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<br />l'EGIONAL REGRESSION ANALYSIS. The corps of Enclineers' Generalized <br />Computer Program 704-G1-L2020 "Multiple Linear Regression" <br />(September 1970) analyzed the peak flow~ and basin areas from the <br />selected stream gages to compute regression equations appropriate <br />t:o each flood frequency. Each regre:ssion equation predicted the <br />frequency peak discharge (the dependent variable) from m'~asurement <br />of the basin area in square miles (thE! independent variable). The <br />program also performed a correlation analysis to measure the <br />accuracy of the relationship described by the regression equation. <br /> <br />Originally, South platte River basin stream gages were omitted <br />fro:u the analysis in an effort to use, data unique to t.he, Arkansas <br />River basin, and attempts were made to correlate only the strearr <br />gages within th,~ Arkansas River basin. stream gages which had 20 <br />yea::s or more of recorded peak flows were analyzed. Ten of t.he <br />original 26 gages met this criterion, and the correlation analysis <br />reported a good fit between the data points and the regression <br />equation. The predicted 1-percent'-chance flood peak for Oak Creek <br />at Florence was 1650 cfs with a standard error of estimate of 0.87, <br />The 10 data points and the generated graph are presented in Linear <br />Regression Analysis No.1 on Plate 2. <br /> <br />The gages with long records are located downstream in the <br />Arkansas River basin and have drainage areas considerably larger <br />than the study basin. Consequently, the regression equation did <br />not satisfactorily predict pea.k flows for basins smaller than <br />several hundred square miles. A correlation was attempted on gages <br />having 15 years or more of record; 13 of the original gages met <br />this criterion. Again, the results werE, unsatis:factory bE~cause the <br />gaging stations I"hich represent drainaqe basins wi th smaL~er areas <br />typi~al of the foothill streams are those stations with shorter <br />peri::>ds of record. To include the foothill streams, another <br />analjsis was made that correlated all of the original 26 Arkansas <br />Ri ve:: basin gages. The resulting equa1:ion predicted a I-percent- <br />chance flood discharge for Oak Creek at Florence of 6,600 cfs with <br />a standard error of estimate of 0.71. The plotted data is <br />presented as Linear Regression Analysis No.2 on Plate 3. <br /> <br />The 26 Arkansas River stream gacles represent a variety of <br />drainage area sizes and physical characteristics. In an at.tempt to <br />use 'Natersheds ..'hich most resembl,;> the basin under study, the <br />drainage areas of the selected gaCj'es were constrained Vlithin 7 <br />square miles and 700 square, representing one magnitude increase or <br />decrease from the 71.58 square miles of Oak Creek at Florence, and <br />gages located on streams draining plains region watersheds were <br />eliminated from the analysis. The resulting regression equation <br />produced a 1-percent-chance flood discharCj'e for Oak Creek at <br />Florence of 10,300 cfs and a standard error of estimate of only <br />0.38. As Linear Regression Analysis No. 3 on Plate 4 shows, the <br />stream gages with drainage areas betwE,en 7 square miles and 700 <br />square miles display considerable scatter when plotted against the <br />peak discharges ccllculated from frequency analyses; this ;;catter is <br /> <br />8 <br />