REGRESSION DIAGNOSTICS Fall 2013 Dec 12/13

WHY REGRESSION DIAGNOSTICS? The validity of a regression model is based on a set of assumptions. Violation of basic assumptions cast doubt on regression results. Regression Diagnostics are a set of “tests” used to check those assumptions. Assumptions: 1. Data Accuracy; Linearity; Absence of Multicollinearity 2. Normality of Errors; Errors Cancel on Average; Homoscedasticity of Errors; Influential Outliers

BEFORE REGRESSION Data Accuracy and Linearity: Identify possible outliers and check for accuracy Creating scatter plots of each independent and the dependent variable Absence of Multicollinearity: Multicollinearity exists when a linear relationship exists between two or more independent variables. Check pair-wise correlation coefficients between independent variables. |r|≥0.8 indicates a multicollinearity problem.

AFTER REGRESSION Calculate residuals Normality of Errors Plot residuals in a histogram and an ogive. The histogram should be bell-shaped and the ogive S-curved if errors are normally distributed. Errors Cancel on Average Check the mode of residuals in the histogram and the mean in Descriptive Statistics. They should be close to zero.

AFTER REGRESSION Homoscedasticity of Errors: Error has a constant variance over the full range of the dependent variable. Plot the residuals against the predicted Y. Outliers One influential observation may change the sign of a slope coefficient or the magnitude substantially. Check standardized residuals: how many standard deviations one residual is away from the mean. A standardized residual greater than 3 in absolute value indicates an outlier.