What is the typical implication of a low Durbin-Watson statistic?

A low Durbin-Watson statistic implies that there is a strong presence of positive autocorrelation in the residuals of a regression model. The Durbin-Watson statistic ranges from 0 to 4, where a value around 2 indicates no autocorrelation, values significantly lower than 2 suggest positive autocorrelation, and values above 2 indicate negative autocorrelation.

When the Durbin-Watson statistic is low (typically below 1.5), it suggests that the residuals (the differences between observed and predicted values) are not independent from one another. This can indicate issues such as an omitted variable in the model or that the model is improperly specified, leading to systematic patterns in the residuals rather than random errors, which is a key assumption of regression analysis.

In contrast, a value closer to 2 supports the notion of random errors, meaning that the residuals are behaving as expected under ideal conditions without systematic patterns. The other options imply various scenarios of model fit or error structures that do not align with the interpretation of a low Durbin-Watson statistic, thus reinforcing the understanding of autocorrelation in this context.