MBA统计学pt .ppt

1 RelationshipamongvariablesFunctionCorrelation statisticalrelationship YdependsonX butisn tmerelydeterminedbyX Example price demandforproducttemperature demandforair conditioningRegression Accordingtoobservantdata establishregressionmodelandmakestatisticalreferenceonvariableshavingstatisticalrelationship Chapter10Regression 2 Whatdoesregressiondo Solvethefollowingproblems Determinewhethertherehasstatisticalrelationshipamongvariables ifhas showtheformula Forecastthevalueofanothervariableaccordingtoonevariableoragroupofvariables 3 LinearRegressionAssumptions NormalityEveryvalueofX YfollowsthenormaldistributionTheerrorprobabilityfollowsthenormaldistributionHomoscedasticity ConstantVariance IndependenceofErrorsLinearity 4 Example X price Y demandfortheproductWehavedata 1 Scatterplot2 Regressionequation OrdinaryLeastSquareEstimation 3 CorrelationcoefficientrTestingtheregressionmodel4 Forecasting5 Regressioncanbelinearitied SimpleLinearRegression 5 LinearRegressionModel Variablesconsistofalinearfunction Y X i i i 0 1 Slope Y Intercept Independent Explanatory Variable Dependent Response Variable RandomError 6 PopulationLinearRegressionModel i randomerror X YX i X 0 1 Y X i i i 0 1 ObservedValue ObservedValue Y 7 SampleLinearRegressionModel e i randomerror Y X Y b b X e i i i 0 1 Y b b X i i 0 1 UnsampledObservedValue SampledObservedValue 8 OrdinaryLeastSquares Theleastsquaresmethodprovidesanestimatedregressionequationthatminimizesthesumofsquareddeviationsbetweentheobservedvaluesofthedependentvariableyiandtheestimatedvaluesofthedependentvariable e 2 Y X e 1 e 3 e 4 Y b b X e i i i 0 1 Y b b X i i 0 1 OLSMin e e e e e i i 2 1 1 2 2 2 3 2 4 2 PredictedValue 9 Coefficient Equations Y b X b X Y n X Y X n X b Y b X i i i i i n i i n 0 1 1 1 2 2 1 0 1 Sampleregressionequation Slopefortheestimatedregressionequation Interceptfortheestimatedregressionequation b 10 EvaluatingtheModel TestCoefficientofDeterminationandStandardDeviationofEstimationResidualAnalysisTestCoefficientsofSignificance 11 MeasuresofVariationinRegression 1 TotalSumofSquares SST MeasurethevariationbetweentheobservedvalueYiandthemeanY 2 ExplainedVariation SSR VariationcausedbytherelationshipbetweenXandY 3 UnexplainedVariation SSE Variationcausedbyotherfactors 12 VariationMeasures Y X Y X i SST Yi Y 2 SSE Yi Yi 2 SSR Yi Y 2 Yi Y b b X i i 0 1 13 CoefficientofDetermination 0 r2 1 r b Y b X Y n Y Y n Y i i i i n i n i i n 2 0 1 2 1 1 2 1 2 Explainedvariation Totalvariation SSR SST Ameasureofthegoodnessoffitoftheestimatedregressionequation Itcanbeinterpretedastheproportionofthevariationinthedependentvariableythatisexplainedbytheestimatedregressionequation 14 CorrelationCoefficient Anumericalmeasureoflinearassociationbetweentwovariablesthattakesvaluesbetween 1and 1 Valuesnear 1indicateastrongpositivelinearrelationship valuesnear 1indicateastrongnegativelinearrelationship andvaluesnearzeroindicatelackofalinearrelationship 15 CoefficientsofDetermination r2 andCorrelation r 16 TestofSlopeCoefficientforSignificance 1 TestsaLinearRelationshipBetweenX Y2 HypothesesH0 1 0 NoLinearRelationship H1 1 0 LinearRelationship 3 TestStatistic 17 ExampleTestofSlopeCoefficient H0 1 0H1 1 0 05df 5 2 3Criticalvalue Statistic Determine Conclusion Rejectat 0 05 Thereisevidenceofarelationship 18 MultipleRegressionModel Thereexistslinearrelationshipamongandependentvariableandtwoormorethantwoindependentvariables Y X X X i i i P Pi i 0 1 1 2 2 slopeofpopulation interceptofpopulationY randomerror DependentVariable IndependentVariables 19 Example NewYorkTimes YouworkintheadvertisementdepartmentofNewYorkTimes NYT Youwillfindtowhatextentdoadssize squareinch andpublishingvolume thousand influencetheresponsetoads hundred Youhavecollectedthefollowingdata responsesizevolume1124881313572644106 20 Example NYT ComputerOutput ParameterEstimatesParameterStandardTforH0 VariableDFEstimateErrorParam 0Prob T INTERCEP10 06400 25990 2460 8214ADSIZE10 20490 05883 6560 0399CIRC10 28050 06864 0890 0264 21 InterpretationofCoefficients 1 Slope b1 Ifthepublishingvolumeremainsunchanged whenadssizeincreasesonesquareinch theresponseisexpectedtoincrease0 2049hundredtimes 2 Slope b2 Ifadssizeremainsunchanged whenpublishingvolumeincreasesonethousand theresponseisexpectedtoin crease0 2805hundredtimes 22 EvaluatingtheModel 1 Howdoesthemodeldescribetherelationshipamongvariables 2 Closenessof BestFit 3 Assumptionsmet4 Significanceofestimates5 Correlationamongvariables6 Outliers unusualobservations 23 TestingOverallSignificance TestwhetherthereislinearrelationshipbetweenYandalltheindependentvariables 2 UseFstatistic HypothesisH0 1 2 P 0ThereisnolinearrelationshipbetweenYandindependentvariables H1 Atleastthereisacoefficientisn tequalto0 AtleastthereisanindependentvariableinfluencesY 24 TestingOverallSignificanceComputerOutput AnalysisofVarianceSumofMeanSourceDFSquaresSquareFValueProb FModel29 24974 624955 4400 0043Error30 25030 0834CTotal59 5000 P n P 1 n 1 M