Applied Linear Regression
Applied Linear Regression
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DOI：
10.1002/0471704091
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发表时间：
2005-01
期刊：
影响因子：
--
通讯作者：
S. Weisberg
中科院分区：
文献类型：
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作者：
S. Weisberg
前言1散点图和回归。1.1散点图。1.2均值函数。1.3方差函数。1.4总结图。1.5观察散点图的工具。1.5.1大小。1.5.2变换。1.5.3均值函数的平滑。1.6散点图矩阵。问题简单线性回归。2.1普通最小二乘估计。2.2最小二乘准则。2.3西格玛估计。2.4最小二乘估计的性质。2.5估计方差。2.6模型比较：方差分析。2.6.1回归的f检验。2.6.2解释p值。2.6.3检验的幂次。2.7决定系数、R2.2.8置信区间和检验。2.8.1截距。2.8.2斜率。2.8.3预测。2.8.4拟合值。2.9残差。问题多个Regression.3.1添加一个术语简单线性回归Model.3.1.1解释Variability.3.1.2 Added-Variable Plots.3.2按多元线性回归Model.3.3 Predictors.3.4普通至少Squares.3.4.1数据和矩阵Notation.3.4.2 Variance-Covariance矩阵Estimates.3.4.5 e.3.4.3普通最小二乘Estimators.3.4.4属性的简单回归分析的矩阵Terms.3.5 Variance.3.5.1 Determination.3.5.2系数假设3.关于其中一项。3.5.3与t统计量的关系。3.5.4 t检验与加变量图。3.5.5其他假设检验。3.5.6方差表的序列分析。3.6预测与拟合值。问题画Conclusions.4.1理解参数Estimates.4.1.1率Change.4.1.2 Estimates.4.1.3解释取决于其他术语的迹象意味着Function.4.1.4等级不足和Over-Parameterized意味着Functions.4.1.5 Tests.4.1.6下降Terms.4.1.7 Logarithms.4.2实验与Observation.4.3抽样从正常Population.4.4更多R2.4.4.1简单线性回归和R2.4.4.2多个线性Regression.4.4.3回归通过Data.4.5.1 Origin.4.5失踪4.5.2替代方案。4.6计算密集型方法。4.6.1无正态回归推断。4.6.2参数的非线性函数。4.6.3用误差测量的预测因子。问题55.1加权最小二乘。5.1.1加权最小二乘的应用。5.1.2附加注释。5.2缺乏拟合的检验，方差已知。5.3缺乏拟合的检验，方差未知。5.4一般F检验。5.4.1非零分布。5.4.2附加注释。5.5联合置信区域。问题多项式和因子。6.1多项式回归。6.1.1带有多个预测因子的多项式。6.1.2使用Delta法估计最小值或最大值。6.1.3分数多项式。6.2因子。6.2.1没有其他预测因子。6.2.2添加一个预测因子：比较回归线。6.2.3附加注释。6.3许多因子。6.4偏一维平均函数。6.5随机系数模型。问题7.变换。7.1变换和散点图。7.1.1功率变换。7.1.2只变换预测变量。7.1.3只变换响应。7.1.4 Box和Cox法。7.2变换和散点图矩阵。7.2.1 1D估计结果和线性相关预测量。7.2.2预测量变换的自动选择。7.3变换响应。7.4非正变量的变换。问题回归诊断:残差。8.1残差。8.1.1 e与e的差。8.1.2 Hat矩阵。8.1.3残差与带权重的Hat矩阵。8.1.4模型正确时的残差。8.1.5模型不正确时的残差。8.1.6油耗数据。8.2曲率检验。8.3非恒定方差。8.3.1方差稳定变换。8.3.2非恒定方差的诊断。8.3.3附加注释。8.4模型评估图。8.4.1均值函数检验。8.4.2检验方差Functions.Problems.9异常值与影响。9.1异常值。9.1.1异常值检验。9.1.2加权最小二乘法。9.1.3异常值检验的显著性水平。9.1.4附加评论。9.2案例的影响。9.2.1库克距离。9.2.2 Di的大小。9.2.3计算Di。9.2.4其他影响度量。9.3正态性假设。问题。10变量选择。10.1活动项。10.1.1共线性。10.1.2共线性和方差。10.2变量选择。10.2.1信息准则。10.2.2计算密集型准则。10.2.3使用主题知识。10.3计算方法。10.3.1子集选择夸大了重要性。10.4风车。10.4.1六个平均函数。10.4.2计算密集型方法。问题。11非线性回归。11.1非线性平均函数的估计。11.2大样本推理。11.3自举推理。11.4参考文献。问题。12Logistic回归。12.1二项回归。12.1.1二项回归的均值函数。12.2拟合Logistic回归。12.2.1单预测例。12.2.2多项。12.2.3偏差。12.2.4拟合优度检验。12.3二项随机变量。12.3.1最大似然估计。12.3.2 Logistic回归的对数似然。12.4广义线性模型。问题。附录a .1Web Site.A.2随机变量的均值和方差。a .2.1 E符号。a .2.2 Var符号。a .2.3 Cov符号。a .2.4条件矩。a .3简单回归的最小二乘法最小二乘估计的均值和方差使用平滑器估计E（Y |X）矩阵与向量简介。A.6.1加法与减法。A.6.2标量乘法。A.6.3矩阵乘法。A.6.4矩阵的转置。A.6.5矩阵的逆。A.6.6正交性。A.6.7矩阵的线性相关与秩。A.7随机Vectors.A.8a .8.1估计的性质。a .8.2残差平方和。a .8.3方差的估计QR分解最大似然估计变换的Box-Cox法。a .11.1单变量情况。a .11.2多变量情况。a .12线性回归中的案例删除。参考文献。作者索引。主题索引。
