copyright © 2013 pearson education, inc. all rights reserved chapter 11 simple linear regression

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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