Copyright © 2012 Pearson Education, Inc. All rights reserved. Chapter 5 Principles of Model Building

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

Chapter 5

Principles of Model Building


Section 5.1

Introduction: Why Model Building Is Important


Section 5.2

The Two Types of Independent Variables: Quantitative and Qualitative


Section 5.3

Models with a Single Quantitative Independent Variable

Copyright © 2012 Pearson Education, Inc. All rights reserved.5- 5

Figure 5.1 Modeling exam score, y, as a function of study time, x





Figure 5.2 Graphs for two second-order polynomial models


Figure 5.3 Example of the use of a quadratic model


Figure 5.4 Graphs of two third-order polynomial models




Figure 5.5 MINITAB scatterplot for power load data


Figure 5.6 MINITAB output for third-order model of power load


Figure 5.7 MINITAB output for second-order model of power load


Section 5.4

First-Order Models with Two or More Quantitative Independent Variables


Figure 5.8 Response surface for first-order model with two quantitative independent variables



Figure 5.9 Contour lines of E(y) for

x2 = 1,2,3 (first-order model)


Section 5.5

Second-Order Models with Two or More Quantitative Independent Variables


Figure 5.10 Response surface for an interaction model (second-order)


Figure 5.11 Contour lines of E(y) for x2 = 1,2,3 (first-order model plus interaction)




Figure 5.12 Graphs of three second-order surfaces


Figure 5.13 Contours of E(y) for x2 = -1,0,1 (complete second-order model)




Figure 5.14 SAS output for complete second-order model of quality


Figure 5.15 Graph of second-order least squares model for Example 5.3


Section 5.6

Coding Quantitative Independent Variables (Optional)




Figure 5.16 MINITAB printout for the quadratic model, Example 5.4


Figure 5.17 MINITAB descriptive statistics for temperature, x



Figure 5.18 MINITAB printout for the quadratic model with coded temperature


Section 5.7

Models with One Qualitative Independent Variable





Figure 5.19 SPSS printout for dummy variable model, Example 5.5


Section 5.8

Models with Two Qualitative Independent Variables



Figure 5.20 Main effects model: Mean response as a function of F and B when F and B affect E(y) independently



Figure 5.21 Interaction model: Mean response as a function of F and B when F and B interact to affect E(y)




Figure 5.22 SAS printout for main effects model, Example 5.10


Figure 5.23 SAS printout for interaction model, Example 5.10


Figure 5.24 MINITAB graph of sample means for engine performance


Figure 5.25 SAS printout for nested model F-test of interaction


Section 5.9

Models with Three or More Qualitative Independent Variables



Section 5.10

Models with Both Quantitative and Qualitative Independent Variables


Figure 5.26 Model for E(y) as a function of engine speed


Figure 5.27 Model for E(y) as a function of fuel type and engine speed (no interaction)


Figure 5.28 Graph of E(y) as a function of fuel type and engine speed (interaction)


Figure 5.29 A graphical portrayal of three factors - two qualitative and one quantitative - on DDT level


Figure 5.30 DDT curves for stages 1 and 2


Section 5.11

External Model Validation (Optional)


Figure 5.31 MINITAB printout for the multiplicative model of executive salary

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Copyright © 2012 Pearson Education, Inc. All rights reserved. Chapter 5 Principles of Model Building