USGS Scientific Investigations Report 2010–5008 Use of Continuous Monitors and Autosamplers to Predict Unmeasured Water-Quality Constituents in Tributaries of the Tualatin River, Oregon

Table 12. Preliminary model statistics for correlation of Escherichia coli bacteria with continuous parameters at Fanno Creek near Durham, Oregon.

[No Scenario 2 data sets were available because USGS did not collect E. coli data during the study period. Regression models are of the form E. coli = a*Turb+ b*Q + c*SC + d, where a, b, and c are regression coefficients and d is the intercept, Turb, Q, and SC are the explanatory variables turbidity (in Formazin Nephelometric Units), discharge (in cubic feet per second), and specific conductance (in microsiemens per centimeter), respectively, and E. coli is the dependent variable, E. coli bacteria counts, in colonies per 100 milliliters. In some models, as indicated by the model form column, the dependent or explanatory variables were log transformed. Where E. coli is log transformed, a bias transformation factor (BCF; Duan, 1983) is multiplied by 10^(log^{E. coli}⁾ to get the final value. RMSE values are in colonies per 100 mL. The maximum Variance Inflation Factor (VIF) indicates the largest VIF obtained for any one variable in the correlation. Abbreviations: n, number of samples; Adj.-R², adjusted R², a coefficient of determination which adjusts for degrees of freedom and penalizes the use of too many explanatory variables; f, a function of indicated constituents; E. coli, Escherichia coli bacteria; log, base 10 logarithm; RMSE, root mean square error; USGS, U.S. Geological Survey; –, not included in the regression]

Model No. and form	Model calibration								Model validation—Goodness-of-fit evaluation
	Value of coefficient, when used					Correlation statistics			Model validation—Goodness-of-fit evaluation
	a	b	c	d	BCF	n	Adj.-R²	Maximum VIF	Mean error	Validation RMSE	Coefficient of determination	Nash-Sutcliffe coefficient	z-statistic from sign test
Scenario 1	Calibration data set—Autosamplers only								Validation data set—Clean Water Services ambient monitoring data
1. logE. coli=f(Turb)	0.014	–	–	2.53	1.22	54	0.692	–	528.3	196.6	0.50	-2.2	5.45
2. logE. coli=f(logTurb, logQ)	1.69	-0.702	–	1.76	1.19	54	0.713	¹2.7	219.2	1,760	0.36	0.25	2.09
Scenario 3	Calibration data set—Peak autosampler plus first monthly and high flow monitoring samples from Clean Water Services dataset								Validation data set—Remaining monthly low flow Clean Water Services ambient monitoring + non-peak autosampler data
3. logE. coli=f(Turb)	0.014	–	–	2.17	1.53	40	0.590	–	-454	996	0.31	0.16	1.86
4. logE. coli=f(Turb, Q)	0.016	-0.002	–	2.21	1.42	40	0.586	¹2.6	-407	2,470	0.31	0.07	2.06
5. logE. coli=f(Turb, logQ)	0.016	-0.18	–	2.39	1.43	40	0.595	¹1.7	-410	1,077	0.28	0.004	2.06
6. E. coli=f(Turb,Q)	103.7	-28.4	–	-2.39	–	40	0.7	¹2.3	-81	1,425	0.69	0.69	1.07

¹Exceeds a threshold VIF value, calculated as {1/(1– (Adj.-R²)} and indicates possible multicollinearity.