Which statement describes the purpose of the Durbin-Watson statistic in regression analysis?

Which statement describes the purpose of the Durbin-Watson statistic in regression analysis?

• A. Testing for multicollinearity among predictors
• B. Detecting autocorrelation in the residuals
• C. Assessing the normality of residuals
• D. Measuring variance of residuals across predictors

Answer: (B)

The Durbin-Watson statistic measures whether residuals from a regression are correlated with their immediate predecessor—first-order autocorrelation. It is calculated from the differences between consecutive residuals; a value near 2 suggests the residuals are uncorrelated. Values below 2 indicate positive autocorrelation (residuals tend to have the same sign across adjacent observations), while values above 2 indicate negative autocorrelation (residuals tend to alternate in sign). Detecting autocorrelation matters because it violates the OLS assumption that errors are independent, which can make standard errors and t-statistics unreliable and lead to misleading inferences. If autocorrelation is present, you might model the data with autoregressive terms, use generalized least squares, or apply robust standard errors to obtain valid inference. This statistic does not measure multicollinearity among predictors, assess normality of residuals, or quantify how residual variance changes across predictors, which require different diagnostics.

The Durbin-Watson statistic measures whether residuals from a regression are correlated with their immediate predecessor—first-order autocorrelation. It is calculated from the differences between consecutive residuals; a value near 2 suggests the residuals are uncorrelated. Values below 2 indicate positive autocorrelation (residuals tend to have the same sign across adjacent observations), while values above 2 indicate negative autocorrelation (residuals tend to alternate in sign). Detecting autocorrelation matters because it violates the OLS assumption that errors are independent, which can make standard errors and t-statistics unreliable and lead to misleading inferences. If autocorrelation is present, you might model the data with autoregressive terms, use generalized least squares, or apply robust standard errors to obtain valid inference. This statistic does not measure multicollinearity among predictors, assess normality of residuals, or quantify how residual variance changes across predictors, which require different diagnostics.