chapter 1 modeling with linear functions：1章以线性函数建模

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1、2.1UsingLinestoModelData(Page5of21)2.1UsingLinestoModelDataScattergramandLinearModelsThegraphofplotteddatapairsiscalledascattergram.Alinearmodelisastraightlineoranequationthatdescribestherelationshipbetweentwoquantitiesforatrue-to-lifesituation.YearYearssinc

2、e1960tNumberofVisitors(millions)v196019701980199020001.22.32.63.84.8Example1Letvrepresentthenumberofvisitors(inmillions)totheGrandCanyonintheyearthatistyearssince1960.a.Fill-inthetableofvaluesfort.Identifythedependentandindependentvariables.b.Makeascattergra

3、mofthedata.c.Usearulertodraw(“eyeball”)aline(linearmodel)thatfitsthedatawell.Asalways,labelandscalebothaxes.d.Usethelinearmodeltoestimatethenumberofvisitorsin2010(extrapolation).e.Usethelinearmodeltoestimateinwhatyeartherewillbe4millionvisitorstotheGrandCany

4、on(interpolation).2.1UsingLinestoModelData(Page5of21)Interpolation,Extrapolation&ModelBreakdownInterpolationismakingpredictionwithinthedatagiven.Extrapolationismakingapredictionoutsidethedatagiven.Whenamodelyieldsapredictionthatdoesnotmakesenseoranestimateth

5、atisnotagoodapproximation,wesaythatmodelbreakdownhasoccurred.Modelbreakdownmostlyoccurswhentryingtomakeanestimateoutsidetherangegiveninthedata(calledextrapolation).2.1UsingLinestoModelData(Page5of21)Example2YeartNumberofProzacPrescriptions(millions)198919911

6、993199519966.110.012.218.820.7ProzacisanantidepressantthatwasapprovedbytheFDAin1987.LetpbethenumberofprescriptionsofProzac(inmillions)dispensedattyearssince1980.a.Fill-inthetableofvaluesfort.b.Identifythedependentandindependentvariables.c.Makeascattergramoft

7、hedata.d.Usearulertodraw(“eyeball”)aline(linearmodel)thatfitsthedatawell.Asalways,labelandscalebothaxes.e.UsethelinearmodeltoestimatethenumberofProzacprescriptionsin1994.f.UsethelinearmodeltopredictwhenthenumberofProzacprescriptionswillreach30million.YearSal

8、monPopulation(millions)2.1UsingLinestoModelData(Page5of21)P196019651970197519801985199010.0210.007.613.154.593.112.22Example3ThePacificsalmonpopulationsforvariousyearsarelistedinthetable.LetPrep