Statistics for Environmental Engineers

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This is in contrast to what would have been obtained if the experiment had been conducted in a way that prevented autocorrelation from entering. The data for this case are listed in the “no autocorrelation” section of Table 41.1 and the results are shown in Table 41.2. The fitted model is yi = 20.06 + 0.43xi, the confidence interval of the slope is [0.21 to 0.65] and the t-ratio for the slope is 4.4. The slope is statistically significant and the true value of the slope (в = 0.5) falls within the confidence interval.


Table 41.2 summarizes the results of these two regression examples ( p = 0 and p = 0.8). The Durbin-Watson statistic (explained in the next section) provided by the regression program indicates independence in the case where p = 0, and shows serial correlation in the other case.


Data Created Using True Values of yi = 20 + 0.5xi + ai with ai = N(0,1)


TABLE 41.1


No Autocorrelation    Autocorrelation, p = 0.8


x


n


at


yi = n + at


0.8^t1


+


ai


=


et


yt = n + ei


0


20.0


1.0


21.0


0.00


+


1.0


=


1.0


21.0


1


20.5


0.5


21.0


0.80


+


0.5


=


1.3


21.8


2


21.0


-0.7


20.3


1.04


+

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