Slide 1Multiple Regression ModelSlide 3Housing ExampleSlide 5Slide 6Slide 7Assumptions of the Multiple Regression ModelErrors in Multiple Linear RegressionSlide 10Hypothesis Test for the Significance of the ModelAssociated F CurveTest for Ho: i = 0Housing ExampleBB Investments ExampleBB Investments ExampleSlide 17Slide 18Coefficient of DeterminationPartial F TestMotormax ExampleSlide 22Quadratic CurvesSlide 24Error From ExtrapolationMulticollinearityMulticollinearity ExampleSlide 28Slide 29Slide 30Dummy VariablesDummy Variable ExampleStepwise ProceduresStepwise RegressionChecking Model AssumptionsDetecting Sample OutliersCook’s Distance MeasureResidual AnalysisSlide 39Slide 40Prediction Using Multiple RegressionSlide 42Slide 43Slide 44Interaction EffectsSlide 46Quadratic and Second-Order ModelsFinancial ExampleSlide 49Slide 50Slide 51©2006 Thomson/South-Western 1Chapter 14 –Chapter 14 –Multiple Linear Multiple Linear RegressionRegressionSlides prepared by Jeff HeylLincoln University©2006 Thomson/South-WesternConcise Managerial StatisticsConcise Managerial StatisticsKVANLIPAVURKEELINGKVANLIPAVURKEELING©2006 Thomson/South-Western 2Multiple Regression ModelMultiple Regression ModelYY = = 00 + + 11XX11 + + 22XX22 + + kkXXkk + + eeDeterministic componentDeterministic component00 + + 11XX11 + + 22XX22 + + kkXXkkLeast Squares EstimateLeast Squares EstimateSSE = ∑(SSE = ∑(YY - - YY))22^^©2006 Thomson/South-Western 3Multiple Regression ModelMultiple Regression ModelFigure 14.1Figure 14.1YYXX11XX22YY = = 00 + + 11XX11 + + 22XX22ee (positive) (positive)ee (negative) (negative)©2006 Thomson/South-Western 4Housing ExampleHousing ExampleY = Home square footage (100s)Y = Home square footage (100s)X1 = Annual Income ($1,000s)X1 = Annual Income ($1,000s)X2 = Family SizeX2 = Family SizeX3 = Combined years of X3 = Combined years of education beyond high education beyond high school for all household school for all household membersmembers©2006 Thomson/South-Western 5Multiple Regression ModelMultiple Regression ModelFigure 14.2Figure 14.2©2006 Thomson/South-Western 6Multiple Regression ModelMultiple Regression ModelFigure 14.3Figure 14.3©2006 Thomson/South-Western 7Multiple Regression ModelMultiple Regression ModelFigure 14.4Figure 14.4©2006 Thomson/South-Western 8Assumptions of the Assumptions of the Multiple Regression ModelMultiple Regression ModelThe errors follow a normal The errors follow a normal distribution, centered at zero, distribution, centered at zero, with common variancewith common varianceThe errors are independentThe errors are independent©2006 Thomson/South-Western 9Errors in Multiple Linear Errors in Multiple Linear RegressionRegressionFigure 14.5Figure 14.5YYXX11XX22YY = = 00 + + 11XX11 + + 22XX22XX11 = 30, = 30, XX2 2 = 8= 8XX11 = 50, = 50, XX22 = 2 = 2eeee©2006 Thomson/South-Western 10Multiple Regression ModelMultiple Regression ModelAn estimate ofAn estimate of ee22ss22 = = ee22 = = = =SSESSEnn - ( - (kk + 1) + 1)SSESSEnn - - kk - 1 - 1^^©2006 Thomson/South-Western 11Hypothesis Test for the Hypothesis Test for the Significance of the ModelSignificance of the ModelHHoo: : 11 = = 22 = … = = … = kkHHaa: at least one of the : at least one of the ’s ≠ 0’s ≠ 0Reject Reject HHoo if if FF > > FF,,kk,,nn--kk-1-1FF = =MSRMSRMSEMSE©2006 Thomson/South-Western 12Associated F CurveAssociated F Curvereject reject HH00FF,,vv , ,vv1122Area = Area = Figure 14.6Figure 14.6©2006 Thomson/South-Western 13Test for HTest for Hoo: : ii = 0= 0reject reject HHoo if | if |tt| > | > tt ./2,./2,nn--kk-1-1t t == bb11ssbb11HHoo: : 11 = 0 ( = 0 (XX11 does not contribute) does not contribute)HHaa: : 11 ≠ 0 ( ≠ 0 (XX11 does contribute) does contribute)HHoo: : 22 = 0 ( = 0 (XX22 does not contribute) does not contribute)HHaa: : 22 ≠ 0 ( ≠ 0 (XX22 does contribute) does contribute)HHoo: : 33 = 0 ( = 0 (XX33 does not contribute) does not contribute)HHaa: : 33 ≠ 0 ( ≠ 0 (XX33 does contribute) does contribute)bbii - - tt/2,/2,nn--kk-1-1ssbb to b to bii + + tt/2,/2,nn--kk-1-1ssbb iiii(1-(1- ) 100%) 100% Confidence Interval Confidence Interval©2006 Thomson/South-Western 14Housing Example Housing Example Figure 14.7Figure 14.7©2006 Thomson/South-Western 15BB Investments ExampleBB Investments ExampleBB Investments wants to develop a model to BB Investments wants to develop a model to predict the amount of money invested by predict the amount of money invested by various clients in their portfolio of high-risk various clients in their portfolio of high-risk securitiessecuritiesY = Investment Amount ($)Y = Investment Amount ($)X1 = Annual Income ($1,000s)X1 = Annual Income ($1,000s)X2 = Economic Index, X2 = Economic Index, showing expected showing expected increase in interest levels, manufacturing increase in interest levels, manufacturing costs, and price inflation (1 -100 scale)costs, and price inflation (1 -100 scale)©2006 Thomson/South-Western 16BB Investments Example BB Investments Example Figure 14.8Figure 14.8©2006 Thomson/South-Western 17BB Investments Example BB Investments Example Figure 14.9Figure 14.9©2006 Thomson/South-Western 18BB Investments Example BB Investments Example Figure 14.10Figure 14.10©2006 Thomson/South-Western 19Coefficient of DeterminationCoefficient of DeterminationSSTSST= total sum of squares= total sum of squares= SS= SSYY= ∑(= ∑(YY - - YY))22= ∑= ∑YY22 - -(∑(∑YY))22nnRR22 = 1 - = 1 -SSESSESSTSSTFF = =RR22 / / kk(1 - (1 - RR22) / () / (nn - - kk - 1) - 1)©2006 Thomson/South-Western 20Partial F TestPartial F TestRRcc22 = the value of = the value of RR22 for the complete model for the complete modelRRrr22 = the value of = the value of RR22 for the reduced model for the reduced modelTest statisticTest statisticFF = =((RRcc22 - - RRrr22) / ) / vv11(1 - (1 - RRcc22) / ) / vv22©2006 Thomson/South-Western 21Motormax ExampleMotormax ExampleMotormax produces electric motors in Motormax produces electric motors in home furnaces. They want to study home furnaces. They want to study the relationship between the dollars the relationship between the dollars spent per week in inspecting
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