Question

# In testing the assumption that the successive error terms are uncorrelated, we check the Durbin-Watson test...

In testing the assumption that the successive error terms are uncorrelated, we check the Durbin-Watson test statistic. Which one of the following statements is correct?

a. If successive error terms are uncorrelated, the test statistic will be close to 2

b. If successive error terms are negatively correlated, the test statistic will be close to -1

c. If successive error terms are positively correlated, the test statistic will be close to 4

d. If successive error terms are uncorrelated, the test statistic will be close to zero

e. none of the other answers are correct

the correct answer is option (a)  If successive error terms are uncorrelated, the test statistic will be close to 2

Explanation: We know that the Durbin-Watson test statistic can be used to measure the presence of multicollinearity or whether successive error terms are uncorrelated. It is defined as

D-W= . and we make a decision on the basis of the following criteria as below:

• If 1.5 DW 2.5 then there is no autocorrelation.
• If 0< DW< 1.5 then there is positive autocorrelation.
• If 2.5< DW< 4 then there is a negative autocorrelation.

Thus, from the above statement is clear that if successive error terms are uncorrelated i.e no multicollinearity then the value of DW i.e. test statistic will be close to 2.

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