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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 />III(0.62554) (-0.32771) - (0.06952) (0.45470) + (0.33512) (0.70605) =0
<br />0=0 Check (to five places)
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<br />Solving for C42, C43, and C44:
<br />I :;8(x,')C., + :;8(x,x,)C., + :;8(x,x,)c..=O
<br />II :;8(x,x,)C., + :;8(x,')C., + :;8(x,x,)c..=O
<br />III :;8(x,x,)C., + :;8(x,x,)c" + :;8 (x.') c.. = 1
<br />I 10.20183c., + 6.38133c" + 0.62554c..=0
<br />I' -c" -0.6255080" -0.061316c..=0
<br />II 6.38133c" + 6.90632c" - 0.06952c..=0
<br />(-0.625508) I -6.38133.c" - 3.99157c" - 0.39128c,,=0
<br />:;8, 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) :;8, 0.07285c..-0
<br />:;8, 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 Check
<br />Computing b coefficients and checking against those previously computed:
<br />b,=c,,:;8(XIX,) +C,,:;8(XIX,) +C,,:;8(XIX,),
<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,,:;8(XIX,) +C33:;8(XIX,) +C,,:;8(XIX,),
<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,,(:;8(XIX,) +c,,:;8(x,x,) +c,,:;8(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 />Computation of standard errors of b coefficients (Bennett and Franklin, 1954, p. 249) :
<br />81.2,,=0.0584 from previous computation.
<br />8,,=8,.331 .JC;;=0.0584.v0.34688= (0.0584) (0.589),
<br />= 0.0344 Standard error of b2.
<br />8,,=81.33' JC33=0.0584.v0.4547 = (0.0584) (0.6743)
<br />=0.0394 Standard error of b,.
<br />8"=8,.,,, .JC:=0.0584,,'4.466= (0.0584) (2.113),
<br />=0.1234 Standard error of b,;
<br />Computation of confidence intervals of fJ coefficients (Bennett and Franklin, 1954, p. 250) :
<br />1,6.0.95=2.03 (Dixon and Massey, 1957, table A-5, p. 384)
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