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<br />38 <br /> <br />TECHNICAL MANUAL <br /> <br />REGRESSION ANALYSIS <br /> <br />Standard multiple regression techniques were used to develop equations <br />by relating flood characteristics at gaged sites to basin and climatic param- <br />eters. Initial regression equations were obtained for each flood character- <br />istic using all four basin variables and then redefining the relations by <br />successively el iminating the least significant basin or cl imatic parameter <br />unti I only one parameter remained. The final regress'ion equations are based <br />on basin and cl ;matic parameters for which all coefficients were significant <br />at the 5 percent level. <br /> <br />The first regression trial was made using gaging-station records for all <br />natural-flow streams in Colorado and selected streams in adjoining States. <br />The accuracy of the results was extremely poor and no significant trends could <br />be identified from plots of residuals from the regression equations. The poor <br />result was attributed to the extremely varied topography of the State and the <br />several sources and forms of precipitation which produce floods. Additional <br />regression runs were made using numerous combinations of areas to obtain rea- <br />sonable regional subdivisions. <br /> <br />The final regression results indicate that the flood characteristics of <br />natural-flow streams in Colorado can best be defined by dividing the State <br />into four regions. The regions as shown in figure 2 are Plains, Mountain, <br />Northern Plateau, and Southern Plate~u. A brief description of each region Is <br />given in the following paragraphs and the flood-characteristic equations for <br />each region are listed in tables 1-4. The equations for the 100-year flood <br />discharges and depths can be solved graphically by using figures 3-10. <br />