20) Quarterly figures for e-commerce retail sales were obtained from the first q

Question

20) Quarterly figures for e-commerce retail sales were obtained from the first quarter of 2001 through the fourth quarter of 2007. A regression model was estimated to describe the trend in e-commerce retail sales over time. The Durbin Watson statistic was calculated as 1.727. Using a = .01, we can conclude that there is (Hint, the sample size n=4*7=28, and k=1) A) an inconclusive test. B) no evidence of positive or negative autocorrelation. C) evidence of an outlier. D) evidence of positive autocorrelation. E) evidence of negative autocorrelation.

Explanation / Answer

We know that n=28 and k-1. We look at the table for Durbin-Watson test for alpha=0.01 and find that

d_l=1.10 and d_u=1.24 and the calculated test statistics is d=1.727

First we test for the existance of positive correlation

We have the following rules

We can see that d=1.727 is greater than d_u=1.24, and hence we conclude that there is no evidence of a positive auto correlation

Next we test for the existence of negative auto correlation. The rules are

since d=1.727 is less than 4-d_u=4-1.24=2.76 we can say that there is no evidence of first order negative correlation

That means we can say that there is no evidence of positive or negative autocorrelation

We could have done a 2 tail test at alpha=0.02 level and conclude that there is no auto-correlation (change in the language and alpha) as d is between d_u and 4-d_u

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