Copyright © 2012 Pearson Education, Inc. All rights reserved. Chapter 3 Simple Linear Regression.
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Transcript of Copyright © 2012 Pearson Education, Inc. All rights reserved. Chapter 3 Simple Linear Regression.
Copyright © 2012 Pearson Education, Inc. All rights reserved.
Chapter 3
Simple Linear Regression
Copyright © 2012 Pearson Education, Inc. All rights reserved.
Section 3.1
Introduction
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Section 3.2
The
Straight-Line Probabilistic Model
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Figure 3.1 The straight-line model
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Section 3.3
Fitting the Model: The Method of Least Squares
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Figure 3.2 Scatterplot for data in Table 3.1
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Figure 3.3 Visual straight-line fit to data in Table 3.1
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Figure 3.4 Plot of the least squares line y = .1 .7x^
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Figure 3.5a SAS printout for advertising-sales regression
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Figure 3.5b SPSS printout for advertising-sales regression
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Figure 3.5c MINITAB printout for advertising-sales regression
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Section 3.4
Model Assumptions
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Figure 3.6 The probability distribution of
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Section 3.5
An Estimator of 2
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Figure 3.7 SAS printout for advertising-sales regression
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Section 3.6
Assessing the Utility of the Model: Making Inferences About the Slope 1
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Figure 3.8 Graphing the model with 1 = 0: y = 0 +
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Figure 3.9 Sampling distribution of 1^
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Figure 3.10 Rejection region and calculated t-value for testing whether the slope 1 = 0
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Figure 3.11 SAS printout for advertising-sales regression
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Copyright © 2012 Pearson Education, Inc. All rights reserved.
Section 3.7
The Coefficient of Correlation
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Figure 3.12a&b Values of r and their implications
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Figure 3.12c&d Values of r and their implications
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Figure 3.12e&f Values of r and their implications
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Figure 3.13 MINITAB correlation printout for Example 3.1
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Figure 3.14 MINITAB scatterplot for Example 3.1
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Figure 3.15 SPSS correlation analysis of tire data
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Figure 3.16 SPSS scatterplot of tire data
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Section 3.8
The Coefficient of Determination
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Figure 3.17 A comparison of the sum of squares of deviations for two models
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Figure 3.18 Portion of SPSS printout for advertising-sales regression
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Figure 3.19 MINITAB graph of simple linear model relating price (y) to floor height (x)
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Section 3.9
Using the Model for Estimation and Prediction
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Figure 3.20 Estimated mean value and predicted individual value of sales revenue y for x = 4
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Figure 3.21 SAS printout showing 95% confidence intervals for E(y)
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Figure 3.22 SAS printout showing 95% prediction intervals for y
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Figure 3.23 Error of estimating the mean value of y for a given value of x
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Figure 3.24 Error of predicting a future value of y for a given value of x
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Figure 3.25 Comparison of widths of 95% confidence and prediction intervals
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Section 3.10
A Complete Example
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Figure 3.26 SAS printout for fire damage linear regression
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Figure 3.27 Least squares model for the fire damage data
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Section 3.11
Regression Through the Origin (Optional)
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Figure 3.28 SPSS regression through origin printout for Example 3.6
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Figure 3.29 MINITAB scatterplot for data in Example 3.6
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Figure 3.30 SPSS spreadsheet with 95% prediction intervals
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Figure 3.31 Using a straight line to approximate a curvilinear relationship when the true relationship passes through the origin