Goodness of Model Fit (Regression)

Goodness of Model Fit (Regression)

1. A scatterplot can be used to visually examine the fit of the regression model

2. Errors of Fit

   • • Covariance: How far a point falls from the diagonal

3. Standardising

4. Residual Plot Analysis

5. Removal of Outliers

   • Effect on R^2
     • Removing an outlier may increase or decrease R^2 and F statistics depending on how this outlier was influencing the results prior to its removal
     • Generally, removing a case high in leverage but low in std. residual would decrease R^2. Cases with very low or very high covariance ratios have to be assessed on a case by case basis
   • Effect on F
     • Removal of an outlier may increase or decrease R^2 and D statistics, depending on how this outlier was influencing the results prior to removal
     • The F value is dependent on R^2. Removal of cases reduces the sample size and, therefore, the F value. However, this effect is relatively small compared to a change in R^2

6. Assumptions

   • Independence
   • Linearity
   • Bivariate Normality
   • Homoscedasticity
   • Violations of Assumptions

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