Inorganic Blind Sample Project (IBSP)

Regression Equations

Regression Equation Development

The Standard Reference Samples (SRSs) used in the Inorganic Blind Sample Project are analyzed through a round-robin evaluation program described by Farrar and Long (1997). A statistical summary of the round-robin results is prepared for each set of samples. Until 1988, the SRS project used means and standard deviations in the summary reports. After 1988, the SRWS project used median and f-pseudosigma in the summary reports as a measure of location and variability. The mean or median data reported in the SRWS summaries have been referred to as most probable values (MPVs). The f-pseudosigma is defined by Hoaglin and others (2000) as:

f-pseudosigma = (data [Fourth-spread])/1.349

where the Fourth-spread is analogous to the interquartile range (3rd quartile - 1st quartile) of the data. In addition, they show that the f-pseudosigma yields an unbiased estimate of standard deviation when the data distribution is Gaussian. However, it is recognized that some of the SRWS project data sets may not have Gaussian data distributions, the regression equations will be derived from a combination of parametric and nonparametric results.

The SRS project MPVs are used to estimate the MPVs (or target values) of the Inorganic Blind Sample Project mixes based on the proportion of the SRS used. Likewise, if deionized water is used in the preparation of a blind sample mix, then a sample concentration of zero is applied to estimate the resultant MPV based on the proportion used. The resulting MPVs are used in the Inorganic Blind Sample Project to compare with analytical results.

For each constituent, a regression equation was used to estimate the f-pseudosigma (F_S), over a continuous range of concentrations. The equations were derived by regressing the f-pseudosigma or standard deviation against the MPV using ordinary least-squares. Helsel and Hirsch (1992) provide a general model for estimation of ordinary least-squares regression,

F_Si = β₀ + β₁MPV_i + ε_i            i = 1,2,...,n

where

  F_Si = the ith observation of the response (or dependent) variable, F_S 
  MPV_i = the ith observation of the explanatory (or independent) variable, MPV 
  β₀ = the intercept
  β₁ = the slope
  ε_i = the random error or residual for the ith observation, and 
  n = the sample size.

SRS project summary data for semi-annual round-robin sample studies (14 studies over the course of seven years) were used to derive regression equations for each constituent. The table below presents, by FY, the concentration range of SRS samples used, the derived F_S equation, and the coefficient of determination.

As of FY16, reference materials are submitted unaltered from their round-robin form (except for re-bottling into NWQL-required bottle types). The MPV (or target value) and  F_S  come straight from the round-robin studies coordinated by the Standard Reference Sample Project and therefore require no regression equation. (In FY16, one "trace metals" blind-sample and one "major ions" blind sample were mixed in the historical fashion; and thus, required a regression equation to determine control limits. In addition, one nutrient blind-sample is prepared with a 1:9 dilution with ASTM Type I "blank" water for low-level analytical methods. FY16 regression equations are used every year to determine control limits for this blind nutrient sample.)

 

References

Farrar, Jerry W., Long, H. Keith, 1997, Report on the U.S. Geological Survey's evaluation program for standard reference samples distributed in September 1996. U.S. Geological Survey, Open File Report 97-20 p. 9.

Hoaglin, D.C., Mosteller, F., and Tukey, J.W., Eds. 2000, Understanding robust and exploratory data analysis: New York, NY, John Wiley, Inc., p. 38-41.

 

