MultipleRegression-CompleteAnalysis.ppt

Social Work Statistics Strategy for Complete Regression Analysis Additional issues in regression analysis Assumption of independence of errors Influential cases Multicollinearity Adjusted R2 Strategy for Solving problems Sample problems Complete regression analysis Assumption of independence of errors - 1 Multiple regression assumes that the errors are independent and there is no serial correlation. Errors are the residuals or differences between the actual score for a case and the score estimated using the regression equation. No serial correlation implies that the size of the residual for one case has no impact on the size of the residual for the next case. The Durbin-Watson statistic is used to test for the presence of serial correlation among the residuals. The value of the Durbin-Watson statistic ranges from 0 to 4. As a general rule of thumb, the residuals are not correlated if the Durbin-Watson statistic is approximately 2, and an acceptable range is 1.50 - 2.50. Assumption of independence of errors - 2 Serial correlation is more of a concern in analyses that involve time series. If it does occur in relationship analyses, its presence can be usually be understood by changing the sequence of cases and running the analysis again. If the problem with serial correlation disappears, it may be ignored. If the problem with serial correlation remains, it can usually be handled by using the difference between successive data points as the dependent variable. Multicollinearity - 1 Multicollinearity is a problem in regression analysis that occurs when two independent variables are highly correlated, e.g. r = 0.90, or higher. The relationship between the independent variables and the dependent variables is distorted by the very strong relationship between the independent variables, leading to the likelihood that our interpretation of relationships will be incorrect. In the worst case, if the variables are perfectly correlated, the regression cannot be compute