Normal view

## Applied regression analysis / N. R. Draper, H. Smith.

Editor: New York : Wiley, c1966Descripción: ix, 407 p. : il. ; 24 cmISBN: 0471221708Otra clasificación: 62Jxx
Contenidos:
```1 Fitting a Straight Line by Least Squares 
1.0 Introduction: The Need for Statistical Analysis 
1.1 Linear Relationships between Two Variables 
1.2 Linear Regression: Fitting a Straight Line 
1.3 The Precision of the Estimated Regression 
1.4 Examining the Regression Equation 
1.5 Lack of Fit and Pure Error 
1.6 The Correlation between X and Y 
Exercises 
2 The Matrix Approach to Linear Regression 
2.0 Introduction 
2.1 Fitting a Straight Line in Matrix Terms: The Estimates of and B0 and B1 
2.2 The Analysis of Variance in Matrix Terms 
2.3 The Variances and Covariance of b0 and b1 from the Matrix Calculation 
2.4 The Variance of Ŷ Using the Matrix Development 
2.5 Summary of Matrix Approach to Fitting a Straight Line 
2.6 The General Regression Situation 
2.7 The “Extra Sum of Squares” Principle 
2.8 Orthogonal Columns in the X-Matrix 
2.9 Partial F-Tests and Sequential F-Tests 
2.10 Testing a General Linear Hypothesis in Regression Situations 
2.11 Weighted Least Squares 
2.12 Bias in Regression Estimates 
3 The Examination of Residuals 
3.0 Introduction 
3.1 Overall Plot 
3.2 Time Sequence Plot 
3.3 Plot Against Ŷi 
3.4 Plot Against the Independent Variables Xji, = 1, 2, ..., n 
3.5 Other Residual Plots 
3.6 Statistics for Examination of Residuals 
3.7 Correlations among the Residuals 
3.8 Outliers 
3.9 Examining Runs in the Time Sequence Plot of Residuals 
Exercises 
4 Two Independent Variables 
4.0 Introduction 
4.1 Multiple Regression with Two Independent Variables as a Sequence of Straight-Line Regressions 
4.2 Examining the Regression Equation 
Exercises 
5 More Complicated Models 
5.0 Introduction 
5.1 Polynomial Models of Various Orders in the Xj 
5.2 Models Involving Transformations Other Than Integer Powers 
5.3 The Use of “Dummy” Variables in Multiple Regression 
5.4 Preparing the Input Data Matrix for General Regression Problems 
5.5 Orthogonal Polynomials 
5.6 Transforming X Matrices to Obtain Orthogonal Columns 
Exercises 
6 Selecting the “Best” Regression Equation 
6.0 Introduction 
6.1 All Possible Regressions 
6.2 The Backward Elimination Procedure 
6.3 The Forward Selection Procedure 
6.4 The Stepwise Regression Procedure 
6.5 Two Variations on the Four Previous Methods 
6.6 The Stagewise Regression Procedure 
6.7 A Summary of the Least Squares Equations from Methods Described 
6.8 Computational Method for Stepwise Regression 
Exercises 
7 A Specific Problem 
7.0 Introduction 
7.1 The Problem 
7.2 Examination of the Data 
7.3 Choosing the First Variable to Enter Regression 
7.4 Construction of New Variables 
7.5 The Addition of a Cross-Product Term to the Model 
7.6 Enlarging the Model 
Exercises 
8 Multiple Regression and Mathematical Model Building 
8.0 Introduction 
8.1 Planning the Model Building Process 
8.2 Development of the Mathematical Model 
8.3 Verification and Maintenance of the Mathematical Model 
9 Multiple Regression Applied to Analysis of Variance Problems 
9.0 Introduction 
9.1 The One-Way Classification 
9.2 Regression Treatment of the One-Way Classification Using the Original Model 
9.3 Regression Treatment of the One-Way Classification: Independent Normal Equations 
9.4 The Two-Way Classification with Equal Numbers of Observations in the Cells 
9.5 Regression Treatment of the Two-Way Classification with Equal Numbers of Observations in the Cells 
9.6 Example: The Two-Way Classification 
Exercises 
10 An Introduction to Nonlinear Estimation 
10.1 Introduction 
10.2 Least Squares in the Nonlinear Case 
10.3 Estimating the Parameters of a Nonlinear System 
10.4 An Example 
10.5 A Note on Reparameterization of the Model 
10.6 The Geometry of Linear Least Squares 
10.7 The Geometry of Nonlinear Least Squares 
Exercises 
Nonlinear Bibliography 
Percentage Points of the t-Distribution 
Percentage Points of the F-Distribution ``` Average rating: 0.0 (0 votes)
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Bibliografía: p. 309-316.

