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To remove the effects of these two vaziables (the flow and the rise), the value predicted <br />from the regression equation is subtracted from the measured value. This is called the <br />residual, and is the distance the observed point lies above or below the regression line. <br />The residual contains the variation due to all other variables than the two removed by the <br />regression. <br />In order to be able to compare the residuals when the Y variable (zinc concentration) is <br />transformed (ie, the analysis uses the natural logaritlun of the zinc concentration), it is <br />important to "standardize" the residuals by dividing all the residual values by the standard <br />errors. In this way, the magnitude and importance of the residual can be judged. For <br />instance, a 50 ug/L residual has much more importance if the predicted value is 100 ug/I, <br />(50% difference) than if the predicted value is 800 ug/L (6 % difference). The <br />standardized residual is calculated as Follows: <br />StR = ((ln[ZnA_~z act)) - (ln[Zna-7z Pred])) / S (3) <br />Where: <br />StR = Standazdized Residual <br />In(ZnA_~z n°t) =the natural logarithm of measured dissolved zinc concentration <br />(in ug/L) at A-72 <br />ln(ZriA_~z Brea) =the natural logarithm of predicted dissolved zinc concentration <br />(in ugJL) at A-72, from equation (1) <br />S = standard error of the prediction equation, in this case 0.1532 <br />A plot of the standardized residuals displays the degree of departure of the actual zinc <br />concentration from the predicted zinc concentration. Figure A-3 displays the standardized <br />residuals for the baseline data set. Bars that descend below the centerline indicate sanlples <br />where the actual value is less than the predicted value; bars that extend above the <br />centerline indicate satnples where the actual value is greater than the predicted value. <br />t This standardizing technique is an approximation, since the standard error in Table A-2 is the standard error a[ the <br />mean. At flow values much higher or much lower than the mean, the standard error will be slightly different than <br />the 0.1532 provided in Table A-2. For purposes of tracking water quality at A-72, the standard ettor of 0.1532 is <br />adequate. <br />Appendix A 5 <br />232565 <br />