Checking Assumptions Primary Assumptions Secondary Assumptions Adequate variance in each IV (do your predictor variables vary?) Absence of influential cases, e.g., outliers (do all cases exert approximately the same influence on the regression coefficients?) Linearity – does a straight line fit the data points reasonably well? Secondary Assumptions Constant Error Variance (homoscedasticity) Normally distributed error variance In cases that involve moderate violations of these assumptions, the regression analysis is weaken, not invalidated (Tabachnick & Fidell, 1996).

Outliers A case that differs substantially from the main trend of the data Affect the values of the estimated regression coefficients and cause bias Changes in the slope and intercept Detect outliers by examining frequency distributions for individual variables or assessing residuals for multivariate outliers.

r = .62 M = 18.1 Outlier r = .95 M = 19.3

Influential Case – This case is exerting a massive influence on the data, but the outlier produces a very small standardized residual.

Multicollinearity Strong correlation between two or more independent variables in the regression model. Avoid putting two variable that are essentially the same into the equation. Perfect collinearity makes it impossible to obtain unique estimates of the regression coefficients. If two IVs are perfectly correlated then the value of b for each variable is interchangeable Low levels of collinearity pose little threat to regression models As collinearity increases so does the SE of the b-coefficients, Increased standard errors in turn means that coefficients for some independent variables may be found not to be significantly different from 0. In other words, by overinflating the standard errors, multicollinearity makes some variables statistically insignificant when they should be significant. So examine the bivariate correlations between the IVs, and look for “big” values