Copyright © 2012 Pearson Education, Inc. All rights reserved Chapter 12 Multiple Regression and...

Copyright © 2012 Pearson Education, Inc. All rights reserved

Chapter 12

Multiple Regression and Model Building

12 - 2 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure SIA12.1 Layout of condominium complex


Table SIA12.1


12.1

Multiple-Regression Models


Procedure


Part l

First-Order Models with Quantitative Independent Variables


12.2

Estimating and Making Inferences about the Parameters


Procedure


Table 12.1


Figure 12.1 MINITAB side-by-side scatterplots for the data of Table 12.1


Figure 12.2 MINITAB analysis of the auction price model


Procedure


Figure 12.3 MINITAB graph of for1 2( ) 1 2E y x x 2 0,1,2,x


Figure 12.4 MINITAB 3-dimensional graph of 1 2( ) 1 2E y x x


Procedure


Figure 12.5 Rejection Region for

0 2 2: 0 . : 0H vs H


12.3

Evaluating Overall Model Utility


Procedure


Figure 12.6 SAS analysis of the auction price model


Procedure


12.4

Using the Model for Estimation and Prediction


Figure 12.7 MINITAB printout with 95% confidence intervals for grandfather clock model


Figure SIA12.2 MINITAB scatterplots for CONDO data


Figure SIA12.3 MINITAB regression output for first-order model of condominium unit sale price


Figure SIA12.4 MINITAB printout with 95% confidence and prediction intervals


Part ll

Model Building in Multiple Regression


12.5

Interaction Models


Figure 12.8 MINITAB graphs of for1 2 1 21 2 3x x x x 2 0,1, 2x


Procedure


Figure 12.9 MINITAB 3-dimensional graphs of 1 2 1 21 2 3x x x x


Figure 12.10 Examples of no-interaction and interaction models


Figure 12.11 MINITAB printout of interaction model of auction price


Quadratic and Other Higher Order Models

12.6


Figure 12.12 Graphs of two quadratic models


Procedure


Table 12.2


Figure 12.13 MINITAB scatterplot for electrical usage data


Figure 12.14 SAS regression output for electrical usage model


Figure 12.15 MINITAB plot of least squares model for electrical usage


Figure 12.16 Potential misuse of quadratic model


Procedure


Figure 12.17 Graphs for three second-order surfaces


Qualitative (Dummy) Variable Models

12.7


Figure 12.18 Bar chart comparing E(y) for males and females


Procedure


Table 12.3


Figure 12.19 MINITAB output for model with dummy variables


Models with Both Quantitative and Qualitative Variables (Optional)

12.8


Figure 12.20 Graphs of the relationship between mean sales E(y) and advertising expenditure x


Figure 12.21 The relationship between E(y) and x1 is the same for all media


Figure 12.22 Parallel response lines for the three media


Figure 12.23 Different response lines for the three media


Table 12.4


Figure 12.24 MINITAB printout of the complete model for the casting media


Figure 12.25 MINITAB plot of prediction equations for two plants


Figure 12.26 The relationship between E(y) and x1 is the same for all media


Figure 12.27 The response curves have the same shapes, but different y-intercepts


Figure 12.28 The response curves for the three media differ


Comparing Nested Models (Optional)

12.9


Definition


Procedure


Table 12.5


Figure 12.29 SAS printout of complete second-order model for height


Figure 12.30 Plot of second-order least squares model for Example 12.12


Figure 12.31 SAS printout of first-order model for height


Definition


Procedure


Figure SIA12.5 SAS printout of second-order model for condo sale price-quantitative variables only


Figure SIA12.6 SAS regression printout for the complete second-order model of condo sale price-qualitative variables added


Stepwise Regression (Optional)

12.10


Table 12.6


Figure 12.32 MINITAB stepwise regression printout for executive salary data


Multiple Regression Diagnostics

Part lll


Residual Analysis: Checking the Regression Assumptions

12.11


Figure 12.33 Actual random error and regression residual ̂


Definition


Procedure


Table 12.7


Figure 12.34a MINTAB printout for straight-line model of electrical usage


Figure 12.34b MINITAB printout for quadratic model of electrical usage


Figure 12.35a MINITAB residual plot for straight-line model of electrical usage


Figure 12.35b MINITAB residual plot for quadratic model of electrical usage


Figure 12.36 Residual plots showing changes in the variance of


Table 12.8


Table 12.8 (cont’d)


Figure 12.37 SPSS regression printout for first-order model of salary


Figure 12.38 SPSS residual plots for first-order model of salary


Figure 12.39 SPSS regression printout for model of log salary


Figure 12.40 SPSS residual plots for model of ln(salary)


Definition


Table 12.9


Figure 12.41 MINITAB regression printout for altered grandfather clock data


Figure 12.41 MINITAB regression printout for altered grandfather clock data (cont’d)


Figure 12.42 MINITAB residual plot of altered grandfather clock data


Figure 12.43 MINITAB regression printout when outlier is deleted


Figure 12.44 MINITAB residual plot when outlier is deleted


Figure 12.45a MINITAB graphs of regression residuals for grandfather clock model (outlier included)


Figure 12.45b MINITAB graphs of regression residuals for grandfather clock model (outlier included) (cont’d)


Figure 12.46a MINITAB graphs of regression residuals for grandfather clock model (outlier deleted)


Figure 12.46b MINITAB graphs of regression residuals for grandfather clock model (outlier deleted) (cont’d)


Figure 12.47 Hypothetical residual plot for time-series data


Procedure


Figure SIA12.7 MINITAB histogram of residuals from second-order model of condo sale price


Figure SIA12.8 MINITAB plot of residuals versus predicted values from second-order model of condo sale price


Figure SIA12.9 MINITAB list of outliers for the second-order model of condo sale price


Figure SIA12.10 MINITAB printout of second-order model of condo sale price with outliers deleted


Some Pitfalls: Estimability, Multicollinearity, and Extrapolation

12.12


Figure 12.48 Yield and fertilizer expenditure data three years


Figure 12.49 Only two x values observed: quadratic model is not estimable


Definition


Procedure


Table 12.10


Figure 12.50 SAS printout for model of CO content, Example 12.18


Procedure


Figure 12.51 Using a regression model outside the experimental region

Copyright © 2012 Pearson Education, Inc. All rights reserved Chapter 12 Multiple Regression and...

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