Multiple_linear_regression

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1、MultipleLinearRegressionTheconceptsandprinciplesdevelopedindealingwithsimplelinearregression(i.e.,oneexplanatoryvariable)maybeextendedtodealwithseveralexplanatoryvariablesThemultipleregressionanalysisdescribestheeffectofmorethanoneexplanatoryvariableactingjointlyonthedependentvar

2、iableMultipleLinearRegressionExamplesWhatpredicts(orinfluences)consumers’brandchoice?Brandreputation,brandattitude,price,advertisingspending,etc.Whatpredicts(orinfluences)voter’scandidatechoice?Voter’spartymembership,candidate’scredibility,candidate’sissuepositions,mediacoverag

3、e,etc.Inreality,it’shardtofindacasewhereonlyonepredictorfullyexplainsadependentvariableMultipleLinearRegressionEquationY=β0+β1X1+β2X2……βnXnWhentwoexplanatory(independent)variablesareexamined,theregressionequationinsuchacasebecomes:Y=β+βX+βX01122whereYistheestimatedscoreforthede

4、pendentvariableXisthescoreforthefirstindependentvariableandX12isthescoreforthesecondindependentvariablebistheslopeoftheregressionlineforthefirst1independentvariableandb2istheslopeoftheregressionlineforthesecondindependentvariableMultipleLinearRegressionTheBcoefficientforeachexpl

5、anatoryvariableindicatestheeffectofthevariableonthedependentvariablewhilecontrollingfortheotherexplanatoryvariablesintheregressionmodelMulticollinearity:Whentwoormoreexplanatoryvariablesarehighlycorrelated,theyconveyessentiallythesameinformationanddonotsignificantlycontributetothe

6、explanatorypowerofthemodel2RindicatesthetotalvarianceofthedependentvariablethatcanbeaccountedforbyallexplanatoryvariablesMultipleLinearRegressionTypically,explanatoryvariablesinregressionanalysisarecontinuous.However,explanatoryvariablesthatarecategoricalcanbeincludedinmultiplere

7、gressionanalysisforsimultaneousexaminationofmultipleexplanatoryvariablestogether.Categoricalexplanatoryvariablesarehandledspeciallyandcalled“dummy”variables.Theyaretransformedtohavetwovaluesforthecategorysuchthatvalue‘1’isassignedtotheonegroupand‘0’totheother.Requestthemultiplelin

8、earregressionToconductasim