1 Fitting a Straight Line by Least Squares  --
1.0 Introduction: The Need for Statistical Analysis  --
1.1 Linear Relationships between Two Variables  --
1.2 Linear Regression: Fitting a Straight Line  --
1.3 The Precision of the Estimated Regression  --
1.4 Examining the Regression Equation  --
1.5 Lack of Fit and Pure Error  --
1.6 The Correlation between X and Y  --
Exercises  --
2 The Matrix Approach to Linear Regression  --
2.0 Introduction  --
2.1 Fitting a Straight Line in Matrix Terms: The Estimates of and B0 and B1  --
2.2 The Analysis of Variance in Matrix Terms  --
2.3 The Variances and Covariance of b0 and b1 from the Matrix Calculation  --
2.4 The Variance of Ŷ Using the Matrix Development  --
2.5 Summary of Matrix Approach to Fitting a Straight Line  --
2.6 The General Regression Situation  --
2.7 The “Extra Sum of Squares” Principle  --
2.8 Orthogonal Columns in the X-Matrix  --
2.9 Partial F-Tests and Sequential F-Tests  --
2.10 Testing a General Linear Hypothesis in Regression Situations  --
2.11 Weighted Least Squares  --
2.12 Bias in Regression Estimates  --
3 The Examination of Residuals  --
3.0 Introduction  --
3.1 Overall Plot  --
3.2 Time Sequence Plot  --
3.3 Plot Against Ŷi  --
3.4 Plot Against the Independent Variables Xji, = 1, 2, ..., n  --
3.5 Other Residual Plots  --
3.6 Statistics for Examination of Residuals  --
3.7 Correlations among the Residuals  --
3.8 Outliers  --
3.9 Examining Runs in the Time Sequence Plot of Residuals  --
Exercises  --
4 Two Independent Variables  --
4.0 Introduction  --
4.1 Multiple Regression with Two Independent Variables as a Sequence of Straight-Line Regressions  --
4.2 Examining the Regression Equation  --
Exercises  --
5 More Complicated Models  --
5.0 Introduction  --
5.1 Polynomial Models of Various Orders in the Xj  --
5.2 Models Involving Transformations Other Than Integer Powers  --
5.3 The Use of “Dummy” Variables in Multiple Regression  --
5.4 Preparing the Input Data Matrix for General Regression Problems  --
5.5 Orthogonal Polynomials  --
5.6 Transforming X Matrices to Obtain Orthogonal Columns  --
Exercises  --
6 Selecting the “Best” Regression Equation  --
6.0 Introduction  --
6.1 All Possible Regressions  --
6.2 The Backward Elimination Procedure  --
6.3 The Forward Selection Procedure  --
6.4 The Stepwise Regression Procedure  --
6.5 Two Variations on the Four Previous Methods  --
6.6 The Stagewise Regression Procedure  --
6.7 A Summary of the Least Squares Equations from Methods Described  --
6.8 Computational Method for Stepwise Regression  --
Exercises  --
7 A Specific Problem  --
7.0 Introduction  --
7.1 The Problem  --
7.2 Examination of the Data  --
7.3 Choosing the First Variable to Enter Regression  --
7.4 Construction of New Variables  --
7.5 The Addition of a Cross-Product Term to the Model  --
7.6 Enlarging the Model  --
Exercises  --
8 Multiple Regression and Mathematical Model Building  --
8.0 Introduction  --
8.1 Planning the Model Building Process  --
8.2 Development of the Mathematical Model  --
8.3 Verification and Maintenance of the Mathematical Model  --
9 Multiple Regression Applied to Analysis of Variance Problems  --
9.0 Introduction  --
9.1 The One-Way Classification  --
9.2 Regression Treatment of the One-Way Classification Using the Original Model  --
9.3 Regression Treatment of the One-Way Classification: Independent Normal Equations  --
9.4 The Two-Way Classification with Equal Numbers of Observations in the Cells  --
9.5 Regression Treatment of the Two-Way Classification with Equal Numbers of Observations in the Cells  --
9.6 Example: The Two-Way Classification  --
Exercises  --
10 An Introduction to Nonlinear Estimation  --
10.1 Introduction  --
10.2 Least Squares in the Nonlinear Case  --
10.3 Estimating the Parameters of a Nonlinear System  --
10.4 An Example  --
10.5 A Note on Reparameterization of the Model  --
10.6 The Geometry of Linear Least Squares  --
10.7 The Geometry of Nonlinear Least Squares  --
Exercises  --
Nonlinear Bibliography  --
Percentage Points of the t-Distribution  --
Percentage Points of the F-Distribution  --

MR, 35 #2415

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