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<br />O,,~Q'Q <br />u.J.lJ.......~~ <br /> <br />Survey. [5] <br />values were <br />shown:* <br /> <br />The following number of pairs of area and capacity <br />used, resulting in the coefficient of determination <br /> <br />Reservoir No. pairs <br /> <br />Coefficient of determination <br /> <br />Lake Powell 36 <br />Lake Mead 35 <br />Lake Mohave 9 <br />Lake Havasu 6 <br /> <br />0.999672 <br />0.998991 <br />0.999910 <br />0.999001 <br /> <br />Errors in the normal operating range due to use of the polynominal <br />relationship are tabulated as follows: <br /> <br />Reservoir <br /> <br />Approximate normal error <br />1,000 acre~ Percent <br /> <br />Lake Powe 11 <br />Lake Mead <br />Lake Mohave <br />Lake Havasu <br /> <br />0.7 <br />2.2 <br />0.05 <br />0.1 <br /> <br />0.5 <br />2.2 <br />0.2 <br />0.5 <br /> <br />Coefficients C1 through Cs are presented in Table I. <br /> <br />I=N <br />* The total variation of Area A is defined as L: (A i - i\) 2 which is <br />i=l <br />the sum of the squares of the deviations of the Ai values from the <br />mean A based on the N data sets. This total variation can also be <br />expressed by: <br /> <br />i=N i=N <br />L (A i-A) 2 = L: <br />i=l i=l <br /> <br />i=N <br />(Ai - Aiest)2 + L <br />i=l <br /> <br />-2 <br />(A i est - A) <br /> <br />where Aiest is the area estimated from the regression relationship. <br />The first summation on the right-hand side is the variation which <br />is unexplained by the correlation, while the second is the explained <br />variation. The unexplained variation behaves in a random manner. <br />The coefficient of determination is defined as the ratio of the <br />explained to the total variation. A value of one indicates a perfect <br />fit because all variation has been explained. <br /> <br />9 <br />