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...
Main Authors: | , |
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Format: | eBook |
Language: | English |
Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1990, 1990
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Edition: | 1st ed. 1990 |
Series: | Springer Texts in Statistics
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Subjects: | |
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