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Unformatted text preview: 14 1Chapter FourteenMultiple Regression and Correlation AnalysisMultiple Regression and Correlation AnalysisGOALSWhen you have completed this chapter, you will be ableto:ONEDescribe the relationship between two or more independent variables and the dependent variable using a multiple regression equation.TWOCompute and interpret the multiple standard error of estimate and the coefficient of determination.THREEInterpret a correlation matrix.FOURSetup and interpret an ANOVA table.Goals14 2Multiple Regression AnalysisGreek letters are used for a(α29and b(β29when denoting population parameters.Y a b X b X b Xk k' ...= + + + +1 1 2 2Multiple Regression and Correlation AnalysisMultiple Regression and Correlation AnalysisThe general multiple regression with kindependent variables is given by:X1to Xkare the independent variables.ais the Yintercept.14 3Multiple Regression AnalysisBecause determining b1, b2, etc. is very tedious, a software package such as Excel or MINITAB is recommended. bjis the net change in Yfor each unit change in Xjholding all other values constant, where j=1 to k. It is called a partial regression coefficient, a net regression coefficient, or just a regression coefficient. The least squares criterion is used to develop this equation.14 4Multiple Standard Error of EstimateIt is difficult to determine what is a large value and what is a small value of the standard error.The Multiple Standard Error of EstimateMultiple Standard Error of Estimateis a measure of the effectiveness of the regression equation.It is measured in the same units as the dependent variable. )1()'(2...12.+Σ=knYYskyThe formula is:14 5Multiple Regression and Correlation AssumptionsSuccessive values of the dependent variable must be uncorrelated.Assumptions In Multiple Regression and CorrelationAssumptions In Multiple Regression and CorrelationThe independent variables and the dependent variable have a linear relationship.The dependent variable must be continuous and at least intervalscaled....
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 Fall '11
 Ms.Deppen
 Regression Analysis, independent variables

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