Do I need to run a Durbin-Watson test if I am finding regressions for the number of second-language words learnt in a week based on age in years? All the results are from different participants.
If so, are values of 2.382 and 2.626 close enough to 2 to be able to calculate linear regressions?
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Salut. Frankly speaking, I did not get what exactly you are going to explain in the model, but if it is a times series regression, you need to check autocorrelation. Better choice than Durbin-Watson test is e.g. Langrange multiplier test. You can easily check 'why' in any book in basic econometrics. To determine, whether values of 2.382 and 2.626 are close enough to 2, you need to check number of parameters and number of observations in the model. See table od bound values for Durbin-Watson test on page 4: https://www3.nd.edu/~wevans1/econ30331/Durbin_Watson_tables.pdf


Fortran must die
Durbin Watson only tests for first order autocorrelation so it has strict limits. Breusch Godfrey is a much more general test and Durbin created other more general statistics such as the durbin t statistic which are useful if you can find them.

You should always test for autocorrelation - even when not time series. Time is the most common, but not the only cause of autocorrelation.