A regression model has 2 independent variables and 16 observations, and the calculated Durbin-Watson d statistic is 2.78. What, if any, conclusion will be reached in testing for autocorrelation of the residuals with a:
a. two-tail test at the 0.05 level of significance?
b. Test the negative autocorrelation at the 0.01 level?
statistics - MathMate, Tuesday, August 18, 2009 at 8:43am
2 independent variables (k=2)
Durbin-Watson statistic = 2.78 (possible negative correlation)
Null Hypothesis: No autocorrelation exists in the residuals.
a. At the 0.05 level of significance for k=2 and 16 observations, DL=0.982, DU=1.539 for positive correlation. Complement of the Durbin-Watson statistic is 4-2.78=1.22.
Since 1.22 is about half-way between DL and DU, the Durbin-Watson test is inconclusive at the 5% level of significance, and the null hypothesis is not rejected. (i.e. absence of negative autocorrelation is not confirmed)
b. At the 0.01 level for k=2 and 16 observations, DL=0.738 and DU=1.253.
Since 1.22 is just slightly below the DU value of 1.253, we conclude that the null hypothesis is not rejected. (i.e. absence of negative autocorrelation)