Nutrients
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2016	NH4	0.0462	0.005	0.75	0.07 - 1.2 mg/L
2016	NH4 + Org N	0.0629	0.046	0.52	0.1 - 1.3 mg/L
2016	NH4 + NO2 + NO3 + Org N	0.0378	0.028	0.67	0.3 - 2.3 mg/L
2016	NO2 + NO3	0.0325	0.003	0.91	0.09 - 1.4 mg/L
2016	NO2 + NO3 (low level)	0.0347	0.002	0.93	0.09 - 1.0 mg/L
2016	Orthophosphate	0.0317	0.001	0.90	0.04 - 1.5 mg/L
2016	Phosphorus	0.0310	0.004	0.85	0.04 - 1.5 mg/L
2016	Phosphorus (low level)	0.0375	0.001	0.57	0.04 - 0.2 mg/L
Trace Metals and Silica
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2016	Aluminum	0.0611	0.881	0.90	16 - 320 µg/L
2016	Antimony	0.0419	0.024	0.89	0.06 - 5.0 µg/L
2016	Arsenic	0.0624	0.020	0.99	0.20 - 24 µg/L
2016	Barium	0.0311	0.293	0.76	6.8 - 72 µg/L
2016	Beryllium	0.0427	0.019	0.37	0.09 - 0.75 µg/L
2016	Boron	0.0472	1.615	0.45	4.6 - 69 µg/L
2016	Cadmium	0.0353	0.017	0.90	0.02 - 3.9 µg/L
2016	Chromium	0.0396	0.094	0.70	0.35 - 5.6 µg/L
2016	Cobalt	0.0462	0.013	0.96	0.09 - 5.6 µg/L
2016	Copper	0.0578	0.061	0.98	0.94 - 21 µg/L
2016	Iron	0.0460	2.926	0.94	33 -1,900 µg/L
2016	Lead	0.0432	0.041	0.93	0.12 - 11 µg/L
2016	Lithium	0.0510	0.330	0.84	0.99 - 73 µg/L
2016	Manganese	0.0453	0.396	1.00	6.0 - 1,800 µg/L
2016	Mercury	0.1382	0.000	0.76	0.01 - 0.05 µg/L
2016	Molybdenum	0.0540	0.046	0.95	0.33 - 46 µg/L
2016	Nickel	0.0491	0.160	0.87	0.40 - 19 µg/L
2016	Selenium	0.1078	0.137	0.43	0.38 - 3.1 µg/L
2016	Silica	0.0486	0	n/a	4.7 - 270 mg/L
2016	Silver	0.0657	0.087	0.43	0.05 - 4.4 µg/L
2016	Strontium	0.0474	0	n/a	21 - 410 µg/L
2016	Thallium	0.0475	0.025	0.88	0.48 - 5.0 µg/L
2016	Uranium	0.0510	-0.003	0.79	0.37 - 1.9 µg/L
2016	Vanadium	0.0552	0.160	0.84	0.19 - 28 µg/L
2016	Zinc	0.0633	0.029	1.00	6.2 - 1,100 µg/L
Major Ions
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2016	Bromide	0.0466	0.033	0.47	0.07 - 1.4 mg/L
2016	Calcium	0.0414	0	n/a	0.13 - 55 mg/L
2016	Chloride	0.0272	0.080	0.95	0.28 - 59 mg/L
2016	Fluoride	0.0454	0.013	0.90	0.04 - 1.8 mg/L
2016	Magnesium	0.0396	0	n/a	0.05 - 24 mg/L
2016	Potassium	0.0384	0.034	0.86	0.08 - 10 mg/L
2016	Potassium (low level)	0.0429	0.012	0.84	0.08 - 1.0 mg/L
2016	Sodium	0.0379	0.000	n/a	0.12 - 50 mg/L
2016	Sulfate	0.0287	0.12252	0.99	0.19 - 178 mg/L
Physical Properties
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2016	Acid Neutralizing Capacity	0.0262	0.571	0.77	24 - 85 mg/L
2016	Alkalinity	0.0262	0.571	0.77	24 - 85 mg/L
2016	ROE (105 deg C)	0	10.40	n/a	58 - 410 mg/L
2016	ROE (180 deg C)	0	10.40	n/a	58 - 410 mg/L
2016	Specific Conductance	0.0183	1.354	0.84	4.8 - 640 µS/cm
Nutrients
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2015	NH4	0.0462	0.005	0.75	0.07 - 1.2 mg/L
2015	NH4 + Org N	0.0629	0.046	0.52	0.1 - 1.3 mg/L
2015	NH4 + NO2 + NO3 + Org N	0.0378	0.028	0.67	0.3 - 2.3 mg/L
2015	NO2 + NO3	0.0325	0.003	0.91	0.09 - 1.4 mg/L
2015	NO2 + NO3 (low level)	0.0347	0.002	0.93	0.09 - 1.0 mg/L