Preface.1 Scatterplots and Regression.1.1 Scatterplots.1.2 Mean Functions.1.3 Variance Functions.1.4 Summary Graph.1.5 Tools for Looking at Scatterplots.1.5.1 Size.1.5.2 Transformations.1.5.3 Smoothers for the Mean Function.1.6 Scatterplot Matrices.Problems.2 Simple Linear Regression.2.1 Ordinary Least Squares Estimation.2.2 Least Squares Criterion.2.3 Estimating sigma 2.2.4 Properties of Least Squares Estimates.2.5 Estimated Variances.2.6 Comparing Models: The Analysis of Variance.2.6.1 The F-Test for Regression.2.6.2 Interpreting p-values.2.6.3 Power of Tests.2.7 The Coefficient of Determination, R2.2.8 Confidence Intervals and Tests.2.8.1 The Intercept.2.8.2 Slope.2.8.3 Prediction.2.8.4 Fitted Values.2.9 The Residuals.Problems.3 Multiple Regression.3.1 Adding a Term to a Simple Linear Regression Model.3.1.1 Explaining Variability.3.1.2 Added-Variable Plots.3.2 The Multiple Linear Regression Model.3.3 Terms and Predictors.3.4 Ordinary Least Squares.3.4.1 Data and Matrix Notation.3.4.2 Variance-Covariance Matrix of e.3.4.3 Ordinary Least Squares Estimators.3.4.4 Properties of the Estimates.3.4.5 Simple Regression in Matrix Terms.3.5 The Analysis of Variance.3.5.1 The Coefficient of Determination.3.5.2 Hypotheses Concerning One of the Terms.3.5.3 Relationship to the t -Statistic.3.5.4 t-Tests and Added-Variable Plots.3.5.5 Other Tests of Hypotheses.3.5.6 Sequential Analysis of Variance Tables.3.6 Predictions and Fitted Values.Problems.4 Drawing Conclusions.4.1 Understanding Parameter Estimates.4.1.1 Rate of Change.4.1.2 Signs of Estimates.4.1.3 Interpretation Depends on Other Terms in the Mean Function.4.1.4 Rank Deficient and Over-Parameterized Mean Functions.4.1.5 Tests.4.1.6 Dropping Terms.4.1.7 Logarithms.4.2 Experimentation Versus Observation.4.3 Sampling from a Normal Population.4.4 More on R2.4.4.1 Simple Linear Regression and R2.4.4.2 Multiple Linear Regression.4.4.3 Regression through the Origin.4.5 Missing Data.4.5.1 Missing at Random.4.5.2 Alternatives.4.6 Computationally Intensive Methods.4.6.1 Regression Inference without Normality.4.6.2 Nonlinear Functions of Parameters.4.6.3 Predictors Measured with Error.Problems.5 Weights, Lack of Fit, and More.5.1 Weighted Least Squares.5.1.1 Applications of Weighted Least Squares.5.1.2 Additional Comments.5.2 Testing for Lack of Fit, Variance Known.5.3 Testing for Lack of Fit, Variance Unknown.5.4 General F Testing.5.4.1 Non-null Distributions.5.4.2 Additional Comments.5.5 Joint Confidence Regions.Problems.6 Polynomials and Factors.6.1 Polynomial Regression.6.1.1 Polynomials with Several Predictors.6.1.2 Using the Delta Method to Estimate a Minimum or a Maximum.6.1.3 Fractional Polynomials.6.2 Factors.6.2.1 No Other Predictors.6.2.2 Adding a Predictor: Comparing Regression Lines.6.2.3 Additional Comments.6.3 Many Factors.6.4 Partial One-Dimensional Mean Functions.6.5 Random Coefficient Models.Problems.7 Transformations.7.1 Transformations and Scatterplots.7.1.1 Power Transformations.7.1.2 Transforming Only the Predictor Variable.7.1.3 Transforming the Response Only.7.1.4 The Box and Cox Method.7.2 Transformations and Scatterplot