How to perform a Durbin-Watson test?

To perform a Durbin-Watson test, calculate the test statistic and compare it to the critical values.

The Durbin-Watson test is used to test for autocorrelation in a regression model. Autocorrelation occurs when the errors in a regression model are correlated with each other. This violates the assumption of independence of errors, which is necessary for valid inference in regression analysis.

To perform a Durbin-Watson test, first calculate the test statistic using the formula:

DW = ∑(ei - ei-1)² / ∑ei²

where ei is the residual at time i and ei-1 is the residual at time i-1. The test statistic ranges from 0 to 4, with values close to 2 indicating no autocorrelation, values less than 2 indicating positive autocorrelation, and values greater than 2 indicating negative autocorrelation.

Next, compare the test statistic to the critical values in a Durbin-Watson table. The critical values depend on the sample size, the number of regressors, and the level of significance. For example, for a sample size of 20 and 2 regressors at the 5% level of significance, the critical values are 0.95 and 1.65.

If the test statistic is less than the lower critical value, there is evidence of positive autocorrelation. If the test statistic is greater than the upper critical value, there is evidence of negative autocorrelation. If the test statistic is between the critical values, there is no evidence of autocorrelation.

In conclusion, the Durbin-Watson test is a useful tool for detecting autocorrelation in regression models. By calculating the test statistic and comparing it to the critical values, we can determine whether there is evidence of autocorrelation and adjust our analysis accordingly.