2015	Orthophosphate	0.0317	0.001	0.90	0.04 - 1.5 mg/L
2015	Phosphorus	0.0310	0.004	0.85	0.04 - 1.5 mg/L
2015	Phosphorus (low level)	0.0375	0.001	0.57	0.04 - 0.2 mg/L
Trace Metals and Silica
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2015	Aluminum	0.0611	0.881	0.90	16 - 320 µg/L
2015	Antimony	0.0419	0.024	0.89	0.06 - 5.0 µg/L
2015	Arsenic	0.0624	0.020	0.99	0.20 - 24 µg/L
2015	Barium	0.0311	0.293	0.76	6.8 - 72 µg/L
2015	Beryllium	0.0427	0.019	0.37	0.09 - 0.75 µg/L
2015	Boron	0.0472	1.615	0.45	4.6 - 69 µg/L
2015	Cadmium	0.0353	0.017	0.90	0.02 - 3.9 µg/L
2015	Chromium	0.0396	0.094	0.70	0.35 - 5.6 µg/L
2015	Cobalt	0.0462	0.013	0.96	0.09 - 5.6 µg/L
2015	Copper	0.0578	0.061	0.98	0.9 - 21 µg/L
2015	Iron	0.0460	2.926	0.94	33 -1,900 µg/L
2015	Lead	0.0432	0.041	0.93	0.12 - 11 µg/L
2015	Lithium	0.0510	0.330	0.84	0.99 - 73 µg/L
2015	Manganese	0.0453	0.396	1.00	6.0 - 1,800 µg/L
2015	Mercury	0.1382	0.000	0.76	0.01 - 0.05 µg/L
2015	Molybdenum	0.0540	0.046	0.95	0.33 - 46 µg/L
2015	Nickel	0.0491	0.160	0.87	0.40 - 19 µg/L
2015	Selenium	0.1078	0.137	0.43	0.38 - 3.1 µg/L
2015	Silica	0.0486	0	n/a	4.7 - 270 mg/L
2015	Silver	0.0657	0.087	0.43	0.05 - 4.4 µg/L
2015	Strontium	0.0474	0	n/a	21 - 410 µg/L
2015	Thallium	0.0475	0.025	0.88	0.48 - 5.0 µg/L
2015	Uranium	0.0510	-0.003	0.79	0.37 - 1.9 µg/L
2015	Vanadium	0.0552	0.160	0.84	0.19 - 28 µg/L
2015	Zinc	0.0633	0.029	1.00	6.2 - 1,100 µg/L
Major Ions
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2015	Bromide	0.0466	0.033	0.47	0.07 - 1.4 mg/L
2015	Calcium	0.0414	0	n/a	0.13 - 55 mg/L
2015	Chloride	0.0272	0.080	0.95	0.28 - 59 mg/L
2015	Fluoride	0.0454	0.013	0.90	0.04 - 1.8 mg/L
2015	Magnesium	0.0396	0	n/a	0.05 - 24 mg/L
2015	Potassium	0.0384	0.034	0.86	0.08 - 10 mg/L
2015	Potassium (low level)	0.0429	0.012	0.84	0.08 - 1.0 mg/L
2015	Sodium	0.0379	0.000	n/a	0.12 - 50 mg/L
2015	Sulfate	0.0287	0.12252	0.99	0.19 - 178 mg/L
Physical Properties
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2015	Acid Neutralizing Capacity	0.0262	0.571	0.77	24 - 85 mg/L
2015	Alkalinity	0.0262	0.571	0.77	24 - 85 mg/L
2015	ROE (105 deg C)	0	10.40	n/a	58 - 410 mg/L
2015	ROE (180 deg C)	0	10.40	n/a	58 - 410 mg/L
2015	Specific Conductance	0.0183	1.354	0.84	4.8 - 640 µS/cm
Nutrients
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2014	NH4	0.0462	0.005	0.75	0.07 - 1.2 mg/L
2014	NH4 + Org N	0.0629	0.046	0.52	0.1 - 1.3 mg/L
2014	NH4 + NO2 + NO3 + Org N	0.0378	0.028	0.67	0.3 - 2.3 mg/L
2014	NO2 + NO3	0.0325	0.003	0.91	0.09 - 1.4 mg/L
2014	NO2 + NO3 (low level)	0.0347	0.002	0.93	0.09 - 1.0 mg/L
2014	Orthophosphate	0.0317	0.001	0.90	0.04 - 1.5 mg/L
2014	Phosphorus	0.0310	0.004	0.85	0.04 - 1.5 mg/L
2014	Phosphorus (low level)	0.0375	0.001	0.57	0.04 - 0.2 mg/L
Trace Metals and Silica
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2014	Aluminum	0.0611	0.881	0.90	16 - 320 µg/L
2014	Antimony	0.0419	0.024	0.89	0.06 - 5.0 µg/L
2014	Arsenic	0.0624	0.020	0.99	0.20 - 24 µg/L
