Use Statistical Tables to test for positive serial correlation given the following Durbin- Watson d statistics for serial correlation. State your hypothesis. You MUST identify "acceptance", "rejection", and "inconclusive" regions. N=31, K=3, α=5%, d=1.62

 

Null hypothesis = there is presence of no positive autocorrelation in the model.

Alternative hypothesis = there is a  positive autocorrelation in the model.

As the observed value is 1.62, it falls in the region of acceptance of the null hypothesis, that is there is presence of no positive autocorrelation in the model. 

Acceptance region is the region which is than the upper statistical value, Rejection region is the region lower than the lower statistical value and Inconclusive region is the area between lower and upper statistical values.

Step-by-step explanation

Given : d-statistic = 1.62

N = 31

K = 3

Confidence interval () = 5%

In a regression analysis, Durbin-Watson is a test to check the presence of autocorrelation in the error term. The statistics of the test lies between 0 to 4, such that when the value for the test is 2, there is presence of no autocorrelation in the analysis but if the value is greater than 2, the model has negative autocorrelation, while if the value is less than 2, the model has positive autocorrelation.

As per the given information,

Null hypothesis = there is presence of no  positive autocorrelation in the model

Alternative hypothesis = there is a presence of  positive autocorrelation in the model.

As per the Durbin-Watson statistical table, when N = 31 and K = 3, the upper limit of the test that is dU = 1.4250 and lower limit that is dL= 1.022. so,If the given observed value is less than the lower limit value given in the table, that is 1.022, we reject the null hypothesis that there is presence of no autocorrelation in the model called region of rejection.

 if the given observed value is greater than the tabulated upper limit value that is 1.4250, we accept the null hypothesis that there is presence of no autocorrelation in the model called region of acceptance.

If the observed value lies between the upper limit that is 1.4250 and lower limit that is 1.022, we call it region of inconclusiveness that we cannot predict whether there is autocorrelation is present in the model or not

.

So as the observed value d = 1.62,

It is greater than the upper limit, that is 1.4250, that is it falls in the acceptance region of the null hypothesis and we accept the null hypothesis that there is no positive serial correlation in the model.