Durbin Watson Statistic

The Durbin Watson Statistic lets us know when good statistical regression analysis has gone bad...like a donut that looks good on the outside, but is actually super stale. Nobody likes a stale donut.

The Durbin Watson Statistic tests a time-series regression for autocorrelation, which we don’t want. Other tests might say “hey, you, your regression is looking good!” while the Durbin Watson Statistic test might say “uhmmm, actually, you should take another look...something’s not right, even if the others tests checked out.” The Durbin Watson Statistic gives a value of 2 if there’s not autocorrelation, or a value above or below 2 (within 0 - 4 range), which means there’s negative or positive autocorrelation.

So what is autocorrelation, and why is it bad? Regressions are functions that try to use a bunch of data to predict something. Basically, regressions are a statistical method to find correlations (it can’t prove causations, though...for that we’ve gotta have experiments) by fitting data to a line. Finding the best line for the data is the goal. How far the data points are from the line is the error, which we want to minimize to get the best fit line.

When there’s autocorrelation, that means your error value of your regression is correlated, either negatively or positively. If your regression “fits” the data well and your errors are correlated, that means something’s wrong. For instance, it could mean that you missed a really important variable that has some explanatory power, which shouldn’t be nested in your error, but a part of your regression line (omitted variable bias).

You can also get autocorrelation when your regression is functionally misspecified, which means your regression doesn’t actually fit the data well, because you have equal errors on both sides of your regression line, showing that you missed something in the relationship...which is kinda the point of doing a regression.

A third way you can get autocorrelation is measurement error in the independent variable, which will cause your independent variable and your error variable to both reflect that measurement error, and you’ll find your errors correlating over time with that measurement error.