Estimation of Nutrient Loads and Water-Quality Analyses 27 Additionally, other factors contributing to differences between sample types could be related to the degree of mixing at the sample location based upon physical char- acteristics of the channel, such as distance upstream or downstream from the control structures and configura- tion of the channel. Model Development An ordinary least-squares regression technique was used to develop predictive equations for the pur- pose of estimating total nitrogen and total phosphorus loads discharged from the east coast canals to Biscayne Bay. The predictive equations can be used to estimate the value of a dependent variable from observations on a related or independent variable. In this study, load was used as the dependent or response variable and dis- charge as the independent or explanatory variable. Because discharge is used in the computation of load, linearity and the best fit equation can be established or developed more easily by relating load to discharge rather than concentration to discharge. Using more than one independent variable, such as stage, rainfall, gate opening, and discharge, multiple linear regression was attempted to improve the predic- tive equations. However, because discharge is com- puted from stage and gate openings and is based upon rainfall, collinearity between independent variables precluded this approach. A smoothing procedure, called locally weighted scatterplot smooth (LOWESS), was used by plotting load as a function of discharge to deter- mine the degree of linearity between the two variables. When it was deemed necessary to improve the linear relation between load and discharge, transformations of the independent variable were made based upon the relation of the curve to the Mosteller and Tukey bulging rule (Helsel and Hirsch, 1992, p. 229). Improvement in the models was based on increases in the adjusted coefficient of determination (R²), which explains the amount of variation in the load determined by discharge and reduction in the predicted error sums of squares (PRESS) statistic. The models selected were those having the highest adjusted R² and the lowest PRESS statistic as well as the lowest root mean square error or standard error of the regression. The null hypothesis of no linear relation between load and discharge was rejected at the 0.05 significance level (a level) when the attained significance level (p-value) was less than 0.05. An important part of model development is resid- uals analysis. Two assumptions of an ordinary least- squares regression are: (1) variance of the residuals is constant (homoscedastic) over the range of values, and (2) residuals are independent. Plots of predicted values against residuals were examined, and where noncon- stant variance (heteroscedasticity) over the range of values was observed, log transformations of the response variables were made. Because of errors in comparing log space with real space, no comparisons were made with this analogy between transformed and nontransformed models based on the adjusted R² or PRESS statistics. A key element in model development is regres- sion diagnostics. Basing model adequacy solely on the adjusted R² may prove to be inadequate because there may be no indication as to whether the data have been well fitted. Examination of data points for leverage, influence, or outliers was required to verify model ade- quacy. Outliers in the x direction were determined to be significant if they exceeded 3 p/n where p is the number of coefficients and n equals the number of samples (Helsel and Hirsch, 1992, p. 247). Studentized residuals were used to examine outliers in the y direction, and Cook’s D was used to determine influence from outli- ers. Observations were considered to have high influ- ence if Cook’s D exceeded the value for the F distribution for p +1, n - p at a = 0.1 (Helsel and Hirsch, 1992, p. 249). Numerous data values demonstrated high leverage, but only a few data values showed both high leverage and high influence. The ESTIMATOR Program Because continuous discharge data are currently being computed and long-term water-quality data are available at site S-26 along Miami Canal, a software program, called ESTIMATOR, was used in the devel- opment of nitrogen and phosphorus load models and for the estimation of loads at the site. The ESTIMATOR program develops models and computes loads based on mean daily discharge and water-quality data files. This program was used at site S-26 (formerly part of the NASQAN network as previously discussed) because of the continuous discharge data available and the require- ment that about 50 water samples should have been col- lected over at least a 2-year period. The ESTIMATOR program consists of a seven-parameter log/linear model employing the following regressors: a constant, a qua- dratic fit to the natural logarithm of discharge, a qua- dratic fit to time, and a sinusoidal first-order Fourier