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<br />. 600,000
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<br />
<br />SOME STATISTICAL TOOLS IN HYDROLOGY
<br />
<br />31
<br />
<br /> !
<br /> I /
<br /> ~ -! II '/
<br /> r!J ,;., '" r/
<br /> 'b zm~
<br /> II '"
<br /> II :7~
<br /> rl .>I'
<br /> 'V"./~ "
<br />II '/ I '/'" ",,, ~~ "
<br /> . ,,OJ
<br /> "'i;ii:'i
<br /> v rps
<br /> Wt I
<br /> I i
<br /> /, i
<br />) / 7 I
<br />~ I / / 1
<br />
<br />300,000
<br />200,000
<br />
<br />100,000
<br />
<br />'i;
<br />o
<br />Q
<br />
<br />10,000
<br />
<br />1000
<br />100
<br />
<br />1000
<br />
<br />Q,.
<br />
<br />1
<br />
<br />10
<br />A
<br />
<br />100
<br />
<br />Figure 22.-Cooxial graphical multiple regression.
<br />
<br />in which 78 is the intercept at P= 1.2, the
<br />increase in K per tenth is 1.36, and the factor
<br />1O(P-1.2) is the number of tenths above 1.2.
<br />Substituting the values of K and n gives, for
<br />the first relation
<br />
<br />Q..,=78(1.36)lO,P.U)AU8, (1)
<br />
<br />The second relation,
<br />
<br />Q.., j(8, QlO)
<br />
<br />is handled by considering again that Q.., is the
<br />dependent variable. Neglecting 8, the model
<br />would be
<br />Q..,=KQ,~.
<br />
<br />The slope m is 1.78 by scaling. The intercept K
<br />is computed at 8=1, Q..,=100,000, and
<br />Q,.=19,000, as follows:
<br />
<br />100,000=K(19,000),.78,
<br />
<br />or
<br />
<br />log 100,OOO=log K+1.78 log 19,000,
<br />log K=5-7,60=-2,60=7.40-1O,
<br />K=O,0025,
<br />
<br />The spacing of the lines in a vertical direction
<br />(parallel to the Q.., scale) is twice the paper
<br />scale. Therefore, the intercept K varies directly
<br />as 8', and the equation is
<br />
<br />Q..,=O,00258'QI6". (2)
<br />
<br />Equating equations 1 and 2 gives
<br />
<br />0.00258'Ql6"= 78 (1.36)' o,p.,,') A"",
<br />
<br />which, in logarithmic form, is
<br />
<br />log 0.0025+2 log 8+1.78 log QlO=log 78
<br />
<br />+ 10(P-1.2) log 1.36+ 1.28 log A.
<br />
<br />Solving for Q,. gives
<br />
<br />log QlO=1.61+0.72 log A-1.l2 log 8+0.75P,
<br />
<br />which is the desired result.
<br />
<br />Other Tools
<br />
<br />Analysis of variance
<br />
<br />Analysis of variance is a procedure by which
<br />the variation embodied in the data of the
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