Regression Analysis

Theory, Methods, and Applications

Inbunden, Engelska, 1990

AvAshish Sen,Muni Srivastava

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This book gives an up-to-date, rigorous, and lucid treatment of the theory, methods, and applications of regression analysis. It is ideally suited for those interested in the theory of regression analysis as well as to those whose interests lie primarily with applications. It is further enhanced through real-life examples drawn from many disciplines showing the difficulties typically encountered in the practice of the craft of regression analysis. Consequently, this book provides a sound foundation in the theory of this important subject. "I found this to be the most complete and up-to-date regression text I have come across...this text has much to offer." Journal of the American Statistical Association "The material is presented in a lucid and easy-to-understand style...can be ranked as one of the best textbooks on regression in the market." Mathematical Reviews "...a successful mix of theory and practice...It will serve nicely to teach both the logic behind regression and the data-analytic use of regression." SIAM Review

Produktinformation

Utgivningsdatum1990-07-13
Mått155 x 235 x 26 mm
Vikt717 g
FormatInbunden
SpråkEngelska
SerieSpringer Texts in Statistics
Antal sidor348
Upplaga1990
FörlagSpringer-Verlag New York Inc.
ISBN9780387972114

Tillhör följande kategorier

1 Introduction.- 1.1 Relationships.- 1.2 Determining Relationships: A Specific Problem.- 1.3 The Model.- 1.4 Least Squares.- 1.5 Another Example and a Special Case.- 1.6 When Is Least Squares a Good Method?.- 1.7 A pleasure of Fit for Simple Regression.- 1.8 Mean and Variance of b0 and b1.- 1.9 Confidence Intervals and Tests.- 1.10 Predictions.- 2 Multiple Regression.- 2.1 Introduction.- 2.2 Regression Model in Matrix Notation.- 2.3 Least Squares Estimates.- 2.4 Examples 31 2..- 2.6 Mean and Variance of Estimates Under G-M Conditions.- 2.7 Estimation of ?.- 2.8 Measures of Fit 39?2.- 2.9 The Gauss-Markov Theorem.- 2.10 The Centered Model.- 2.11 Centering and Scaling.- 2.12 *Constrained Least Squares.- 3 Tests and Confidence Regions.- 3.1 Introduction.- 12 Linear Hypothesis.- 3.3 *Likelihood Ratio Test.- 3.4 *Distribution of Test Statistic.- 3.5 Two Special Cases.- 3.6 Examples.- 3.7 Comparison of Repression Equations.- 3.8 Confidence Intervals and Regions.- 4 Indicator Variables.- 4.1 Introduction.- 4.2 A Simple Application.- 4.3 Polychotomous Variables.- 4.4 Continuous and Indicator Variables.- 4.5 Broken Line Regression.- 4.6 Indicators as Dependent Variables.- 5 The Normality Assumption.- 5.1 Introduction.- 5.2 Checking for Normality.- 5.3 Invoking Large Sample Theory.- 5.4 *Bootstrapping.- 5.5 *Asymptotic Theory.- 6 Unequal Variances.- 6.1 Introduction.- 6.2 Detecting Heteroscedasticity.- 6.3 Variance Stabilizing Transformations.- 6.4 Weighing.- 7 *Correlated Errors.- 7.1 Introduction.- 7.2 Generalized Least Squares: Case When ? Is Known.- 7.3 Estimated Generalized Least Squares.- 7.4 Nested Errors.- 7.5 The Growth Curve Model.- 7.6 Serial Correlation.- 7.7 Spatial Correlation.- 8 Outliers and Influential Observations.- 8.1 Introduction.- 8.2 The Leverage.- 8.3The Residuals.- 8.4 Detecting Outliers and Points That Do Not Belong to the Model 157.- 8.5 Influential Observations.- 8.6 Examples.- 9 Transformations.- 9.1 Introduction.- 9.2 Some Common Transformations.- 9.3 Deciding on the Need for Transformations.- 9.4 Choosing Transformations.- 10 Multicollinearity.- 10.1 Introduction.- 10.2 Multicollinearity and Its Effects.- 10.3 Detecting Multicollinearity.- 10.4 Examples.- 11 Variable Selection.- 11.1 Introduction.- 11.2 Some Effects of Dropping Variables.- 11.3 Variable Selection Procedures.- 11.4 Examples.- 12 *Biased Estimation.- 12.1 Introduction 2..- 12.2 Principal Component. Regression.- 12.3 Ridge Regression.- 12.4 Shrinkage Estimator.- A Matrices.- A.1 Addition and Multiplication.- A.2 The Transpose of a Matrix.- A.3 Null and Identity Matrices.- A.4 Vectors.- A.5 Rank of a Matrix.- A.6 Trace of a Matrix.- A.7 Partitioned Matrices.- A.8 Determinants.- A.9 Inverses.- A.10 Characteristic Roots and Vectors.- A.11 Idempotent Matrices.- A.12 The Generalized Inverse.- A.13 Quadratic Forms.- A.14 Vector Spaces.- Problems.- B Random Variables and Random Vectors.- B.1 Random Variables.- B.1.1 Independent. Random Variables.- B.1.2 Correlated Random Variables.- B.1.3 Sample Statistics.- B.1.4 Linear Combinations of Random Variables.- B.2 Random Vectors.- B.3 The Multivariate Normal Distribution.- B.4 The Chi-Square Distributions.- B.5 The F and t Distributions.- B.6 Jacobian of Transformations.- B.7 Multiple Correlation.- Problems.- C Nonlinear Least Squares.- C.1 Gauss-Newton Type Algorithms.- C.1.1 The Gauss-Newton Procedure.- C.1.2 Step Halving.- C.1.3 Starting Values and Derivatives.- C.1.4 Marquardt Procedure.- C.2 Some Other Algorithms.- C.2.1 Steepest Descent Method.- C.2.2 Quasi-Newton Algorithms.- C.2.3 The Simplex Method.- C.2.4 Weighting.- C.3 Pitfalls.- C.4 Bias, Confidence Regions and Measures of Fit.- C.5 Examples.- Problems.- Tables.- References.- Author Index.

"I found this to be the most complete and up-to-date regression text I have come across...this text has much to offer." -Journal of the American Statistical Association "The material is presented in a lucid and easy-to-understand style...can be ranked as one of the best textbooks on regression in the market." -mathermatical Reviews "...a successful mix of theory and practice...It will serve nicely to teach both the logic behind regression and the data-analytic use of regression." -SIAM Review