If the d-statistic in the Durbin-Watson Test is 0.5,

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Question restatement: If the d-statistic in the Durbin-Watson Test is 0.5, which statement is implied by the result?

Option a: 'we do not reject the null hypothesis.' In the Durbin-Watson framework, the null hypothesis typically posits no first-order serial correlation in the residuals. A DW value as low as 0.5 suggests a strong positive autocorrelation, making it unlikely to fail to reject the null. Therefore, this option is inconsistent with a DW of 0.5.

Option b: 'there is no serial correlation in the residuals.' This directly contradicts the meaning of a very small DW statistic. A value near 0 indicates strong positive serial correlation, not the absence of it. Hence this statement is incorrect for a DW of 0.5.

Option c: 'there are some problems about the test.' While no statistical test is perfect, this option is vague and does not address the specific interpretation of a DW value of 0.5. The question asks for what the statistic indicates about residuals, not about test validity. This makes the statement not informative about the result indicated by 0.5.

Option d: 'there is serial correlation in the residuals.' This is the direct, correct interpretation for a low Durbin-Watson value like 0.5. A small DW statistic signals positive first-order autocorrelation in the residuals, meaning successive residuals are correlated rather than independent. This aligns with the typical interpretation of DW values significantly below 2.

Additional context to reinforce understanding: The Durbin-Watson statistic ranges from 0 to 4. A value around 2 suggests no autocorrelation. Values substantially below 2 imply positive autocorrelation, while values substantially above 2 imply negative autocorrelation. A DW of 0.5 is far from 2 and points toward meaningful positive serial correlation in the error terms, which has implications for standard errors and model specification. However, the exact decision against a null hypothesis would depend on critical value tables or p-values for the sample size and number of regressors. In any case, the direction indicated by 0.5 is consistent with the presence of serial correlation in residuals, rather than its absence.

ECON7950 (1) [2024 B2] In-Class Quiz 2

If the d-statistic in the Durbin-Watson Test is 0.5,

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