Matrices.7.2.1 The 1D Estimation Result and Linearly Related Predictors.7.2.2 Automatic Choice of Transformation of Predictors.7.3 Transforming the Response.7.4 Transformations of Nonpositive Variables.Problems.8 Regression Diagnostics: Residuals.8.1 The Residuals.8.1.1 Difference Between e and e.8.1.2 The Hat Matrix.8.1.3 Residuals and the Hat Matrix with Weights.8.1.4 The Residuals When the Model Is Correct.8.1.5 The Residuals When the Model Is Not Correct.8.1.6 Fuel Consumption Data.8.2 Testing for Curvature.8.3 Nonconstant Variance.8.3.1 Variance Stabilizing Transformations.8.3.2 A Diagnostic for Nonconstant Variance.8.3.3 Additional Comments.8.4 Graphs for Model Assessment.8.4.1 Checking Mean Functions.8.4.2 Checking Variance Functions.Problems.9 Outliers and Influence.9.1 Outliers.9.1.1 An Outlier Test.9.1.2 Weighted Least Squares.9.1.3 Significance Levels for the Outlier Test.9.1.4 Additional Comments.9.2 Influence of Cases.9.2.1 Cook's Distance.9.2.2 Magnitude of Di .9.2.3 Computing Di .9.2.4 Other Measures of Influence.9.3 Normality Assumption.Problems.10 Variable Selection.10.1 The Active Terms.10.1.1 Collinearity.10.1.2 Collinearity and Variances.10.2 Variable Selection.10.2.1 Information Criteria.10.2.2 Computationally Intensive Criteria.10.2.3 Using Subject-Matter Knowledge.10.3 Computational Methods.10.3.1 Subset Selection Overstates Significance.10.4 Windmills.10.4.1 Six Mean Functions.10.4.2 A Computationally Intensive Approach.Problems.11 Nonlinear Regression.11.1 Estimation for Nonlinear Mean Functions.11.2 Inference Assuming Large Samples.11.3 Bootstrap Inference.11.4 References.Problems.12 Logistic Regression.12.1 Binomial Regression.12.1.1 Mean Functions for Binomial Regression.12.2 Fitting Logistic Regression.12.2.1 One-Predictor Example.12.2.2 Many Terms.12.2.3 Deviance.12.2.4 Goodness-of-Fit Tests.12.3 Binomial Random Variables.12.3.1 Maximum Likelihood Estimation.12.3.2 The Log-Likelihood for Logistic Regression.12.4 Generalized Linear Models.Problems.Appendix.A.1 Web Site.A.2 Means and Variances of Random Variables.A.2.1 E Notation.A.2.2 Var Notation.A.2.3 Cov Notation.A.2.4 Conditional Moments.A.3 Least Squares for Simple Regression.A.4 Means and Variances of Least Squares Estimates.A.5 Estimating E(Y |X) Using a Smoother.A.6 A Brief Introduction to Matrices and Vectors.A.6.1 Addition and Subtraction.A.6.2 Multiplication by a Scalar.A.6.3 Matrix Multiplication.A.6.4 Transpose of a Matrix.A.6.5 Inverse of a Matrix.A.6.6 Orthogonality.A.6.7 Linear Dependence and Rank of a Matrix.A.7 Random Vectors.A.8 Least Squares Using Matrices.A.8.1 Properties of Estimates.A.8.2 The Residual Sum of Squares.A.8.3 Estimate of Variance.A.9 The QR Factorization.A.10 Maximum Likelihood Estimates.A.11 The Box-Cox Method for Transformations.A.11.1 Univariate Case.A.11.2 Multivariate Case.A.12 Case Deletion in Linear Regression.References.Author Index.Subject Index.