# Durbin Watson test

Problem 12, solution on page 436. The null is NO positive serial correlation. DW=1.8953 is > 1.78 (from the table). Usually, when that happens we reject the null, but here it says we cannot reject the null. What gives?

I think you are just confusing critical levels from other tests with DW. If DW > du, you FAIL to reject the null hypothesis of no positive serial corr. The bigger the DW, the more you are NOT positively serially correlated. Without looking things up it should be obvious. With no serial correlation, your DW is 2.0. The statistic of 1.8953 is closer to 2.0 than 1.78, so you’re less correlated. I just always think of DW ~ 2(1-p): if p = 1, DW is 0, (perfectively positive) if p = 0, DW is 2, (none) if p = -1, DW of 4 (perfectively negative) Keep that in mind in rejecting/accepting the null against the lookup.

Great that makes sense. So, as in other tests, the null (Ho) says no positive serial correlation. If DW is below the lower end (d_low), then we reject the null and say there is positive serial correlation. But if we are suspecting a negative serial correlation, then as in other tests, the null (Ho) says no negative serial correlation. If DW is above the higher end (d_up), then we reject the null and say there is negative serial correlation. To decide whether we should test for negative or positive serial correlation, we look at the correlation, “r”. If it is positive, test for positive, etc. Can you confirm, so that we can seal this and move on?

yes, that’s how i approach it.

Dreary Wrote: ------------------------------------------------------- > So, as in other tests, the null (Ho) says no > positive serial correlation. If DW is below the > lower end (d_low), then we reject the null and say > there is positive serial correlation. But if DW is above d_low and below d_up, we are in the neutral region, and we cannot conclude anything. Finally, if DW > d_up, we cannot reject the null (that there is no positive serial corr) and conclude that there is no positive serial corr.