Independence of the errors

A normal linear model assumes that the different errors are uncorrelated with each other.

The p-value for the test based on the Durbin-Watson statistic is the probability of getting such a low value of d when there is no serial correlation. An approximate p-value can be obtained from special statistical tables, but it can also be determined with a simulation, as described in the example below.

World rice production

Warning

If a linear model is used for a time series, but the relationship is actually nonlinear, successive residuals also tend to be similar and the Durbin-Watson statistic will also be small.

An unusually small Durbin-Watson statistic can be caused by either serial correlation or nonlinearity.

The test only suggests serial correlation if you are sure that the data are linear.