SHOWS second variable to be chosen to enter regression model explains the

# Shows second variable to be chosen to enter

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SHOWS second variable to be chosen to enter regression model - explains the largest portion of the unexplained variation adjust regression model (equation) as a result of the removed IVs, where p > 0.05 (∞) o Other Notes General stepwise regression always results in model in which all of IVs are statistically significant
Disadvantage to this technique = all possible combos of variables may not be considered when choosing final model - b/c only considering one IV at a time Best Subsets Regression o Best Subsets Regression – examines all combinations of independent variables as possible candidates for the final regression model Limits number of IVs that can be considered For k independent variables, 2^k – 1 = total combinations of regression models to consider In PHStat2, limited to 7 IVs - If more, use a general stepwise regression o The Best Subset Regression – PHStat2 Data – column 1 (DV) and subsequent columns IVs Add-Ins > PHStat2 > Regression > Best Subsets Best Subsets – Data Needed - Y (dependent) variable range - X (independent) variables range (all IV columns) - Check whether labels and 95% CI o Results & What We’re Looking For Want subset with highest Adjusted R² / lowest SE Assigns first IV as x1, etc. When adjusted R² is negative - Could mean large # IV in regression model - b/c when k is larger, R² is smaller Cp Statistic – measures the difference between the true population model and the regression model derived from the sample data - Goal = value that is ≤ (k + 1) - Where k = number of independent variables o Choosing a Selection Method Both models provide same level of performance when predicting value of dependent variable
Choose model with fewer independent variables - b/c less variables reduces chances of multicollinearity o Other Notes If subset regression model gives different solution than stepwise - Probably b/c subset found a combination of variables that the general stepwise method never examined Subset with highest adjusted R² might include IVs that are not statistically significant (p > ∞) Other Selection Methods o Forward Selection Regression – brings one independent variable into the model at a time and does not allow any variables to leave once they have entered P-value to enter criterion for eligibility for model May end up with IVs in model that are not statistically significant Can choose this in Stepwise Regression dialog (data entrance) box Ex: LIKE FAMILY MEMBERS ☺ o Backward Elimination Regression – begins with all of the independent variables in the model; variables that are not significant leave the model one at a time and are never to return P-value to remove value Ex: LIKE AMERICAN IDOL Ensures all remaining IVs will be significant PHStat2 in Stepwise Regression dialogue (data entrance) box o Evaluating Both – Notes Both = stepwise models that look at effect of one IV at a time - → no guarantee that final model will find group

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• Fall '12
• Donnelly
• Normal Distribution, Null hypothesis, Hypothesis testing, Statistical hypothesis testing

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