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<br />26
<br />
<br />TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS
<br />
<br />.
<br />
<br />Table 4.~ta for graphical regression using highly cOlTelated independent variables
<br />[From Riggs (19M)}
<br />
<br />River and location
<br />
<br />lOo-yr
<br />flood
<br />(cfs)
<br />
<br />Mean
<br />annual
<br />flood
<br />(efs)
<br />
<br />Average
<br />discharge
<br />(cfs)
<br />
<br />1. Neosho--Iola, Kans__________________________
<br />2. Big Blue-Randolph, Kans......,..,..,.,....,
<br />3. Miami-Dayton,Ohio___________________.:.____
<br />4. Savannah-Augusta, Ga______________________
<br />5. West Branch Susquehanna-Williamsport, Pa_ __
<br />6. Susquehanna-Towanda, Pa___________________
<br />7. Susquehanna-Harrisburg, Pa_________________
<br />8. Kanawha-Kanawha Falls, W. Va_____________
<br />9. Allegheny-Red House, N.Y___________________
<br />10. Iowa, Iowa City, Iow8________________________
<br />11. Tennessee-Knoxville, Tenn_____ _____ _ ____ _ ___
<br />12. French Broad-Asheville, N.C_________________
<br />13. Des Moines-Ke088ugua, Iowa___________u___
<br />14. Connecticut-White River Junction, Vt_________
<br />15. Cumberland-Nashville, Tenn _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
<br />16. Hudson-Mechanicville, N.Y__________________
<br />17. Ohio-Cincinnati,_ 0000_ _ _____________________
<br />
<br />105, 000
<br />96,700
<br />108,000
<br />350,000
<br />260, 000
<br />236,000
<br />594,000
<br />276,000
<br />56,400
<br />40, 700
<br />228, 000
<br />45,500
<br />103, 000
<br />122,000
<br />208, 000
<br />89, 300
<br />800, 000
<br />
<br />28,300
<br />27,600
<br />35,900
<br />112, 900
<br />104, 100
<br />107,200
<br />282,600
<br />125, 600
<br />24, 500
<br />13,100
<br />94,700
<br />17,500
<br />41, 100
<br />53, 100
<br />122,200
<br />42,500
<br />443,700
<br />
<br />1,680
<br />1,680
<br />2,260
<br />10. 540
<br />8,910
<br />10, 370
<br />34, 700
<br />12,670
<br />2, 795
<br />1,560
<br />12, 820
<br />2,112
<br />5,351
<br />7, 190
<br />20,400
<br />7,430
<br />97, 700
<br />
<br />increases with Q.... it is impossible to tell by
<br />inspection whether use of Q., will improve
<br />the relation.
<br />The following procedure may be used to
<br />define the effect, if any, of Q., on the scatter
<br />of points about curve 1:
<br />1. Plot Q., against Q..33 (as abscissa) and draw
<br />the mean line (curve 2).
<br />2. Divide each Q.. by its value from curve 2
<br />at the same value of Q..,. These divisions
<br />are shown on the graph sheet for each,
<br />plotted point (curve 1). Tbey could have
<br />been obtained directly by measuring the
<br />deviations from curve 2 in percentage with
<br />dividers (only on log paper); in practice
<br />they would be obtained this way.
<br />3. Use the dividends obtained in step 2 as the
<br />third variable.
<br />4. Proceed with the graphical multiple regres-
<br />sion llll described previously.
<br />The triangular symbols near curve 1 are the
<br />points adjusted' for the effect of Q.,. The fact
<br />that they show less scatter than the original
<br />points indicates that estimates of QlOO are im.
<br />proved by using Q., as an additional variable.
<br />It can be shown by computing the equation of
<br />the graphical relation that it is of the form
<br />
<br />log Q,oo=log a+b, 'log Q,.,,-b.log Q.,.
<br />
<br />The introduction of the dividend is merely an
<br />expedient; it cancels out of the final relation.
<br />
<br />Choice of graphical or analytical method
<br />for multiple regression
<br />
<br />A standard graphical method is particularly
<br />useful for exploratory work and for making
<br />preliminary estimates. The graphical method
<br />has the following advantages:
<br />
<br />1. It is rapid,
<br />2. It helps define the appropriate model.
<br />3. It points out the need for transformations,
<br />if any.
<br />4. It brings attention to extremely wild points
<br />if they exist in the data. (~ee the wild
<br />point in fig. 18.)
<br />Disadvantages of a graphical method are:
<br />
<br />1. Small effects of independent variables cannot
<br />be identified.
<br />2. The number of independent variables is
<br />limited to about three because of the cu.
<br />mulative effect of inaccuracies in plotting
<br />and in locating the lines.
<br />3. Tests of significance of the effects of individ.
<br />ualvariables are not available.
<br />4. The resulting relation involving three or
<br />mOre variables is confusing to the user
<br />unless expressed mathematically or re.
<br />plotted in another form.
<br />An analytical method has the following
<br />advantages:
<br />
<br />1. For the model used, it gives the best estimate
<br />
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<br />
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