Applied Regression Modeling

Оглавление

Iain Pardoe. Applied Regression Modeling

Table of Contents

List of Tables

List of Illustrations

Guide

Pages

Applied Regression Modeling

Copyright

Preface

Acknowledgments

INTRODUCTION. I.1 STATISTICS IN PRACTICE

I.2 Learning Statistics

About the Companion Website

Chapter 1 Foundations

1.1 Identifying and Summarizing Data

1.2 Population Distributions

1.3 Selecting Individuals at Random—Probability

1.4 Random Sampling

1.4.1 Central limit theorem—normal version

1.4.2 Central limit theorem—t‐version

1.5 Interval Estimation

1.6 Hypothesis Testing

1.6.1 The rejection region method

1.6.2 The p‐value method

1.6.3 Hypothesis test errors

1.7 Random Errors and Prediction

1.8 Chapter Summary

Problems

Chapter 2 Simple Linear Regression

2.1 PROBABILITY MODEL FOR and

2.2 Least Squares Criterion

2.3 Model Evaluation

2.3.1 Regression standard error

2.3.2 Coefficient of determination—

Correlation

2.3.3 Slope parameter

Slope hypothesis test

Slope confidence interval

2.4 Model Assumptions

2.4.1 Checking the model assumptions

2.4.2 Testing the model assumptions

2.5 Model Interpretation

2.6 Estimation and Prediction

2.6.1 Confidence interval for the population mean, E

2.6.2 Prediction interval for an individual ‐value

2.7 Chapter Summary

2.7.1 Review example

Problems

Chapter 3 Multiple Linear Regression

3.1 Probability Model for (X1, X2, …) and Y

3.2 Least Squares Criterion

Optional—formula for regression parameter estimates

3.3 Model Evaluation

3.3.1 Regression standard error

3.3.2 Coefficient of determination—

Adjusted

Multiple correlation

3.3.3 Regression parameters—global usefulness test

3.3.4 Regression parameters—nested model test

3.3.5 Regression parameters—individual tests

Regression parameter hypothesis tests

Regression parameter confidence intervals

Correlation revisited

Predictor selection

Optional—formula for regression parameter standard errors

3.4 Model Assumptions

3.4.1 Checking the model assumptions

3.4.2 Testing the model assumptions

3.5 Model Interpretation

3.6 Estimation and Prediction

3.6.1 Confidence interval for the population mean, E

3.6.2 Prediction interval for an individual ‐value

Optional—formulas for standard errors of estimation and prediction

3.7 Chapter Summary

Problems

Chapter 4 Regression Model Building I

4.1 Transformations

4.1.1 Natural logarithm transformation for predictors

4.1.2 Polynomial transformation for predictors

Optional—mathematical justification for preserving hierarchy when using polynomial transformations

4.1.3 Reciprocal transformation for predictors

4.1.4 Natural logarithm transformation for the response

4.1.5 Transformations for the response and predictors

Optional—regression parameter interpretations for transformed predictors

4.2 Interactions

4.3 Qualitative Predictors

4.3.1 Qualitative predictors with two levels

4.3.2 Qualitative predictors with three or more levels

Optional—testing equality of regression parameters with the nested model test

4.4 Chapter Summary

Problems

Chapter 5 Regression Model Building II

5.1 Influential Points

5.1.1 Outliers

Optional—formulas for standardized and studentized residuals

5.1.2 Leverage

Optional—formula for leverages

5.1.3 Cook's distance

Optional—formula for Cook's distances

5.2 Regression Pitfalls

5.2.1 Nonconstant variance

5.2.2 Autocorrelation

5.2.3 Multicollinearity

Optional—formula for variance inflation factors

5.2.4 Excluding important predictor variables

5.2.5 Overfitting

5.2.6 Extrapolation

5.2.7 Missing data

5.2.8 Power and sample size

5.3 Model Building Guidelines

5.4 Model Selection

5.5 Model Interpretation Using Graphics

5.6 Chapter Summary

Problems

Bibliography

Glossary

Index

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Отрывок из книги

Third Edition

Iain Pardoe Thompson Rivers University The Pennsylvania State University

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Under very general conditions, t has an approximate t‐distribution with degrees of freedom. The two differences from the normal version of the central limit theorem that we used before are that the repeated sample standard deviations, , replace an assumed population standard deviation, , and that the resulting sampling distribution is a t‐distribution (not a normal distribution).

To illustrate, let us repeat the calculations from Section 1.4.1 based on an assumed population mean, , but rather than using an assumed population standard deviation, , we will instead use our observed sample standard deviation, 53.8656 for . To find the 90th percentile of the sampling distribution of the mean sale price, :

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