2014	Barium	0.0311	0.293	0.76	6.8 - 72 µg/L
2014	Beryllium	0.0427	0.019	0.37	0.09 - 0.75 µg/L
2014	Boron	0.0472	1.615	0.45	4.6 - 69 µg/L
2014	Cadmium	0.0353	0.017	0.90	0.02 - 3.9 µg/L
2014	Chromium	0.0396	0.094	0.70	0.35 - 5.6 µg/L
2014	Cobalt	0.0462	0.013	0.96	0.09 - 5.6 µg/L
2014	Copper	0.0578	0.061	0.98	0.9 - 21 µg/L
2014	Iron	0.0460	2.926	0.94	33 -1,900 µg/L
2014	Lead	0.0432	0.041	0.93	0.12 - 11 µg/L
2014	Lithium	0.0510	0.330	0.84	0.99 - 73 µg/L
2014	Manganese	0.0453	0.396	1.00	6.0 - 1,800 µg/L
2014	Mercury	0.1382	0.000	0.76	0.01 - 0.05 µg/L
2014	Molybdenum	0.0540	0.046	0.95	0.33 - 46 µg/L
2014	Nickel	0.0491	0.160	0.87	0.40 - 19 µg/L
2014	Selenium	0.1078	0.137	0.43	0.38 - 3.1 µg/L
2014	Silica	0.0486	0	n/a	4.7 - 270 mg/L
2014	Silver	0.0657	0.087	0.43	0.05 - 4.4 µg/L
2014	Strontium	0.0474	0	n/a	21 - 410 µg/L
2014	Thallium	0.0475	0.025	0.88	0.48 - 5.0 µg/L
2014	Uranium	0.0510	-0.003	0.79	0.37 - 1.9 µg/L
2014	Vanadium	0.0552	0.160	0.84	0.19 - 28 µg/L
2014	Zinc	0.0633	0.029	1.00	6.2 - 1,100 µg/L
Major Ions
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2014	Bromide	0.0466	0.033	0.47	0.07 - 1.4 mg/L
2014	Calcium	0.0414	0	n/a	0.13 - 55 mg/L
2014	Chloride	0.0272	0.080	0.95	0.28 - 59 mg/L
2014	Fluoride	0.0454	0.013	0.90	0.04 - 1.8 mg/L
2014	Magnesium	0.0396	0	n/a	0.05 - 24 mg/L
2014	Potassium	0.0384	0.034	0.86	0.08 - 10 mg/L
2014	Potassium (low level)	0.0429	0.012	0.84	0.08 - 1.0 mg/L
2014	Sodium	0.0379	0.000	n/a	0.12 - 50 mg/L
2014	Sulfate	0.0287	0.12252	0.99	0.19 - 178 mg/L
Physical Properties
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2014	Acid Neutralizing Capacity	0.0262	0.571	0.77	24 - 85 mg/L
2014	Alkalinity	0.0262	0.571	0.77	24 - 85 mg/L
2014	ROE (105 deg C)	0	10.40	n/a	58 - 410 mg/L
2014	ROE (180 deg C)	0	10.40	n/a	58 - 410 mg/L
2014	Specific Conductance	0.0183	1.354	0.84	4.8 - 640 µS/cm
Nutrients
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2013	NH4	0.0462	0.005	0.75	0.07 - 1.2 mg/L
2013	NH4 + Org N	0.0629	0.046	0.52	0.1 - 1.3 mg/L
2013	NH4 + NO2 + NO3 + Org N	0.0378	0.028	0.67	0.3 - 2.3 mg/L
2013	NO2 + NO3	0.0325	0.003	0.91	0.09 - 1.4 mg/L
2013	NO2 + NO3 (low level)	0.0347	0.002	0.93	0.09 - 1.0 mg/L
2013	Orthophosphate	0.0317	0.001	0.90	0.04 - 1.5 mg/L
2013	Phosphorus	0.0310	0.004	0.85	0.04 - 1.5 mg/L
2013	Phosphorus (low level)	0.0375	0.001	0.57	0.04 - 0.2 mg/L
Trace Metals and Silica
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2013	Aluminum	0.0611	0.881	0.90	16 - 320 µg/L
2013	Antimony	0.0419	0.024	0.89	0.06 - 5.0 µg/L
2013	Arsenic	0.0624	0.020	0.99	0.20 - 24 µg/L
2013	Barium	0.0311	0.293	0.76	6.8 - 72 µg/L
2013	Beryllium	0.0427	0.019	0.37	0.09 - 0.75 µg/L
2013	Boron	0.0472	1.615	0.45	4.6 - 69 µg/L
2013	Cadmium	0.0353	0.017	0.90	0.02 - 3.9 µg/L
2013	Chromium	0.0396	0.094	0.70	0.35 - 5.6 µg/L
2013	Cobalt	0.0462	0.013	0.96	0.09 - 5.6 µg/L
2013	Copper	0.0578	0.061	0.98	0.9 - 21 µg/L
