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Copyright 2012 Pearson Education, Inc. All rights reserved.

Chapter 4

MultipleRegressionModels


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Copyright 2012 Pearson Education, Inc. All rights reserved.4- 2


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Figure 4.1 Graphs ofE (y ) = 1+ 2 x 1 + x 2 for x 2 = 0,1,2


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Figure 4.2 MINITAB side-by-sidescatterplots for the data of Table 4.1



Figure 4.3 SAS regression output forthe auction price model, Example 4.1


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Estimation of s 2, the Variance of e



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Section 4.6

Testing theUtility of aModel:The Analysis

of VarianceF -Test



Figure 4.4 Rejection region for theglobal F -test



Figure 4.5 MINITAB regressionprintout for grandfather clock model


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Section 4.7

InferencesAbout theIndividualParameters


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18/57Copyright 2012 Pearson Education, Inc. All rights reserved.

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Figure 4.6 SAS regression output forthe auction price model, Example 4.4


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MultipleCoefficients ofDetermination:R 2 and R 2

Section 4.8

a


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Figure 4.7 A portion of the SPSSregression output for the auction price

model


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Adjusted R 2



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Section 4.10

An InteractionModel withQuantitativePredictors


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Models with Interaction: quantitative predictors



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Figure 4.9 Graphs ofE(Y)=1 + 2 x 1 x 2 + x 1 x 2 for x 2 = 0,1,2


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Figure 4.10 Examples of no-interaction and interaction models


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Figure 4.11 MINITAB regression printoutfor grandfather clock model with interaction


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Section 4.11

A Quadratic(Second-Order)Model with aQuantitative

Predictor


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Figure 4.13 SPSS scatterplot fordata of Example 4.7


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Figure 4.14 SPSS output forquadratic model of Example 4.7


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Figure 4.15 MINITAB graph of leastsquares fit for the quadratic model


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Figure 4.16 Potential misuse ofquadratic model


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Section 4.12

More ComplexMultipleRegressionModels

(Optional)


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Models with qualitative predictors

Qualitative predictors are also called dummy variable.A qualitative predictor with two categories(levels) iscalled binary variable.



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Figure 4.19 MINITAB multiple regression output for Example 4.9


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Fi 4 20 MINITAB l i l


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Figure 4.20 MINITAB multipleregression output for Example 4.10


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Fi 4 22 SAS t t f


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Figure 4.22 SAS output forcomplete model, Example 4.11

Fig 4 23 SAS t t f


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Figure 4.23 SAS output forreduced model, Example 4.11

Fig 4 21 R j ti gi f


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Figure 4.21 Rejection region forthe F -test Ho : b 4 = b 5 = 0


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Section 4.14

A CompleteExample

Fi 4 24 SAS t t f l t


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Figure 4.25 SAS output forreduced model for road cost

Figure 4 26 Plot of the least


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Figure 4.26 Plot of the leastsquares lines for the reduced model

Figure 4 27 SAS output showing


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Figure 4.27 SAS output showingprediction intervals for reduced model

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