copyright © 2012 pearson education, inc. all rights reserved chapter 12 multiple regression and...

Chapter 12

Multiple Regression and Model Building

Figure SIA12.1 Layout of condominium complex

Table SIA12.1

Multiple-Regression Models

Procedure

Part l

First-Order Models with Quantitative Independent Variables

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

Evaluating Overall Model Utility

Procedure

Figure 12.6 SAS analysis of the auction price model

Procedure

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

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

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

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)

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)

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)

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

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

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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