2013	Iron	0.0460	2.926	0.94	33 -1,900 µg/L
2013	Lead	0.0432	0.041	0.93	0.12 - 11 µg/L
2013	Lithium	0.0510	0.330	0.84	0.99 - 73 µg/L
2013	Manganese	0.0453	0.396	1.00	6.0 - 1,800 µg/L
2013	Mercury	0.1382	0.000	0.76	0.01 - 0.05 µg/L
2013	Molybdenum	0.0540	0.046	0.95	0.33 - 46 µg/L
2013	Nickel	0.0491	0.160	0.87	0.40 - 19 µg/L
2013	Selenium	0.1078	0.137	0.43	0.38 - 3.1 µg/L
2013	Silica	0.0486	0	n/a	4.7 - 270 mg/L
2013	Silver	0.0657	0.087	0.43	0.05 - 4.4 µg/L
2013	Strontium	0.0474	0	n/a	21 - 410 µg/L
2013	Thallium	0.0475	0.025	0.88	0.48 - 5.0 µg/L
2013	Uranium	0.0510	-0.003	0.79	0.37 - 1.9 µg/L
2013	Vanadium	0.0552	0.160	0.84	0.19 - 28 µg/L
2013	Zinc	0.0633	0.029	1.00	6.2 - 1,100 µg/L
Major Ions
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2013	Bromide	0.0466	0.033	0.47	0.07 - 1.4 mg/L
2013	Calcium	0.0414	0	n/a	0.13 - 55 mg/L
2013	Chloride	0.0272	0.080	0.95	0.28 - 59 mg/L
2013	Fluoride	0.0454	0.013	0.90	0.04 - 1.8 mg/L
2013	Magnesium	0.0396	0	n/a	0.05 - 24 mg/L
2013	Potassium	0.0384	0.034	0.86	0.08 - 10 mg/L
2013	Potassium (low level)	0.0429	0.012	0.84	0.08 - 1.0 mg/L
2013	Sodium	0.0379	0.000	n/a	0.12 - 50 mg/L
2013	Sulfate	0.0287	0.12252	0.99	0.19 - 178 mg/L
Physical Properties
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2013	Acid Neutralizing Capacity	0.0262	0.571	0.77	24 - 85 mg/L
2013	Alkalinity	0.0262	0.571	0.77	24 - 85 mg/L
2013	ROE (105 deg C)	0	10.40	n/a	58 - 410 mg/L
2013	ROE (180 deg C)	0	10.40	n/a	58 - 410 mg/L
2013	Specific Conductance	0.0183	1.354	0.84	4.8 - 640 µS/cm
Nutrients
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2012	NH4	0.0462	0.005	0.75	0.07 - 1.2 mg/L
2012	NH4 + Org N	0.0629	0.046	0.52	0.1 - 1.3 mg/L
2012	NH4 + NO2 + NO3 + Org N	0.0378	0.028	0.67	0.3 - 2.3 mg/L
2012	NO2 + NO3	0.0325	0.003	0.91	0.09 - 1.4 mg/L
2012	NO2 + NO3 (low level)	0.0347	0.002	0.93	0.09 - 1.0 mg/L
2012	Orthophosphate	0.0317	0.001	0.90	0.04 - 1.5 mg/L
2012	Phosphorus	0.0310	0.004	0.85	0.04 - 1.5 mg/L
2012	Phosphorus (low level)	0.0375	0.001	0.57	0.04 - 0.2 mg/L
Trace Metals and Silica
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2012	Aluminum	0.0611	0.881	0.90	16 - 320 ug/L
2012	Antimony	0.0556	0.546	0.52	3 - 33 ug/L
2012	Arsenic	0.0624	0.020	0.99
2012	Barium	0.0311	0.293	0.76
2012	Beryllium	0.0490	0.272	0.50	8 -26 ug/L
2012	Boron	0.0472	1.615	0.45
2012	Cadmium	0.0596	0.116	0.90	2 - 27 ug/L
2012	Chromium	0.0396	0.094	0.70	0.4 - 5.6 u/L
2012	Cobalt	0.0462	0.013	0.96
2012	Copper	0.0578	0.061	0.98	0.9 - 21 ug/L
2012	Iron	0.0460	2.926	0.94
2012	Lead	0.0432	0.041	0.93
2012	Lithium	0.0562	0.757	0.81	1 - 54 ug/L
2012	Manganese	0.0453	0.396	1.00
2012	Mercury	0.1382	0.000	0.76	0.01 - 0.07 u/L
2012	Molybdenum	0.0540	0.046	0.95
2012	Nickel	0.0491	0.160	0.87
2012	Selenium	0.1078	0.137	0.43
2012	Silica	0.0486	0	n/a
2012	Silver	0.0657	0.087	0.43	0.05 - 4.4 ug/L
2012	Strontium	0.0474	0	n/a
2012	Thallium	0.0475	0.025	0.88
2012	Uranium	0.0510	-0.003	0.79
