copyright © 2013 pearson education, inc. all rights reserved chapter 11 simple linear regression
TRANSCRIPT
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Copyright © 2013 Pearson Education, Inc. All rights reserved
Chapter 11
Simple Linear Regression
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11.1
Probabilistic Models
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Figure 11.1 Possible reaction times y for five different drug percentages x
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Procedure
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Procedure
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Figure 11.2 The straight-line model
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Procedure
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11.2
Fitting the Model: The Least Squares Approach
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Table 11.1
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Figure 11.3 Scatterplot for data in Table 11.1
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Figure 11.4 Visual straight line fitted to the data in Figure 11.3
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Table 11.2
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Definition
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Formula
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Table 11.3
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Figure 11.5 The line fitted to the data
ˆ .1 .7y x
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Table 11.4
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Figure 11.6a SAS printout for the time-drug regression
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Figure 11.6b SPSS printout for the time-drug regression
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Figure 11.6c MINITAB printout for the time-drug regression
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Procedure
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Table SIA11.1
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Figure SIA11.1 MINITAB scatterplot of dowsing data
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Figure SIA11.2 MINITAB simple linear regression for dowsing data
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11.3
Model Assumptions
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Figure 11.7 The probability distribution of
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Procedure
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Figure 11.8 SAS printout for the time-drug regression
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Procedure
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11.4
Assessing the Utility of the Model: Making Inferences about the Slope 1
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Figure 11.9 Graph of the straight-line model when the slope is zero, i.e., 0y
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Procedure
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Figure 11.10 Sampling distribution of 1̂
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Procedure
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Definition
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Figure 11.11 Rejection region and calculated t value for testing versus
1: 0H 0 1: 0H
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Figure 11.12 MINITAB printout for the time-drug regression
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Procedure
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Procedure
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Definition
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Figure 11.13 SPSS printout with 95% confidence intervals for the time-drug regression betas
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Figure SIA11.3 MINITAB simple linear regression for dowsing data
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11.5
The Coefficients of Correlation and Determination
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Procedure
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Figure 11.14 Values of r and their implications
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Table 11.5
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Figure 11.15 MINITAB correlation printout and scatterplot for Example 11.4
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Procedure
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Definition
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Figure 11.16 A comparison of the sum of squares of deviations for two models
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Procedure
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Table 11.6
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Figure 11.17 Portion of SPSS printout for time-drug regression
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Procedure
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Figure SIA11.4 MINITAB printouts with coefficients of correlation and determination for the dowsing data
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Using the Model for Estimation and Prediction
11.6
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Figure 11.18 Estimated mean value and predicted individual value of reaction time y for x = 4
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Procedure
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Procedure
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Procedure
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Figure 11.19 MINITAB printout giving 95% confidence interval for E(y) and 95% prediction interval for y
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Figure 11.20 Error in estimating the mean value of y for a given value of x
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Figure 11.21 Error in predicting a future value of y for a given value of x
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Figure 11.22 Confidence intervals for mean values and prediction intervals for new values
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Figure SIA11.5 MINITAB prediction interval for dowsing data
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A Complete Example
11.7
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Table 11.7
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Figure 11.23 SAS printout for fire damage regression
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Figure 11.24 MINITAB scatterplot with least squares line for fire damage regression analysis