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<br />__ _._-.__'._ _....__.--a.__. <br /> <br />Figure 2 shows the locations of the 246 gaging stations that were used in <br />this analysis. <br /> <br />Multiple-Re~~ession Analvsis <br /> <br />Multiple-linear-regression techniques were used to d~fine relations <br />between flood flows and basin characteristics. Previous studies by Benson <br />(1962) and Guetzkow (1977) have shown that the logarithmic transform of the <br />data results in linear relations between flood flows and basin character- <br />istics _ This study used the logarithmic transformation tbat results in <br />general linear-regression models described by the equations below. <br /> <br />For transformed variables: <br /> <br />Log QT - aO + Bl log Xl + B2 log X2 + ... + Bn log ~ <br /> <br />or as untransformed variables: <br /> <br />Qr - eBO (Xl)Bl (X2)B2 ... (~)Bn <br /> <br />where: <br /> <br />QT is the peak discharge for T-year recurrence interval, <br /> <br />Bi are regression coefficients, <br /> <br />Xi are independent variables (basin characteristics), and <br /> <br />e is the base of the natural logarithms. <br /> <br />The stepwise method of multiple-regression analysis used is described in <br />Hocking (1976). Only those independ~nt variables statistically significant at <br />the lO-percent level of significance are included in the equations. The 10- <br />percent criterion was used to standardize, on a regional bas is, the bas in <br />characteristics used to define flood flows at the various recurrence <br />intervals. The inclusion of the same variables in all equations for a region <br />improves the continuity of the :t:requency curves constructed from the <br />equations_ <br /> <br />Bevington (1969, p. 100-102) and Draper and Smith (1981, p. 108) indicate <br />that when the variance of the dependent variable is not constant for all <br />observations, the equations resulting from the regression analysis may be a <br />poor estimate of the "true" relation. Because it is well known that predicted <br />flow magnitudes are more accurate from long-term gaging records than from <br />short-term records (Linsley and others, 1982, p. 358), residuals were analyzed <br />to determine any trend as a function of gaging-record length. A significant <br />decrease in the variance of the residuals was observed as gaging record <br />increased_ Bobee (1973) defines an equation to estimate the variance of a <br />calculated flood magnitude given the return period, standard deviation, <br />coefficient of skewness, and the number of years of record. The variances of <br />the flood estimates of different return periods were found to be proportional <br />to the return period_ Because of this relationship, only the calculated <br />flood-magnitude variance for each station, for the 10-year return period, was <br /> <br />4 <br />