2012	Vanadium	0.0552	0.160	0.84
2012	Zinc	0.0633	0.029	1.00	6.2 - 1,100 ug/L
Major Ions
Fiscal Yr	Constituent	Slope (β1)	Y-intercept (β0)	r2	Range used
2012	Bromide	0.0466	0.033	0.47	0.07 - 1.4 mg/L
2012	Calcium	0.0414	0	n/a	0.13 - 55 mg/L
2012	Chloride	0.0272	0.080	0.95	0.28 - 59 mg/L
2012	Chloride (low level)	0.0439	0.009	0.64	0.28 - 4.4 mg/L
2012	Fluoride	0.0454	0.013	0.90	0.04 - 1.8 mg/L
2012	Magnesium	0.0396	0	n/a	0.05 - 24 mg/L
2012	Potassium	0.0384	0.034	0.86	0.08 - 10 mg/L
2012	Potassium (low level)	0.0429	0.012	0.84	0.08 - 1.0 mg/L
2012	Sodium	0.0379	0.000	n/a	0.12 - 50 mg/L
2012	Sulfate	0.0287	0.12252	0.99	0.19 - 178 mg/L
2012	Sulfate (low level)	0.0537	0.026	0.94	0.19 - 2.0 mg/L
Physical Properties
Fiscal Yr	Constituent	Slope (β1)	Y-intercept = (β0)	r2	Range used
2012	Alkalinity	0.0262	0.571	0.77
2012	ROE (105 deg C)	0	10.40	n/a
2012	ROE (180 deg C)	0	10.40	n/a
2012	Specific Conductance	0.0183	1.354	0.84
Fiscal Yr	Constituent	Slope = b1	Y-Inter = bo	r-Squared	Range used
2011	Alkalinity	0.0173	1.56	0.805	0.1 - 180
2011	Aluminum	0.0871	3.6	0.475	10.3 - 70.6
2011	Antimony	0.0556	0.546	0.521	3 - 33
2011	Arsenic	0.0561	0.418	0.8	0.2 - 33
2011	Barium	0.0417	0.411	0.932	10 - 185
2011	Beryllium	0.049	0.272	0.5	8 - 26
2011	Boron	0.0514	2.92	0.702	10 - 280
2011	Cadmium	0.0596	0.116	0.897	0.067 - 0.928
2011	Calcium	0.0429	0	n/a	0.1 - 75
2011	Chloride	0.0272	0.4245	0.874	0.1 - 142
2011	Chromium	0.048	0.493	0.832	7 - 49
2011	Cobalt	0.0413	0.397	0.434	1 - 27
2011	Copper	0.0434	0.731	0.682	1 - 38
2011	ROE (DSRD 180)	0	12.64	n/a	50 - 750
2011	Fluoride	0.0582	0.0178	0.913	0.02 - 2.2
2011	Iron	0	6.46	n/a	5 - 100
2011	Lead	0.0533	0.514	0.808	4 - 46
2011	Lithium	0.0562	0.757	0.809	1 - 54
2011	Magnesium	0.0399	0	n/a	0.1 - 26
2011	Manganese	0.0408	0.611	0.902	1 - 98
2011	Molybdenum	0.0423	0.918	0.47	1 - 78
2011	Nickel	0.0483	0.781	0.567	1 - 33
2011	Potassium	0.0547	0.035	0.907	0.1 - 10.2
2011	Selenium	0.0828	0.5403	0.654	2 - 10.2
2011	Silica	0.0605	0	n/a	1 - 24
2011	Silver	0.0518	0.412	0.725	2 - 20
2011	Sodium	0.0423	0	n/a	0.1 - 154
2011	Strontium	0.043	0	n/a	10 - 680
2011	Sulfate	0.0361	0.358	0.971	0.1 - 240
2011	Thallium	0.0731	0.511	0.751	3 - 51
2011	Uranium	0.097	-0.029	0.389	1.1 - 4
2011	Vanadium	0	1.633	n/a	3 - 35
2011	Zinc	0.0494	1.27	0.767	3 - 73
2011	Mercury	0.08	0	n/a	0.015 - 0.100
2011	Bromide	0	0.0415	n/a
2011	Chloride	0	0.1873	n/a	0.2 - 3
2011	Fluoride	0	0.0246	n/a	0.025 - 0.35
2011	Potassium	0.0664	0.0153	0.76	0.10 - 1.0
2011	Sulfate	0.0000	0.247	n/a	0.3 - 3.0
2011	Specific Conductance	0.01825	1.354	0.84
2011	Ammonia	0.0512	0.010	0.90	0.04 - 1.4
2011	NH3 + Org N	0.0667	0.0596	0.539	0.05 - 2.5
2011	NO2 + NO3	0.0554	0.000	n/a	0.036 - 1.75
2011	NO2 + NO3 (low level)	0.0583	0	n/a	0.036 - 1.0
2011	Orthophosphate	0.0467	0.000	n/a	0.038 - 1.6
2011	Phosphorus	0.0367	0.00434	0.939	0.04 - 1.6
2011	Phosphorus (low level)	0.0689	0.000	n/a	0.04 - 0.2
