Copyright © 2012 Pearson Education, Inc. All rights reserved. Chapter 4 Multiple Regression Models.

Copyright © 2012 Pearson Education, Inc. All rights reserved.

Chapter 4

Multiple Regression Models


Section 4.1

General

Form of a Multiple Regression Model


Section 4.2

Model Assumptions


Section 4.3

A First-Order Model with Quantitative Predictors


Figure 4.1 Graphs of E(y) = 1+ 2x1 = x2 for x2 = 0,1,2


Section 4.4

Fitting the Model: The Method of Least Squares


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


Figure 4.3 SAS regression output for the auction price model, Example 4.1


Section 4.5

Estimation of 2, the Variance of


Section 4.6

Testing the Utility of a Model:

The Analysis of Variance

F-Test


Figure 4.4 Rejection region for the global F-test


Figure 4.5 MINITAB regression printout for grandfather clock model


Section 4.7

Inferences About the Individual Parameters


Figure 4.6 SAS regression output for the auction price model, Example 4.4


Multiple Coefficients of Determination:

R2 and R2

Section 4.8

a


Figure 4.7 A portion of the SPSS regression output for the auction price model


Section 4.9

Using the Model for Estimation and Prediction


Figure 4.8 MINITAB printout with 95% confidence intervals for grandfather clock model


Section 4.10

An Interaction Model with Quantitative Predictors


Figure 4.9 Graphs of 1 + 2x1 – x2 + x1x2 for x2 = 0,1,2


Figure 4.10 Examples of no-interaction and interaction models


Figure 4.11 MINITAB regression printout for grandfather clock model with interaction


Section 4.11

A Quadratic (Second-Order)

Model with a Quantitative Predictor


Figure 4.12 Graphs for two quadratic models


Figure 4.13 SPSS scatterplot for data of Example 4.7


Figure 4.14 SPSS output for quadratic model of Example 4.7


Figure 4.15 MINITAB graph of least squares fit for the quadratic model


Figure 4.16 Potential misuse of quadratic model


Section 4.12

More Complex Multiple Regression Models (Optional)


Figure 4.17 Graph of E(y) = 1 + 7x1 - 10x2 + 5x1x2 – + 32

1x22x


Figure 4.18 SAS multiple regression output for Example 4.8


Figure 4.19 MINITAB multiple regression output for Example 4.9


Figure 4.20 MINITAB multiple regression output for Example 4.10


Section 4.13

A Test for Comparing Nested Models


Figure 4.21 Rejection region for the F-test Ho: 4 = 5 = 0


Figure 4.22 SAS output for complete model, Example 4.11


Figure 4.23 SAS output for reduced model, Example 4.11


Section 4.14

A Complete Example


Figure 4.24 SAS output for complete second-order model for road cost


Figure 4.25 SAS output for reduced model for road cost


Figure 4.26 Plot of the least squares lines for the reduced model


Figure 4.27 SAS output showing prediction intervals for reduced model

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