Regression
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This document discusses various methods of regression analysis including hierarchical, stepwise, and forward/backward regression. It also discusses how to assess the fit of a regression model by identifying outliers and influential cases using standardized residuals, unstandardized residuals, and studentized residuals. Residual statistics like deleted residuals, Cook's distance, and leverage values can help evaluate the influence of individual cases and determine if they significantly impact the regression model.
Regression
- 1. Regression
- 2. Forced MethodsofRegression Hierarchical Step Wise Then Unknown Known First Then Others More Important First All are forced Simultaneously Only useful for Theory Testing Forward Backward Based on Mathematical Criterion More correlated is entered first and then other
- 3. Assessing The Regression Model Two Important Questions Does the model fit the observed data well, or is it influenced by a small number of cases? Can my model Generalize to other samples? Question 1 Question 2
- 4. Answering the Model Fit Outliers Influential Cases The one different from others A case which stands out Case with Large Residual
- 5. Outliers With Residuals Standardized Residuals Un standardized Residuals Can not tell how big residual will be considered big. Using the Properties of Normal Distribution helps us in making a rule for deciding large or small Rule of 3.28 Rule of 2.58 Rule of 1.96 There be no value with more than 3.28 SR Model is unacceptable if more than 5% cases have Standardized Residual>2.58 Model is unacceptable if more than 1% cases have Standardized Residual>2.58
- 6. OutliersWithResiduals Standardized Residuals Un standardized Residuals Studentized Residuals Real Residuals Residuals with mean zero and standard deviation of one Un-standardized residual divided by an estimate of its standard deviation
- 7. Influential Cases By Excluding a certain case, the slope and intercept of the regression line is affected. It means the model is not stable and changes its coefficients from one sample to another.
- 8. Residual Statistics to Assess the Effect of a Particular CaseDeleted Residual Adjusted predicted Value Studentized Deleted Residual A new model is calculated with using a particular case. Then that particular case is predicted. This value is called APV. If the case is not an influential one, then the adjusted predicted value will be very near the originally predicted value. difference between the adjusted predicted value and the original observed value = DR Studentized Deleted Residual = DR/ Standard Deviation This residual can be compared across different regression analyses because it is measured in standard units.
- 9. Residual Statistics to Assess the Effect of a Particular Case Deleted Residuals Can not Provide any information about how a case influences the model as a whole Deleted Residuals Can Assess the influence of a case on the ability of the model to predict that case. So how we can assess the influence Cook’s Distance Mahalanobis Distances Leverage