Statistics for Environmental Engineers

Скачать в pdf «Statistics for Environmental Engineers»

For both data sets, the true underlying trend is zero (the models contain no term for slope). If trend is examined by fitting a model of the form n = ft0 + P1t, where t is time, the results are in Table 41.4.

For Series A in Figure 41.3, the fitted model is y = 9.98 + 0.005t, but the confidence interval for the slope includes zero and we simplify the model to y = 10.11, the average of the observed values.

For Series B in Figure 41.3, the fitted model is y = 9.71 + 0.033t. The confidence interval of the slope does not include zero and the nonexistent upward trend seems verified. This is caused by the serial correlation. The serial correlation causes the time series to drift and over a short period of time this drift looks like an upward trend. There is no reason to expect that this upward drift will continue. A series

generated with a different set of at’s could have had a downward trend. The Durbin-Watson statistic did give the correct warning about serial correlation.


We have seen that autocorrelation can cause serious problems in regression. The Durbin-Watson statistic might indicate when there is cause to worry about autocorrelation. It will not always detect autocorrelation, and it is especially likely to fail when the data set is small. Even when autocorrelation is revealed as a problem, it is too late to eliminate it from the data and one faces the task of deciding how to model it.

Скачать в pdf «Statistics for Environmental Engineers»