经典和现代回归分析及其应用

《经典和现代回归分析及其应用》是2005年5月1日高等教育出版出版的图书，作者是麦尔斯。本书主要介绍了回归分析、多种回归模型以及最佳模型选择准则等内容来自。

• 书名 经典和现代回归分析及其应用
• 别名 classical and modern regression with applications
• 作者 (美)麦尔斯
• 出版社 高等教育出版社
• 出版时间 2005年5月1日

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作者简介

　　束陈氧七害吗意十然械作者:(美国)麦尔斯(My许费使采灯另富ers.R.H)

目录

　　CHAPTER 1

　　INTRODUCTION: REGRESSION ANALYSIS

　　Regression mo答存型九讲知旧副dels

　　Formal uses of regression analysis

　　The data base

　　References

　　CHAPTER 2

　　THE SIMPLE LINEAR REGRESSION MODEL

　　The model descript溶城氧脸米缺才英回ion

　　Assumption结本s and interpr来自etation o计二山语负量免掌保f model par360百科ameters

　　Least squares f防ormulation

　　Maximum likelihood estimation

　　Pa施官所孔许rtioning total variability

　　Tests of hypothesis on slope and intercept

　　Simple reg误元儿优或如刚汉士结总ression through the origin (Fixed intercept)

　　Quality of fitted model

　　Confidence intervals on m项音阿ean response and prediction intervals

　　些义Simultaneous inference i食权氧绍n simple linear regression

　　A complete ann罪调则道预圆弦otated computer printout

　　A look at residuals

　　Both x and y random

　　Exercises

　　References

　　CHAPTER 3

　　THE MULTIPLE LINE袁收讲富便祖AR REGRESSION MODEL

　　Model description and assumptions

　　The general linear mode] and the least squares procedure

　　Properties of least squares estimators under ideal conditions

　　Hypothesis testing in multiple linear regression

　　Confide记nce intervals and prediction intervals in multiple regressions

　学记　Data with repeated observ问台里志义团把女粮举ations

　　Simulta乐燃鲜叶越neous inference in multiple regression

　　Multicollinearity in mult卷令规材川溶副福括稳扩iple regression data

　　Quality fit, quality prediction, and the HAT matrix

　　Categorical or indicator variables (Regression models and ANOVA models)

　　Exerci种班经胞让露较艺跑ses

　　References

　　CHAPTER 4

　　CRITERIA FOR CHOICE OF BEST MODEL

　　Standard criteria for comparing models

　　Cross validation for model selection and determination of model performance

　　Conceptual predictive criteria (The Cp statistic)

　　Sequential variable selection procedures

　　Further comments and all possible regressions

　　Exercises

　　References

　　CHAPTER 5

　　ANALYSIS OF RESIDUALS 209

　　Information retrieved from residuals

　　Plotting of residuals

　　Studentized residuals

　　Relation to standardized PRESS residuals

　　Detection of outliers

　　Diagnostic plots

　　Normal residual plots

　　Further comments on analysis of residuals

　　Exercises

　　References

　　CHAPTER 6

　　INFLUENCE DIAGNOSTICS

　　Sources of influence

　　Diagnostics: Residuals and the HAT matrix

　　Diagnostics that determine extent of influence

　　Influence on performance

　　What do we do with high influence points?

　　Exercises

　　References

　　CHAPTER 7

　　NONSTANDARD CONDITIONS, VIOLATIONS OF ASSUMPTIONS,AND TRANSFORMATIONS

　　Heterogeneous variance: Weighted least squares

　　Problem with correlated errors (Autocorrelation)

　　Transformations to improve fit and prediction

　　Regression with a binary response

　　Further developments in models with a discrete response (Poisson regression)

　　Generalized linear models

　　Failure of normality assumption: Presence of outliers

　　Measurement errors in the regressor variables

　　Exercises

　　References

　　CHAPTER 8

　　DETECTING AND COMBATING MULTICOLLINEARITY

　　Multicollinearity diagnostics

　　Variance proportions

　　Further topics concerning multicollinearity

　　Alternatives to least squares in cases of multicollinearity

　　Exercises

　　References

　　CHAPTER 9

　　NONLINEAR REGRESSION

　　Nonlinear least squares

　　Properties of the least squares estimators

　　The Gauss-Newton procedure for finding estimates

　　Other modifications of the Gauss-Newton procedure

　　Some special classes of nonlinear models

　　Further considerations in nonlinear regression

　　Why not transform data to linearize?

　　Exercises

　　References

　　APPENDIX A

　　SOME SPECIAL CONCEPTS IN MATRIX ALGEBRA

　　Solutions to simultaneous linear equations

　　Quadratic form

　　Eigenvalues and eigenvectors

　　The inverses of a partitioned matrix

　　Sherman-Morrison-Woodbury theorem

　　References

　　APPENDIX B

　　SOME SPECIAL MANIPULATIONS

　　Unbiasedness of the residual mean square

　　Expected value of residual sum of squares and mean square

　　for an underspecified model

　　The maximum likelihood estimator

　　Development of the PRESS statistic

　　Computation of s _ i

　　Dominance of a residual by the corresponding model error .Computation of influence diagnostics

　　Maximum likelihood estimator in the nonlinear model

　　Taylor series

　　Development of the C~-statistic

　　References

　　APPENDIX C

　　STATISTICAL TABLES

　　INDEX