TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters

Appendix B-12: Multiple Regression Model for Stream SCI 
TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters

B12-1 

Appendix B-12. Multiple Regression Model for Stream SCI 

Multiple regression models can effectively model the extent to which different environmental 

factors (e.g., nutrient concentrations, habitat quality) account for variations in the stream 

condition index (SCI). Predictions from such models can then inform nutrient criterion decisions. 

Concurrent measurements of SCI and different environmental factors were provided by the 

Florida Department of Environmental Protection (FDEP) in the Excel file “Stream file2 for 

Xufeng_021009.” Samples were collected at 249 distinct stations, coded as different STORET 

numbers. One to three samples were collected from each station. To characterize the 

environmental conditions at each station, averages were calculated over all samples at a given 

site for the following measurements: log total nitrogen (TN), log total phosphorus (TP), log 

specific conductivity, habitat score, log color, and pH. Each station was also characterized by its 

geographic location (degrees latitude and longitude) and by a Landscape Disturbance Intensity 

Index (LDI). Once average conditions at each station were calculated, they were combined with 

individual sampled values of SCI, giving a total of 344 samples with complete environmental 

and biological data. 

The strengths of correlation between most environmental variables were moderate (Table B12-

1). As expected, log TP and log TN were strongly correlated (r = 0.52). 

Because log TP and log TN were strongly correlated, their relationships with SCI were modeled 

separately by fitting two multiple regression models. Each model included either log TP or log 

TN plus all the other covariates for which data were available as explanatory variables. 

Model results for log TN: 

Coefficients: 

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) 78.67225 63.96867 1.230 0.21961 

logtn -10.74999 3.90684 -2.752 0.00625 ** 

hab 0.26784 0.04349 6.159 2.1e-09 *** 

LDI -0.94130 0.58045 -1.622 0.10582 

pH -0.01423 1.49463 -0.010 0.99241 

LONGITUDE 0.65861 0.74644 0.882 0.37823 

LATITUDE 0.06150 0.87522 0.070 0.94402 

logcond -8.53654 3.55382 -2.402 0.01685 * 

color 2.27513 2.57929 0.882 0.37837 

--- 

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 14.4 on 335 degrees of freedom 

Multiple R-squared: 0.3704, Adjusted R-squared: 0.3554 

F-statistic: 24.63 on 8 and 335 DF, p-value: < 2.2e-16 
TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters

B12-2 

Model results for log TP: 

Coefficients: 

 Estimate Std. Error t value Pr(>|t|) 

(Intercept) 66.31642 64.53766 1.028 0.30490 

logp -0.19659 1.92279 -0.102 0.91863 

hab 0.26958 0.04423 6.095 3.01e-09 *** 

LDI -1.08353 0.58908 -1.839 0.06675 . 

pH 0.60466 1.52958 0.395 0.69286 

LONGITUDE 0.56124 0.75620 0.742 0.45850 

LATITUDE 0.40722 0.87909 0.463 0.64350 

logcond -10.77206 3.49839 -3.079 0.00225 ** 

color 0.15219 2.64265 0.058 0.95411 

--- 

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 14.56 on 335 degrees of freedom 

Multiple R-squared: 0.3562, Adjusted R-squared: 0.3408 

F-statistic: 23.17 on 8 and 335 DF, p-value: < 2.2e-16

In both models, the relationship between SCI and habitat score (hab) and log conductivity 

(logcond) was significantly different from zero. Log TN (logtn) also was significantly associated 

with SCI (p < 0.01), whereas log TP was not. 

The R2 values for both models were not high (R2 = 0.37 and 0.36); however, the degree to which 

the models accounted for variability in SCI should be interpreted with respect to the variability 

that one expects to explain with environmental variables. More specifically, SCI values 

calculated from samples collected from the same site are known to vary substantially. In a 

different analysis, the standard deviation of this within-site variability of SCI values was 

estimated as 13.4 (FDEP 2007, page 23). This within-site variability cannot be explained by 

differences in environmental conditions across sites, and therefore the R2

 value should be 

adjusted to account for known, within-site variance. 

R2

 values can be adjusted to account for within- versus across-site variance by decomposing the 

total observed variance in SCI values. The total observed variance of SCI observations in the 

data set was 321.5. Of this variance, 179.6 (i.e., 13.42

) can be attributed to within-site variance, 

leaving an across-site variance of 141.9 to be explained by the regression models. In the log TN 

model, the variance explained by the model can be calculated by subtracting the variance of the 

residuals (202.4) from the total observed variance (321.5), giving 119.1. Then, an R2

 value that 

expresses the proportion of the across-site variability that is explained by the model can be 

computed as the variance explained by the model divided by the across-site variance: 

119.1/141.9 = 0.84. 

In the log TN model, both habitat score and log conductivity were significantly associated with 

SCI values, and therefore selecting a TN criterion value to achieve a minimum SCI value 

requires that one assume representative values of conductivity and habitat score. FDEP has 

determined that SCI = 40 is a threshold above which sites meet their designated use for 

supporting aquatic life. This SCI threshold can be used with the regression model shown above 

to compute candidate TN criterion values. First, values for predictor variable that were not 

statistically significant (i.e., LDI, pH, latitude, longitude, and color) are fixed at their mean 

values, and SCI is fixed at 40, giving the following equation: 
TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters

B12-3 

mean mean

mean mean mean

Latitude Cond Color

TN Habitat LDI pH Longitude

0615.0 log54.8 log28.2

268.0log7.107.7840 941.0 0142.0 659.0

 

     

This equation can be simplified to 

 TN  268.0log7.107.2740 Habitat  log54.8 Cond

If one specifies a habitat score and a log conductivity in this equation, a log TN criterion value 

can be calculated that, on average, is associated with SCI = 40. This calculation is summarized in 

Figure B12-1, where the symbols indicate observed values of habitat score and log conductivity, 

and the contour lines indicate TN criterion values associated with SCI = 40 and with a particular 

combination of habitat score and log conductivity value. Each contour line is labeled by a log TN 

value, which can be interpreted as a candidate criterion value. Each contour line is also labeled in 

parentheses with the percentile of the observed TN distribution represented by the candidate 

criterion value. For example, approximately 55% of observed TN values in the data set were less 

than log TN = 0 (TN = 1 mg/L). 

In the upper left quadrant of the plot, conductivity values are high and habitat scores are low, 

both of which were associated with reductions in SCI value. Consequently, the log TN values 

required to achieve SCI = 40 for these sites were very low. Estimated candidate criterion values 

for log TN in these sites were less than one, a concentration lower than any concentration 

observed in the data set. 

Table B12-1. Correlations between Environmental Variables 

log TP log TN log cond Habitat log color LDI Latitude Longitude

log TN 0.52 

log cond 0.38 0.32 

Habitat -0.27 -0.12 -0.29 

log color 0.26 0.39 -0.21 0.15 

LDI 0.28 0.14 0.38 -0.69 -0.27 

Latitude -0.36 -0.38 -0.61 0.25 -0.06 -0.27 

Longitude 0.41 0.45 0.56 -0.07 0.3 0.16 -0.66 

pH 0.25 0.04 0.77 -0.3 -0.48 0.37 -0.42 0.29 
TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters

B12-4 

Figure B12-1. Observed values of habitat score versus log(conductivity). Contours indicate 

candidate TN criterion values associated with each combination of habitat and conductivity 

values. The percentile of the observed TN distribution associated with each candidate criterion 

value is shown in parentheses.