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<br />, <br /> <br />1. <br /> <br /> <br />tv <br />~... <br />o <br />~ <br /> <br />Indicators of salt pickup: <br /> <br />1, < Irrigated area (annual value), <br />2. Consumptive use in the preceding month. <br />3. Consumptive use in the second preceding month. <br />4. Consumptive use in the third preceding month. <br />5, Consumptive use in the fourth preceding month. <br /> <br />For downstream sites (table 1), these variables were summed for all tributary <br />upstream reaches. The models then were calibrated using variables that <br />indicated the total water-resources development upstream from the site, <br /> <br />Selection of independent variables for individual sites was made using <br />stepwise-regression procedures. Four separate methods were used: (1) Back- <br />ward elimination, (2) forward selection, (3) stepwise selection, and <br />(4) maximum R2 improvement (SAS Institute Inc., 1985). Also, the diversion <br />indicators were divided into three groups to evaluate the effects of col- <br />linearity among the diversion indicators, One group included only total <br />adjustments; the second included only the components of total adjustments-- <br />consumptive use, net other diversions, and net release; and the third included <br />all four of the diversion indicators. This combination of 4 methods and 3 <br />groups of variables produced 12 separate selection options for a particular <br />model calibration, <br /> <br />Several secondary criteria were applied to distinguish among options and <br />determine the overall best variable set. The first of these secondary cri- <br />teria was to minimize the mean-square error. The second criterion was that <br />the Mallows' Cp statistic approximately equal the number of parameters in the <br />model. This minimizes the bias in the standard error caused by an over- <br />parameterized model (Montgomery and Peck, 1982). The third criterion was that <br />the coefficients for the development variables have the expected sign. The <br />fourth criterion was that the model contain no strongly correlated variables <br />or combinations of variables. This criterion was intended to decrease the <br />collinearity among the independent variables. As a check for possible col- <br />linearity, the variance inflation factors (VIF's) were evaluated for the <br />selected variable sets, The VIF for a coefficient is a measure of the <br />increase in the variance of that coefficient caused by correlation among the <br />independent variables in the model. If VIF's are large, the associated <br />coefficients may be poorly estimated (Montgomery and Peck, 1982). <br /> <br />In practice, the variable sets selected by the four stepwise regression <br />procedures usually were identical; therefore, the choice was only among the <br />three variable groups. Normally, one of these groups was clearly superior in <br />regard to all the secondary selection criteria, <br /> <br />15 <br />