# Statistics for Environmental Engineers

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The test examines whether the first-order autocorrelation parameter p is zero. In the case where p = 0, the errors are independent. The test statistic is:

n

et e,-1 )2 D = -2-

n

!(ei )2

i=1

where the et are the residuals determined by fitting a model using least squares.

Durbin and Watson (1971) obtained approximate upper and lower bounds (dL and dU) on the statistic D. If dL < D < dU, the test is inconclusive. However, if D > dU, conclude p = 0; and if D < dL, conclude p > 0. A few Durbin-Watson test bounds for the 0.05 level of significance are given in Table 41.3. Note that this test is for positive p. If p < 0, a test for negative correlation is required; the test statistic to be used is 4 — D, where D is calculated as before.

Results of Trend Analysis of Data in Figure 41.3

 Result Time Series A Time Series B Generating model yt = 10 + at yt = 10 + 0.8et_1 + at Fitted model y t = 9.98 + 0.0051 y t = 9.71 + 0.033Г Confidence interval of Д [ -0.012 to 0.023] [0.005 to 0.061] Standard error of Д 0.009 0.014 Conclusion regarding в в = 0 в > 0 Durbin-Watson statistic 2.17 0.44 Скачать в pdf «Statistics for Environmental Engineers» P. M. Berthouex, L. C. BrownISBN 1-56670-592-4Метки учебные пособия