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Chapter 4
Multiple Regression Models
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Section 4.1
General
Form of a Multiple Regression Model
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Section 4.2
Model Assumptions
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Section 4.3
A First-Order Model with Quantitative Predictors
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Figure 4.1 Graphs of E(y) = 1+ 2x1 = x2 for x2 = 0,1,2
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Section 4.4
Fitting the Model: The Method of Least Squares
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Figure 4.2 MINITAB side-by-side scatterplots for the data of Table 4.1
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Figure 4.3 SAS regression output for the auction price model, Example 4.1
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Section 4.5
Estimation of 2, the Variance of
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Section 4.6
Testing the Utility of a Model:
The Analysis of Variance
F-Test
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Figure 4.4 Rejection region for the global F-test
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Figure 4.5 MINITAB regression printout for grandfather clock model
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Section 4.7
Inferences About the Individual Parameters
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Figure 4.6 SAS regression output for the auction price model, Example 4.4
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Multiple Coefficients of Determination:
R2 and R2
Section 4.8
a
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Figure 4.7 A portion of the SPSS regression output for the auction price model
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Section 4.9
Using the Model for Estimation and Prediction
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Figure 4.8 MINITAB printout with 95% confidence intervals for grandfather clock model
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Section 4.10
An Interaction Model with Quantitative Predictors
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Figure 4.9 Graphs of 1 + 2x1 – x2 + x1x2 for x2 = 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 printout for grandfather clock model with interaction
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Section 4.11
A Quadratic (Second-Order)
Model with a Quantitative Predictor
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Figure 4.12 Graphs for two quadratic models
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Figure 4.13 SPSS scatterplot for data of Example 4.7
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Figure 4.14 SPSS output for quadratic model of Example 4.7
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Figure 4.15 MINITAB graph of least squares fit for the quadratic model
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Figure 4.16 Potential misuse of quadratic model
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Section 4.12
More Complex Multiple Regression Models (Optional)
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Figure 4.17 Graph of E(y) = 1 + 7x1 - 10x2 + 5x1x2 – + 32
1x22x
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Figure 4.18 SAS multiple regression output for Example 4.8
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Figure 4.19 MINITAB multiple regression output for Example 4.9
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Figure 4.20 MINITAB multiple regression output for Example 4.10
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Section 4.13
A Test for Comparing Nested Models
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Figure 4.21 Rejection region for the F-test Ho: 4 = 5 = 0
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Figure 4.22 SAS output for complete model, Example 4.11
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Figure 4.23 SAS output for reduced model, Example 4.11
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Section 4.14
A Complete Example
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Figure 4.24 SAS output for complete second-order model for road cost
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Figure 4.25 SAS output for reduced model for road cost
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Figure 4.26 Plot of the least squares lines for the reduced model
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Figure 4.27 SAS output showing prediction intervals for reduced model