Final answer:
A negative serial correlation in the Durbin-Watson statistic indicates that there is a pattern where one period's error is opposite in sign to the subsequent period's error.
Step-by-step explanation:
A negative serial correlation in the Durbin-Watson statistic indicates that the error terms in a regression analysis are negatively autocorrelated.
This situation occurs when the Durbin-Watson statistic is substantially greater than 2, suggesting that one period's error is, on average, opposite in sign to the error of the following period.
If the test concludes that the correlation coefficient is significantly different from zero, we say the correlation coefficient is significant.
However, in the case of the Durbin-Watson statistic, we are looking for evidence of autocorrelation in the residuals of a regression analysis.
A negative serial correlation happens when successive residuals are, more often than not, opposite in sign to each other, which could imply that the regression model is oscillating and may not be picking up some pattern in the data.
On the other hand, if the test concludes the correlation coefficient is not significantly different from zero (it is close to zero), we say the correlation coefficient is not significant.
In terms of Durbin-Watson, values close to 2 indicate no autocorrelation, which is the desirable outcome.