For a combination of α (level of significance) = 0.05, n (sample size) = 25, k (number of independent variables in the model) = 1 and D (Durbin-Watson statistic) = 1.30 , what statistical decision should be made when testing the null hypothesis of no negative autocorrelation? a. Accept the null hypothesis. b. Neither reject nor not reject the null hypothesis. c. Do not reject the null hypothesis. d. Accept the alternative hypothesis.
Question
For a combination of α (level of significance) = 0.05, n (sample size) = 25, k (number of independent variables in the model) = 1 and D (Durbin-Watson statistic) = 1.30 , what statistical decision should be made when testing the null hypothesis of no negative autocorrelation?
a. Accept the null hypothesis. b. Neither reject nor not reject the null hypothesis. c. Do not reject the null hypothesis. d. Accept the alternative hypothesis.
Solution
The Durbin-Watson statistic is a test for autocorrelation in the residuals from a statistical regression analysis. The null hypothesis of the test is that there is no serial correlation. The test statistic is approximately equal to 2*(1-r) where r is the sample autocorrelation of the residuals. Thus, for r=0, indicating no serial correlation, the test statistic equals 2. This implies that a value below 2 suggests positive autocorrelation and a value above 2 suggests negative autocorrelation.
Given that the Durbin-Watson statistic (D) is 1.30, this suggests positive autocorrelation. However, the null hypothesis is testing for no negative autocorrelation. Since the test statistic suggests positive autocorrelation, we do not have evidence to reject the null hypothesis of no negative autocorrelation.
Therefore, the correct answer is:
c. Do not reject the null hypothesis.
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