BusinessStatisticsADecisionMakingApproach6thedition1

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1、Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.Chap 13-1Business Statistics: A Decision-Making Approach6th EditionChapter 13Introduction to Linear Regression and Correlation AnalysisBusiness Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.Chap 13-2Chap

2、ter GoalsAfter completing this chapter, you should be able to: nCalculate and interpret the simple correlation between two variablesnDetermine whether the correlation is significantnCalculate and interpret the simple linear regression equation for a set of datanUnderstand the assumptions behind regr

3、ession analysisnDetermine whether a regression model is significantBusiness Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.Chap 13-3Chapter GoalsAfter completing this chapter, you should be able to: nCalculate and interpret confidence intervals for the regression coefficientsnRec

4、ognize regression analysis applications for purposes of prediction and descriptionnRecognize some potential problems if regression analysis is used incorrectlynRecognize nonlinear relationships between two variables(continued)Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, In

5、c.Chap 13-4Scatter Plots and CorrelationnA scatter plot (or scatter diagram) is used to show the relationship between two variablesnCorrelation analysis is used to measure strength of the association (linear relationship) between two variablesnOnly concerned with strength of the relationship nNo cau

6、sal effect is impliedBusiness Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.Chap 13-5Scatter Plot ExamplesyxyxyyxxLinear relationshipsCurvilinear relationshipsBusiness Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.Chap 13-6Scatter Plot ExamplesyxyxyyxxStrong

7、 relationshipsWeak relationships(continued)Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.Chap 13-7Scatter Plot ExamplesyxyxNo relationship(continued)Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.Chap 13-8Correlation CoefficientnThe populati

8、on correlation coefficient (rho) measures the strength of the association between the variablesnThe sample correlation coefficient r is an estimate of and is used to measure the strength of the linear relationship in the sample observations(continued)Business Statistics: A Decision-Making Approach,

9、6e 2005 Prentice-Hall, Inc.Chap 13-9Features of and rnUnit freenRange between -1 and 1nThe closer to -1, the stronger the negative linear relationshipnThe closer to 1, the stronger the positive linear relationshipnThe closer to 0, the weaker the linear relationshipBusiness Statistics: A Decision-Mak

10、ing Approach, 6e 2005 Prentice-Hall, Inc.Chap 13-10r = +.3r = +1Examples of Approximate r Valuesyxyxyxyxyxr = -1r = -.6r = 0Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.Chap 13-11Calculating the Correlation Coefficient)yy()xx()yy)(xx(r22where:r = Sample correlation coe

11、fficientn = Sample sizex = Value of the independent variabley = Value of the dependent variable )y()y(n)x()x(nyxxynr2222Sample correlation coefficient:or the algebraic equivalent:Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.Chap 13-12Calculation ExampleTree HeightTrunk

12、 Diameteryxxyy2x23582801225644994412401812771897294933619810893660137803600169217147441494511495202512151126122601144 =321 =73 =3142 =14111 =713Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.Chap 13-130.886(321)8(14111)(73)8(713)(73)(321)8(3142)y)()yn(x)()xn(yxxynr222222

13、 Trunk Diameter, xTreeHeight, yCalculation Example(continued)r = 0.886 relatively strong positive linear association between x and yBusiness Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.Chap 13-14Excel OutputExcel Correlation OutputTools / data analysis / correlationCorrelation

14、 between Tree Height and Trunk DiameterBusiness Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.Chap 13-15Significance Test for CorrelationnHypotheses H0: = 0 (no correlation) HA: 0 (correlation exists)nTest statisticn (with n 2 degrees of freedom)2nr1rt2Business Statistics: A Dec

15、ision-Making Approach, 6e 2005 Prentice-Hall, Inc.Chap 13-16Example: Produce StoresIs there evidence of a linear relationship between tree height and trunk diameter at the .05 level of significance?H0: = 0 (No correlation)H1: 0 (correlation exists) =.05 , df = 8 - 2 = 64.6828.8861.8862nr1rt22Busines

16、s Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.Chap 13-174.6828.8861.8862nr1rt22Example: Test SolutionConclusion:There is evidence of a linear relationship at the 5% level of significanceDecision:Reject H0Reject H0Reject H0/2=.025-t/2Do not reject H00t/2/2=.025-2.44692.44694.68d.f. = 8-2 = 6