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

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

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

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

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

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