Independence of Residuals - Durbin-Watson Statistic

The next assumption is that the residuals are not correlated serially from one observation to the next. This means the size of the residual for one case has no impact on the size of the residual for the next case. While this is particularly a problem for time-series data, SPSS provides a simple statistical measure for serial correlation for all regression problems. The Durbin-Watson Statistic is used to test for the presence of serial correlation among the residuals. Unfortunately, SPSS does not print the probability for accepting or rejecting the presence of serial correlation, though probability tables for the statistic are available in other texts.

 

The value of the Durbin-Watson statistic ranges from 0 to 4. As a general rule of thumb, the residuals are uncorrelated is the Durbin-Watson statistic is approximately 2. A value close to 0 indicates strong positive correlation, while a value of 4 indicates strong negative correlation.

 

For our problem, the value of Durbin-Waston is 1.910, approximately equal to 2, indicating no serial correlation.