## 3 Results and Discussion
### Linear Regression Measurement Corrections  
Evaluation of the ISEs has been tested using AEP samples. A small amount of sample (0.25-1.0 mL) was diluted with 250-500 mL of deionized water. The ISEs were submerged in this solution and several readings were taken. This process was done with several additions and the average concentration was calculated. However, this process had inconsistent results, with determined concentration varying within an order of magnitude of molarity. The chloride ISE showed the ideal behavior, while the calcium ISE did not. This error was a result of the decreasing activity (compared to concentration) as additions were made. This model failed to properly address measurement interference that results from other ions being in solution (as is expected in any real measurement). With this problem identified, a full regression was completed using numerical methods in MATLAB by adding activity as an independent variable when deriving an equation to describe the relationship between concentration, temperature, and ISE reading. This numerical method replaced the Nernst parameters with a relationship that was fully developed from experimental data. This new regression method was justified as the ISEs had shown highly non-ideal behavior, whereas the Nernst equation is most applicable for ideal or close to ideal electrochemical solutions. Standard Error in Tables 5 and 6 refer to the average discrepancy of experimental values with regressed values and can be viewed as the error of any concentration calculated with these equations. Figure 2: Supplementary Control Experiments Demonstrating Error in The Modified Nernst Equation for (**A**) Chloride; (**B**) Calcium; (**C**) Nitrate; (**D**) Nitrite. Encircled data sets have only variation in ionic strength. This error is directly from assuming direct proportionality of activity and concentration. A multilinear regression considering variables of temperature, concentration of target species, ionic strength of solution, and all interactions of these variables was used with MATLAB to regress an empirical model to describe the performance of each electrode. The generalized equation is shown below in Equations (2) and (3). Variables and labeling corresponds to Tables 5 and 6 respectively, which also have the main results of the regression. C\({}_{\text{i}}\) denotes a constant and X\({}_{\text{i}}\) denotes an experimental parameter. Each regression was completed with a 95% confidence interval. \[E=c_{1}+c_{2}x_{1}+c_{3}x_{2}+c_{4}x_{1}x_{2}+c_{5}x_{1}x_{3}+c_{6}x_{2}x_{3}+ c_{7}x_{1}x_{2}x_{3} \tag{2}\]  
\[x_{1}=\ln(l_{i})\]  
\[x_{2}=\ln\left(\sum_{j:j\
eq i}^{k}I_{j}\right)\]  
\[x_{3}=\text{\emph{temperature}}\left(\text{K}\right)\]  
\[E=Signal\text{\emph{in millivolt}}\left(mV\right)\]  
\[E=c_{1}+c_{2}x_{1}+c_{3}x_{2}+c_{4}x_{1}x_{2} \tag{3}\]  
\[x_{1}=\ln(l_{i})\]  
\[x_{2}=\text{\emph{temperature}}\left(\text{K}\right)\]  
The chloride and calcium electrodes showed serious deviations when subjected to solutions with high ionic strength (in this case high is considered values above 0.1 M). This same level of interference was also not able to be corrected for in the nitrate and nitrate electrodes. Though the two equations use different parameters, the observed inaccuracies in measurements are still below 0.001 M for every electrode. This is comparable to previous studies that have used similar methodologies [7; 10]. A sensitivity analysis was performed on the regression model for each electrode. Standard conditions for comparison were considered at an ionic strength of 0.01 M, concentration of 0.001 M, and temperature of 40 \({}^{\circ}\)C. The sensitivity analysis results are shown in Table 7. At standard and lower ionic strength, each electrode had a significant response to change in concentration, which