Fiscal Yr	Constituent	Slope = b1	Y-Inter = bo	r-Squared	Range used
2010	Alkalinity	0.0173	1.56	0.805	0.1 - 180
2010	Aluminum	0.0871	3.6	0.475	10.3 - 70.6
2010	Antimony	0.0556	0.546	0.521	3 - 33
2010	Arsenic	0.0561	0.418	0.8	0.2 - 33
2010	Barium	0.0417	0.411	0.932	10 - 185
2010	Beryllium	0.049	0.272	0.5	8 - 26
2010	Boron	0.0514	2.92	0.702	10 - 280
2010	Cadmium	0.0596	0.116	0.897	0.067 - 0.928
2010	Calcium	0.0429	0	n/a	0.1 - 75
2010	Chloride	0.0272	0.4245	0.874	0.1 - 142
2010	Chromium	0.048	0.493	0.832	7 - 49
2010	Cobalt	0.0413	0.397	0.434	1 - 27
2010	Copper	0.0434	0.731	0.682	1 - 38
2010	ROE (DSRD 180)	0	12.64	n/a	50 - 750
2010	Fluoride	0.0582	0.0178	0.913	0.02 - 2.2
2010	Iron	0	6.46	n/a	5 - 100
2010	Lead	0.0533	0.514	0.808	4 - 46
2010	Lithium	0.0562	0.757	0.809	1 - 54
2010	Magnesium	0.0399	0	n/a	0.1 - 26
2010	Manganese	0.0408	0.611	0.902	1 - 98
2010	Molybdenum	0.0423	0.918	0.47	1 - 78
2010	Nickel	0.0483	0.781	0.567	1 - 33
2010	Potassium	0.0547	0.035	0.907	0.1 - 10.2
2010	Selenium	0.0828	0.5403	0.654	2 - 10.2
2010	Silica	0.0605	0	n/a	1 - 24
2010	Silver	0.0518	0.412	0.725	2 - 20
2010	Sodium	0.0423	0	n/a	0.1 - 154
2010	Strontium	0.043	0	n/a	10 - 680
2010	Sulfate	0.0361	0.358	0.971	0.1 - 240
2010	Thallium	0.0731	0.511	0.751	3 - 51
2010	Uranium	0.097	-0.029	0.389	1.1 - 4
2010	Vanadium	0	1.633	n/a	3 - 35
2010	Zinc	0.0494	1.27	0.767	3 - 73
2010	Mercury	0.08	0	n/a	0.015 - 0.100
2010	Chloride	0	0.1873	n/a	0.2 - 3
2010	Fluoride	0	0.0246	n/a	0.025 - 0.35
2010	Potassium	0.0664	0.0153	0.76	0.10 - 1.0
2010	Sulfate	0	0.2473	n/a	0.3 - 3.0
2010	Specific Conductance	0.0183	1.354	0.84
2010	Ammonia	0.0512	0.0102	0.901	0.04 - 1.4
2010	NH3 + Org N	0.0667	0.060	0.54	0.05 - 2.5
2010	NO2 + NO3	0.0554	0	n/a	0.036 - 1.75
2010	NO2 + NO3 (low level)	0.0583	0.000	n/a	0.036 - 1.0
2010	Orthophosphate	0.0467	0	n/a	0.038 - 1.6
2010	Phosphorus	0.0367	0.004	0.94	0.04 - 1.6
2010	Phosphorus (low level)	0.0689	0	n/a	0.04 - 0.2
Fiscal Yr	Constituent	Slope = b1	Y-Inter = bo	r-Squared	Range used
2009	Alkalinity	0.0173	1.56	0.805	0.1 - 180
2009	Aluminum	0.0871	3.6	0.475	10.3 - 70.6
2009	Antimony	0.0556	0.546	0.521	3 - 33
2009	Arsenic	0.0561	0.418	0.8	0.2 - 33
2009	Barium	0.0417	0.411	0.932	10 - 185
2009	Beryllium	0.049	0.272	0.5	8 - 26
2009	Boron	0.0514	2.92	0.702	10 - 280
2009	Cadmium	0.0596	0.116	0.897	0.067 - 0.928
2009	Calcium	0.0429	0	n/a	0.1 - 75
2009	Chloride	0.0272	0.4245	0.874	0.1 - 142
2009	Chromium	0.048	0.493	0.832	7 - 49
2009	Cobalt	0.0413	0.397	0.434	1 - 27
2009	Copper	0.0434	0.731	0.682	1 - 38
2009	ROE (DSRD 180)	0	12.64	n/a	50 - 750
2009	Fluoride	0.0582	0.0178	0.913	0.02 - 2.2
2009	Iron	0	6.46	n/a	5 - 100
2009	Lead	0.0533	0.514	0.808	4 - 46
2009	Lithium	0.0562	0.757	0.809	1 - 54
2009	Magnesium	0.0399	0	n/a	0.1 - 26
2009	Manganese	0.0408	0.611	0.902	1 - 98
2009	Molybdenum	0.0423	0.918	0.47	1 - 78
2009	Nickel	0.0483	0.781	0.567	1 - 33
2009	Potassium	0.0547	0.035	0.907	0.1 - 10.2
