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Regression Analysis Theory, Methods and Applications

Any method of fitting equations to data may be called regression. Such equations are valuable for at least two purposes: making predictions and judging the strength of relationships. Because they provide a way of em­ pirically identifying how a variable is affected by other variables, regression met...

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Bibliographic Details
Main Authors: Sen, Ashish K., Srivastava, Muni S. (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1990, 1990
Edition:1st ed. 1990
Series:Springer Texts in Statistics
Subjects:
Mathematical Analysis
Statistical Theory And Methods
Statistics 
Analysis
Analysis (mathematics)
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1 Introduction
  • 2 Multiple Regression
  • 3 Tests and Confidence Regions
  • 4 Indicator Variables
  • 5 The Normality Assumption
  • 6 Unequal Variances
  • 7 *Correlated Errors
  • 8 Outliers and Influential Observations
  • 9 Transformations
  • 10 Multicollinearity
  • 11 Variable Selection
  • 12 *Biased Estimation
  • 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

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