F GRE_Q MAT

Step 4 GRE_Q enters. Now we have every predictor in the model Statistics for Entry DF = 1,25 VariableToleranceModel R-Square F ValuePr > F GRE_Q

Step 5 Once GRE_Q is in the model, AR and GRE_V become eligible for removal. Statistics for Removal DF = 1,25 VariablePartial R-Square Model R-Square F ValuePr > F GRE_Q GRE_V MAT AR

Step 6 AR out, GRE_V still eligible for removal. Statistics for Removal DF = 1,26 VariablePartial R-Square Model R-Square F ValuePr > F GRE_Q GRE_V MAT

Step 7 At this point, no variables in the model are eligible for removal And no variables not in the model are eligible for entry. The final model includes MAT and GRE_Q Same as the final model with backwards selection.

R-Square Selection d: MODEL GPA = GRE_Q GRE_V MAT AR / selection=rsquare cp mse; run; Test all one predictor models, all two predictor models, and so on. Goal is the get highest R 2 with fewer than all predictors.

One Predictor Models Number in Model R-SquareC(p)MSEVariables in Model AR GRE_Q MAT GRE_V

One Predictor Models AR yields the highest R 2 C(p) = 16.74, MSE =.229 Mallows says best model will be that with small C(p) and value of C(p) near that of p (number of parameters in the model). p here is 2 – one predictor and the intercept Howell suggests one keep adding predictors until MSE starts increasing.

Two Predictor Models Number in Model R-SquareC(p)MSEVariables in Model GRE_Q MAT GRE_V AR GRE_Q AR GRE_V MAT MAT AR GRE_Q GRE_V

Two Predictor Models Compared to the best one predictor model, that with MAT and GRE_Q has –Considerably higher R 2 –Considerably lower C(p) –Value of C(p), 5, close to value of p, 3. –Considerably lower MSE

Three Predictor Models Number in Model R-SquareC(p)MSEVariables in Model GRE_Q GRE_V MAT GRE_Q MAT AR GRE_V MAT AR GRE_Q GRE_V AR

Three Predictor Models Adding GRE_V to the best two predictor model (GRE_Q and MAT) –Slightly increases R 2 (from.58 to.62) –Reduces [C(p) – p] from 2 to.6 –Reduces MSE from.16 to.15 None of these stats impress me much, I am inclined to take the GRE_Q, MAT model as being best.

Closer Look at MAT, GRE_Q, GRE_V e: MODEL GPA = GRE_Q GRE_V MAT / STB SCORR2; run; Parameter Estimates VariableDFParameter Estimate Standard Error t ValuePr > |t|Standard ized Estimate Squared Semi- partial Corr Type II Intercept GRE_Q GRE_V MAT

Keep GRE_V or Not ? It does not have a significant partial effect in the model, why keep it? Because it is free info. You get GRE-V and GRE_Q for the same price as GRE_Q along. Equi donati dentes non inspiciuntur. –As (gift) horses age, their gums recede, making them look long in the tooth.

Add AR ? R 2 increases from.617 to.640 C(p) = p (always true in full model) MSE drops from.154 to.150 Getting AR data is expensive Stop gathering the AR data, unless it has some other value.

Conclusions Read p/Stepwise-Voodoo.htm p/Stepwise-Voodoo.htm Treat all claims based on stepwise algorithms as if they were made by Saddam Hussein on a bad day with a headache having a friendly chat with George Bush.