Chapter7_correlation外文

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1、Chapter7Chapter7SimpleLinearCorrelationSimpleLinearCorrelationZhangJin-xin（张晋昕）2011.04.111Inthischapter,wearegoingtostudy:twovariables,linearrelationshipbetweentwovariablesòTwotypesofquestions:Whetherthevariablesarelinearlycorrelated?--LinearcorrelationHowtopredictonevariablebyanother

2、variable?--Linearregression2Example7.2Toexplorethecorrelationbetweentheheightsoffatherandson,20malestudentswererandomlyselectedfromanamelistofgraduatesinahighschool.Theheights(cm)offathersandsonsweremeasured.Table7.1Heights(cm)of20pairsoffatherandsonNo.12345678910Father’sheight,X15015

3、3155158161164165167168169Son’sheight,Y159157163166169170169167169170No.11121314151617181920Father’sheight,X170171172174175177178181183185Son’sheight,Y17317017017617817417317817618037.1Conceptofcorrelation45Function（函数关系）betweenYandXExponentialfunctionLogarithmfunctionSineFunctionThere

4、isadefinitevalueofYcorrespondingtoanygivenvalueofX677.2CorrelationCoefficient7.2CorrelationCoefficient7.2.1Populationcorrelationcoefficient7.2.1PopulationcorrelationcoefficientPearson’sproduct-momentlinearcorrelationcoefficient:Themeanof“productofthetwostandardizedvariables”----simple

5、correlationcoefficient−1≤≤1ρX−µxY−µyρ=E[()()]σσxyE[(X−µ)(Y−µ)]σxyxy==σσσσxyxyσ=E[(X−µ)(Y−µ)]--covariancebetweenXandYxyxy87.2.2Samplecorrelationcoefficient7.2.2SamplecorrelationcoefficientPearson’sproductmomentsamplecorrelationcoefficientr∑(X−X)(Y−Y)lXYr==22ll∑(X−X)∑(Y−Y)XXYYlXY=∑(X−X)

6、(Y−Y)2lXX=∑(X−X)2lYY=∑(Y−Y)9Ameasurementoflinearrelationship:−1≤r≤11)WhetherthereisacorrelationIfthecorrelationcoefficientis0ornotbigenough--nocorrelation2)WhethercorrelationcoefficientislargeenoughThedirectionofcorrelation?--positiveornegativeThestrengthofcorrelation?highorlow?--Isth

7、eabsolutevaluebigenough?Completecorrelation:+1or-1,10Example7.3Calculatethecorrelationcoefficientbetweentheheightsoffatherandson.=1859.2l=1059.4llyy=698.55xyxxlxy1059.4r===0.9296ll1859.2×698.55xxyy117.3InferenceonCorrelationCoefficient7.3InferenceonCorrelationCoefficient7.3.1Hypothesi

8、stest