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<br />SOME STATISTICAL TOOLS IN HYDROLOGY
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<br />17
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<br />I' -c,,- (0.625508)(0.45470) - (0.061316) (0.70605) =0
<br />-c,,-0.28442-0.04329=0
<br />c,,= -0.32771
<br />111(0,62554)( -0.32771) - (0.06952) (0.45470) + (0.33512) (0.70605) =0
<br />0=0 Oheck (to five places)
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<br />Solving for c", .,.., and c,,:
<br />I ;E(x,')c" + ;E(x,x,)c" + ;E(x,x,)c,,=O
<br />II ;E(x,xa)c., + ;E(x,')c., + ;E(x,x,)c,,=O
<br />III ;E(x,x.)c" + ;E(x,x.)c" + ;E(x.')c,,= 1
<br />I 10.20183c" + 6.381330" + 0.625540,,=0
<br />I' -c" -0.625508c" -0.061316c,,=0
<br />II 6.38133c" + 6.90632c" - 0.06952c,,=0
<br />(-0.625508) I -6.38133c., - 3.99157c" - 0.391280,,=0
<br />;E, 2.91475c" - 0.46080c,,-0
<br />II' -c" +0.158092c,,=0
<br />III 0.625540" - 0.06952c" + 0.33512c,,= 1
<br />(-0,061316) I . - 0.03836c,,=0
<br />(0.158092) ;E, - 0.072850,,=0
<br />;E, 0.22391c,,= 1
<br />c,,=4.46608
<br />II' -c,,+0.158092(4.46608)=0
<br />c.,=0.70605
<br />I' -c.,- (0.625508)(0.70605) - (0.061316) (4.46608) =0
<br />-c.,-0.44164-0,27384=0
<br />c.,= -0.71548
<br />III (0.62554) (-0.71548) - (0.06952) (0.70605) + (0.33512)(4.46608) = 1
<br />1.00003::::1 Oheck
<br />Oomputing b coefficients and checking against those previously computed:
<br />b,=c,,;E(X,X,) +c,,;E(x,x,) +c,,;E(x,x.),
<br />= (0.34688)(11.74691) +( -0.32771) (6.57458) + (- 0.71548) (1.16244),
<br />b,=1.08851 (1.08847 from previous computation; check).
<br />b,=c,,;E(x,x,) +c,.;E(x,x,) +c..;E(x,x,),
<br />= ( -0.32771) (11.74691) + (0.45470) (6.57458) + (0.70605) (1.16244),
<br />b,=-0.03938 (-0.03938 from previous computation; check).
<br />b,=c,,(;E(x,x,) +C.,;E(XIX,) +c,,;E(x,x.),
<br />= ( -0. 71548) (11. 74691) + (0.70605) (6.57458) + (4.46608) (1.16244),
<br />b,=1.42885 (1.42883 from previous computation; check).
<br />The coefficient a would be computed as described previously.
<br />Oomputation of standard errors of b coefficients (Bennett and Franklin, 1954, p. 249):
<br />81.2..=0.0584 from previous computation.
<br />8,,=8,.23,-v'C,;=0.0584.vO,34688= (0.0584) (0.589),
<br />= 0.0344 Standard error of b,.
<br />8"=8,.,,, Jcss=0.0584.v0.4547 = (0.0584) (0.6743)
<br />=0.0394 Standard error of b,.
<br />8.,=8,.23'..;c;;,= 0.0584,,'4.466= (0.0584) (2.113),
<br />=0.1234 Standard error of b,.
<br />Oomputation of confidence intervals of fJ coefficients (Bennett and Franklin, 1954, p. 250):
<br />1". .,,,=2.03 (Dixon and Massey, 1957, table A-5, p. 384)
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