2009	Selenium	0.0828	0.5403	0.654	2 - 10.2
2009	Silica	0.0605	0	n/a	1 - 24
2009	Silver	0.0518	0.412	0.725	2 - 20
2009	Sodium	0.0423	0	n/a	0.1 - 154
2009	Strontium	0.043	0	n/a	10 - 680
2009	Sulfate	0.0361	0.358	0.971	0.1 - 240
2009	Thallium	0.0731	0.511	0.751	3 - 51
2009	Uranium	0.097	-0.029	0.389	1.1 - 4
2009	Vanadium	0	1.633	n/a	3 - 35
2009	Zinc	0.0494	1.27	0.767	3 - 73
2009	Mercury	0.08	0	n/a	0.015 - 0.100
2009	Chloride	0	0.1873	n/a	0.2 - 3
2009	Fluoride	0	0.0246	n/a	0.025 - 0.35
2009	Potassium	0.0664	0.0153	0.76	0.10 - 1.0
2009	Sulfate	0	0.2473	n/a	0.3 - 3.0
2009	Specific Conductance	0.0183	1.354	0.84
2009	Ammonia	0.0512	0.0102	0.901	0.04 - 1.4
2009	NH3 + Org N	0.0667	0.0596	0.539	0.05 - 2.5
2009	NO2 + NO3	0.0554	0	n/a	0.036 - 1.75
2009	NO2 + NO3 (low-level)	0.0583	0	n/a	0.036 - 1.0
2009	Orthophosphate	0.0467	0	n/a	0.038 - 1.6
2009	Orthophosphate (low-level)	0	0.00678	n/a	0.038 - 0.2
2009	Phosphorus	0.0367	0.00434	0.939	0.04 - 1.6
2009	Phosphorus (low-level)	0.0689	0	n/a	0.04 - 0.2
Fiscal Yr	Constituent	Slope = b1	Y-Inter = bo	r-Squared	Range used
2008	Alkalinity	0.0173	1.56	0.805	0.1 - 180
2008	Aluminum	0.0871	3.6	0.475	10.3 - 70.6
2008	Antimony	0.0556	0.546	0.521	3 - 33
2008	Arsenic	0.0561	0.418	0.8	0.2 - 33
2008	Barium	0.0417	0.411	0.932	10 - 185
2008	Beryllium	0.049	0.272	0.5	8 - 26
2008	Boron	0.0514	2.92	0.702	10 - 280
2008	Cadmium	0.0596	0.116	0.897	0.067 - 0.928
2008	Calcium	0.0429	0	n/a	0.1 - 75
2008	Chloride	0.0272	0.4245	0.874	0.1 - 142
2008	Chromium	0.048	0.493	0.832	7 - 49
2008	Cobalt	0.0413	0.397	0.434	1 - 27
2008	Copper	0.0434	0.731	0.682	1 - 38
2008	ROE (DSRD 180)	0	12.64	n/a	50 - 750
2008	Fluoride	0.0582	0.0178	0.913	0.02 - 2.2
2008	Iron	0	6.46	n/a	5 - 100
2008	Lead	0.0533	0.514	0.808	4 - 46
2008	Lithium	0.0562		0.809	1 - 54
2008	Magnesium	0.0399	0	n/a	0.1 - 26
2008	Manganese	0.0408	0.611	0.902	1 - 98
2008	Molybdenum	0.0423	0.918	0.47	1 - 78
2008	Nickel	0.0483	0.781	0.567	1 - 33
2008	Potassium	0.0547	0.035	0.907	0.1 - 10.2
2008	Selenium	0.0828	0.5403	0.654	2 - 10.2
2008	Silica	0.0605	0	n/a	1 - 24
2008	Silver	0.0518	0.412	0.725	2 - 20
2008	Sodium	0.0423	0	n/a	0.1 - 154
2008	Strontium	0.043	0	n/a	10 - 680
2008	Sulfate	0.0361	0.358	0.971	0.1 - 240
2008	Thallium	0.0731	0.511	0.751	3 - 51
2008	Uranium	0.097	-0.029	0.389	1.1 - 4
2008	Vanadium	0	1.633	n/a	3 - 35
2008	Zinc	0.0494	1.27	0.767	3 - 73
2008	Mercury	0.08	0	n/a	0.015 - 0.100
2008	Chloride	0	0.1873	n/a	0.2 - 3
2008	Fluoride	0	0.0246	n/a	0.025 - 0.35
2008	Potassium	0.0664	0.0153	0.76	0.10 - 1.0
2008	Sulfate	0	0.2473	n/a	0.3 - 3.0
2008	Ammonia	0.0512	0.0102	0.901	0.04 - 1.4
2008	NH3 + Org N	0.0667	0.0596	0.539	0.05 - 2.5
2008	NO2 + NO3	0.0554	0	n/a	0.036 - 1.75
2008	NO2 + NO3	0.0583	0	n/a	0.036 - 1.0
2008	Orthophosphate	0.0467	0	n/a	0.038 - 1.6
2008	Orthophosphate	0	0.00678	n/a	0.038 - 0.2
2008	Phosphorus	0.0367	0.00434	0.939	0.04 - 1.6
2008	Phosphorus	0.0689	0	n/a	0.04 - 0.2