I am trying to understand whether the Durbin-Watson test is meaningful at all when applied to regression data that have no temporal order (eg. blood pressure ~ bodyMassIndex + exercise).
I would say no, as the autocorrelation should obviously vary with the order of the subjects (which is random), but I wonder whether the durbinWatsonTest in R involves a bootstrapping of the data, where order of the bootstrapping data is shuffled each time, and then perhaps an average autocorrelation is computed over the bootstrapping samples (but then again, shouldn't this average autocorrelation be zero for randomly sampled data?). On the other hand, the value of the statistics seems to be quite stable over multiple runs of the function, so I am even more confused…
I came across it in Andy Field's book "Discovering Statistics with R", where it is used is an example with non-time series data, although in another, more recent book of the same author ("Adventures in Statistics") it does say that the test is applicable only to time series data.
and 
and 
. Since anomalies are present the appropriate regression needs to take into account these effects. Following are the three models ( including any necessary lag structures in the two inputs ) and the appropriate ARIMA structure obtained from an automatic transfer function run using AUTOBOX ( a piece of software I have been developing for the last 42 years )
and 
and 
. We now take the three cleansed series returned from the modelling process and estimate a minimally sufficient common model which in this case would be a comtemporary and 1 lag PDL on tweets and a contemporary PDL on wiki with an ARIMA of (1,0,0)(0,0,0). Estimating this model locally and globally provides insight as to the commonality of coefficients .
with coefficients 
. The test for commonality is easily rejected with an F value of 79 with 3,291 df. Note that the DW statistic is 2.63 from the composite analysis. The summary of coefffici
ents is presented here. The OP poster reflected that the only software he has access to is insufficient to be able to answer this thorny research question.
Best Answer
Autocorrelation is only meaningful when the data is ordered, such as in time series that are naturally ordered along the time scale, or when the distance between the observations is meaningful, such as the case of spatial data. Edit: Another case where the distance between the observations is meaningful is highlighted by @whuber's comment: it may reflect the order in which the data were collected. There, presence of autocorrelation could reflect some peculiarities of the data-collection mechanism.
Without that, autocorrelation is ill-defined. You can randomly permute the data without changing its information content. Therefore, the Durbin-Watson test becomes redundant. (Also, since each permutation of the data will produce a different Durbin-Watson statistic, the statistic is not even uniquely defined.)
If the measured autocorrelation is low for a particular ordering of the data, it may be that permuting the data randomly will not result in high autocorrelation. But try sorting the data by the size of the residuals in your regression and apply the test then. You will most likely find strong autocorrelation. If, on the other hand, you had strong autocorrelation to begin with, randomly reshuffling of the data could destroy it, and thus the test results would change perceptably.
According to @aginensky, this is not the case. Citing him (with all due credit),