Statistics for Environmental Engineers

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x 2.5    22    60    90    105    144    178    210    233    256    300    400


y 16.6    15.3    16.9    16.1    17.1    16.9    18.6    19.3    25.8    28.4    35.5    45.3


40.5 Coagulation. Modify the hockey-stick model of Exercise 40.4 so it describes the intersection of two straight lines with nonzero slopes. Fit the model to the coagulation data (dissolved organic carbon, DOC) given below to estimate the slopes of the straight-line segments and the chemical dose (alum) at the intersection.


Alum Dose (mg/L)


DOC


(mg/L)


Alum Dose (mg/L)


DOC


(mg/L)


0


6.7


35


3.3


5


6.4


40


3.3


10


6.0


49


3.1


15


5.2


58


2.8


20


4.7


68


2.7


25


4.1


78


2.6


30


3.9


87


2.6

Source: White, M. W. et al. (1997). J. AWWA, 89(5).

41

The Effect of Autocorrelation on Regression


KEY WORDS autocorrelation, autocorrelation coefficient, drift, Durbin-Watson statistic, randomization, regression, time series, trend analysis, serial correlation, variance (inflation).


Many environmental data exist as sequences over time or space. The time sequence is obvious in some data series, such as daily measurements on river quality. A characteristic of such data can be that neighboring observations tend to be somewhat alike. This tendency is called autocorrelation. Autocorrelation can also arise in laboratory experiments, perhaps because of the sequence in which experimental runs are done or drift in instrument calibration. Randomization reduces the possibility of autocorrelated results. Data from unplanned or unrandomized experiments should be analyzed with an eye open to detect autocorrelation.

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