What is the implication of a high Durbin-Watson statistic in a regression model?Presence of multicollinearity.Presence of heteroscedasticity.Absence of autocorrelation.High goodness of fit.

The Durbin-Watson statistic is a test statistic used to detect the presence of autocorrelation (a relationship between values separated from each other by a given time lag) in the residuals (prediction errors) from a regression analysis.

Here's a step-by-step explanation of the implications of a high Durbin-Watson statistic in a regression model:

1. The Durbin-Watson statistic ranges from 0 to 4. A value of 2.0 means there is no autocorrelation detected in the sample. Values from 0 to less than 2 indicate positive autocorrelation and values from more than 2 to 4 indicate negative autocorrelation.

2. If the Durbin-Watson statistic is substantially less than 2, there is evidence of positive serial correlation. If the statistic is much more than 2, it indicates negative serial correlation.

3. Therefore, a high Durbin-Watson statistic (i.e., much more than 2) in a regression model implies the presence of negative autocorrelation, or in other words, the error terms (residuals) are inversely related. This means that a positive error for one observation increases the chances of a negative error for another observation and vice versa.

4. The presence of autocorrelation violates one of the assumptions of the classical linear regression model, which states that the error terms are uncorrelated. This violation can lead to inefficient parameter estimates and incorrect inference (e.g., confidence intervals that do not contain the true parameter value 95% of the time).

5. The Durbin-Watson statistic does not provide any information about the presence of multicollinearity, heteroscedasticity, or the goodness of fit of the model. These are different aspects of the model that need to be tested using other methods.