RelationshipamongvariablesFunctionCorrelation(statisticalrelationship)YdependsonX,butisn’tmerelydeterminedbyX.Example:price—demandforproducttemperature—demandforair-conditioningRegression—Accordingtoobservantdata,establishregressionmodelandmakestatisticalreferenceonvariableshavingstatisticalrelationship.Chapter10Regression1
Whatdoesregressiondo?Solvethefollowingproblems:Determinewhethertherehasstatisticalrelationshipamongvariables,ifhas,showtheformula.Forecastthevalueofanothervariableaccordingtoonevariableoragroupofvariables.2
LinearRegressionAssumptionsNormalityEveryvalueofX,YfollowsthenormaldistributionTheerrorprobabilityfollowsthenormaldistributionHomoscedasticity(ConstantVariance)IndependenceofErrorsLinearity3
Example:X-price，Y-demandfortheproductWehavedata:1.Scatterplot2.Regressionequation(OrdinaryLeastSquareEstimation)3.CorrelationcoefficientrTestingtheregressionmodel4.Forecasting5.RegressioncanbelinearitiedSimpleLinearRegressionX(Yuan)708090100110Y(thousand)11.2511.2811.6511.7012.144
LinearRegressionModelVariablesconsistofalinearfunction.YXiii??????01SlopeY-InterceptIndependent(Explanatory)VariableDependent(Response)VariableRandomError5
PopulationLinearRegressionModel?i=randomerrorX???YXiX??01YXiii??????01ObservedValueObservedValueY6
SampleLinearRegressionModelei=randomerrorYXYbbXeiii???01^YbbXii??01UnsampledObservedValueSampledObservedValue7
OrdinaryLeastSquaresTheleastsquaresmethodprovidesanestimatedregressionequationthatminimizesthesumofsquareddeviationsbetweentheobservedvaluesofthedependentvariableyiandtheestimatedvaluesofthedependentvariable.e2YXe1e3e4YbbXeiii???01^YbbXii??01OLSMineeeeeii2112223242??????PredictedValue8
CoefficientEquationsYbXbXYnXYXnXbYbXiiiiiniin???????????011122101SampleregressionequationSlopefortheestimat