国外大学的英文线性回归讲义_linear_regression(1).pptVIP免费

Copyright©2005Brooks/Cole,adivisionofThomsonLearning,Inc.17.1Chapter17SimpleLinearRegressionandCorrelationCopyright©2005Brooks/Cole,adivisionofThomsonLearning,Inc.17.2LinearRegressionAnalysis…Regressionanalysisisusedtopredictthevalueofonevariable(thedependentvariable)onthebasisofothervariables(theindependentvariables).Dependentvariable:denotedYIndependentvariables:denotedX1,X2,…,XkIfweonlyhaveONEindependentvariable,themodeliswhichisreferredtoassimplelinearregression.Wewouldbeinterestedinestimatingβ0andβ1fromthedatawecollect.Copyright©2005Brooks/Cole,adivisionofThomsonLearning,Inc.17.3LinearRegressionAnalysisVariables:X=IndependentVariable(weprovidethis)Y=DependentVariable(weobservethis)Parameters:β0=Y-Interceptβ1=Slopeε~NormalRandomVariable(με=0,σε=???)[Noise]Copyright©2005Brooks/Cole,adivisionofThomsonLearning,Inc.17.4EffectofLargerValuesofσεHousesizeHousePrice25K$Samesquarefootage,butdifferentpricepointse.g.décoroptions,cabinetupgrades,lotlocation…)Lowervs.HigherVariabilityHousePrice=25,000+75(Size)+Copyright©2005Brooks/Cole,adivisionofThomsonLearning,Inc.17.5TheoreticalLinearModelCopyright©2005Brooks/Cole,adivisionofThomsonLearning,Inc.17.61.BuildingtheModel–CollectDataTest2Grade=β0+β1*(Test1Grade)FromData:Estimateβ0Estimateβ1EstimateσεStudentTest1Test2150322513335234453355543665537756398574095841105942116043126144136246146347156448166549176650186751196853206954217055227156237257Copyright©2005Brooks/Cole,adivisionofThomsonLearning,Inc.17.7LinearRegressionAnalysis…PlotofFittedModelTest1Test2405060708090100020406080100PlotofFittedModel60708090100TestB1425262728292TestB2PlotofFittedModelTestB1TestB250607080901005060708090100Copyright©2005Brooks/Cole,adivisionofThomsonLearning,Inc.17.8CorrelationAnalysis…“-1<<1”Ifweareinterestedonlyindeterminingwhetherarelationshipexists,weemploycorrelationanalysis.Example:Student’sheightandweight.PlotofHeightvsWeight100140180220260Weight4.655.45.86.26.67HeightPlotofHeightvsWeight10014018022026...