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Chapter 4
MultipleRegressionModels
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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
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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
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Figure 4.4 Rejection region for theglobal F -test
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Figure 4.5 MINITAB regressionprintout for grandfather clock model
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Section 4.7
InferencesAbout theIndividualParameters
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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 4.24 SAS output for completesecond-order model for road cost
Figure 4 25 SAS output for
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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