Applied regression analysis / N. R. Draper, H. Smith.
Series Wiley series in probability and mathematical statisticsEditor: New York : Wiley, c1981Edición: 2nd edDescripción: xiv, 709 p. : il. ; 24 cmISBN: 0471029955Tema(s): Regression analysisOtra clasificación: 62-01 (62J05) Recursos en línea: Contributor biographical information | Publisher description | Table of contents only1 Fitting a Straight Line by Least Squares [1] 1.0 Introduction: The Need for Statistical Analysis [1] 1.1 Straight Line Relationships between Two Variables [5] 1.2 Linear Regression: Fitting a Straight Line [8] 1.3 The Precision of the Estimated Regression [17] 1.4 Examining the Regression Equation [22] 1.5 Lack of Fit and Pure Error [33] 1.6 The Correlation between X and Y [43] 1.7 Inverse Regression (Straight Line Case) [47] 1.8 Some Practical Implications of Chapter 1 [51] Exercises [55] 2 The Matrix Approach to Linear Regression [70] 2.0 Introduction [70] 2.1 Fitting a Straight Line in Matrix Terms: The Estimates of Bo and B1 [70] 2.2 The Analysis of Variance in Matrix Terms [80] 2.3 The Variances and Covariance of b0 and b1 from the Matrix Calculation [82] 2.4 Variance of Ŷ Using the Matrix Development [83] 2.5 Summary of Matrix Approach to Fitting a Straight Line [84] 2.6 The General Regression Situation [85] 2.7 The “Extra Sum of Squares” Principle [97] 2.8 Orthogonal Columns in the X-Matrix [98] 2.9 Partial F-Tests and Sequential F-Tests [101] 2.10 Testing a General Linear Hypothesis in Regression Situations [102] 2.11 Weighted Least Square [108] 2.12 Bias in Regression Estimates [117] 2.13 Restricted Least Squares [122] 2.14 Some Notes on Errors in the Predictors (As Well as in the Response) [122] 2.15 Inverse Regression (Multiple Predictor Case) [125] Appendix 2A Selected Useful Matrix Results [126] Appendix 2B Expected Value of Extra Sum of Squares [128] Appendix 2C How Significant Should My Regression Be? [129] Appendix 2D Lagrange's Undetermined Multipliers [134] Exercises [136] 3 The Examination of Residuals [141] 3.0 Introduction [141] 3.1 Overall Plot [142] 3.2 Time Sequence Plot [145] 3.3 Plot Against Ŷi [147] 3.4 Plot Against the Predictor Variables Xji, i = 1, 2,..., n [148] 3.5 Other Residuals Plots [149] 3.6 Statistics for Examination of Residuals [150] 3.7 Correlations among the Residuals [151] 3.8 Outliers [152] 3.9 Serial Correlation in Residuals [153] 3.10. Examining Runs in the Time Sequence Plot of Residuals [157] 3.11 The Durbin-Watson Test for a Certain Type of Serial Correlation [162] 3.12 Detection of Influential Observations [169] Appendix 3A. Normal and Half-Normal Plots [177] Exercises [183] 4 Two Predictor Variables [193] 4.0 Introduction [193] 4.1 Multiple Regression with Two Predictor Variables as a Sequence of Straight-Line Regressions [196] 4.2 Examining the Regression Equation [204] Exercises [212] 5 More Complicated Models [218] 5.0 Introduction [218] 5.1 Polynomial Models of Various Orders in the Xj [219] 5.2 Models Involving Transformations Other Than Integer Powers [221] 5.3 Families of Transformations [225] 5.4 The Use of “Dummy” Variables in Multiple Regression [241] 5.5 Centering and Scaling; Performing the Regression in Correlation Form [257] 5.6 Orthogonal Polynomials [266] 5.7 Transforming X Matrices to Obtain Orthogonal Columns [275] 5.8 Regression Analysis of Summary Data [278] Exercises [280] 6 Selecting the “Best” Regression Equation [294] 6.0 Introduction [294] 6.1 All Possible Regressions [296] 6.2 “Best Subset” Regression [303] 6.3 The Backward Elimination Procedure [305] 6.4 The Stepwise Regression Procedure [307] 6.5 A Drawback to Understand but not be Overly Concerned About [311] 6.6 Variations on the Previous Methods [312] 6.7 Ridge Regression [313] 6.8 PRESS [325] 6.9 Principal Component Regression [327] 6.10 Latent Root Regression [332] 6.11 The Stagewise Regression Procedure [337] 6.12 Summary [341] 6.13 Computational Method for Stepwise Regression [342] 6.14 Robust Regression [342] 6.15 Some Comments on Statistical Computer Packages [344] Appendix 6A Canonical Form of Ridge Regression [349] Exercises [352] 7 Two Specific Problems [380] 7.0 Introduction [380] 7.1 The First Problem [380] 7.2 Examination of the Data [381] 7.3 Choosing the First Variable to Enter Regression [383] 7.4 Construction of New Variables [386] 7.5 The Addition of a Cross-Product Term to the Model [386] 7.6 Enlarging the Model [388] 7.7 The Second Problem. Worked Examples of Second-Order Surface Fitting for k = 3 and k = 2 Variables [390] Exercises [404] 8 Multiple Regression and Mathematical Model Building [412] 8.0 Introduction [412] 8.1 Planning the Model Building Process [414] 8.2 Development of the Mathematical Model [418] 8.3 Validation and Maintenance of the Mathematical Model [419] 9 Multiple Regression Applied to Analysis of Variance Problems [423] 9.0 Introduction [423] 9.1 The One-Way Classification : An Example [424] 9.2 Regression Treatment of the One-Way Classification Example [427] 9.3 The One-Way Classification [431] 9.4 Regression Treatment of the One-Way Classification Using the Original Model [432] 9.5 Regression Treatment of the One-Way Classification: Independent Normal Equations [437] 9.6 The Two-Way Classification with Equal Numbers of Observations in the Cells: An Example [439] 9.7 Regression Treatment of the Two-Way Classification Example [441] 9.8 The Two-Way Classification with Equal Numbers of Observations in the Cells [445] 9.9 Regression Treatment of the Two-Way Classification with Equal Numbers of Observations in the Cells [447] 9.10 Example: The Two-Way Classification [451] 9.11 Comments [453] Exercises [454] 10 An Introduction to Nonlinear Estimation [458] 10.0 Introduction [458] 10.1 Least Squares in the Nonlinear Case [459] 10.2 Estimating the Parameters of a Nonlinear System [462] 10.3 An Example [475] 10.4 A Note on Reparameterization of the Model [488] 10.5 The Geometry of Linear Least Squares [489] 10.6 The Geometry of Nonlinear Least Squares [500] 10.7 Nonlinear Growth Models [505] 10.8 Nonlinear Models: Other Work [513] Exercises [517] Normal Distribution [530] Percentage Points of the t-Distribution [532] Percentage Points of the F-Distribution [533]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 62 D765-2 (Browse shelf) | Available | A-5945 |
Incluye índice.
Bibliografía: p. 675-699.
1 Fitting a Straight Line by Least Squares [1] --
1.0 Introduction: The Need for Statistical Analysis [1] --
1.1 Straight Line Relationships between Two Variables [5] --
1.2 Linear Regression: Fitting a Straight Line [8] --
1.3 The Precision of the Estimated Regression [17] --
1.4 Examining the Regression Equation [22] --
1.5 Lack of Fit and Pure Error [33] --
1.6 The Correlation between X and Y [43] --
1.7 Inverse Regression (Straight Line Case) [47] --
1.8 Some Practical Implications of Chapter 1 [51] --
Exercises [55] --
2 The Matrix Approach to Linear Regression [70] --
2.0 Introduction [70] --
2.1 Fitting a Straight Line in Matrix Terms: The Estimates of Bo and B1 [70] --
2.2 The Analysis of Variance in Matrix Terms [80] --
2.3 The Variances and Covariance of b0 and b1 from the Matrix Calculation [82] --
2.4 Variance of Ŷ Using the Matrix Development [83] --
2.5 Summary of Matrix Approach to Fitting a Straight Line [84] --
2.6 The General Regression Situation [85] --
2.7 The “Extra Sum of Squares” Principle [97] --
2.8 Orthogonal Columns in the X-Matrix [98] --
2.9 Partial F-Tests and Sequential F-Tests [101] --
2.10 Testing a General Linear Hypothesis in Regression Situations [102] --
2.11 Weighted Least Square [108] --
2.12 Bias in Regression Estimates [117] --
2.13 Restricted Least Squares [122] --
2.14 Some Notes on Errors in the Predictors (As Well as in the Response) [122] --
2.15 Inverse Regression (Multiple Predictor Case) [125] --
Appendix 2A Selected Useful Matrix Results [126] --
Appendix 2B Expected Value of Extra Sum of Squares [128] --
Appendix 2C How Significant Should My Regression Be? [129] --
Appendix 2D Lagrange's Undetermined Multipliers [134] --
Exercises [136] --
3 The Examination of Residuals [141] --
3.0 Introduction [141] --
3.1 Overall Plot [142] --
3.2 Time Sequence Plot [145] --
3.3 Plot Against Ŷi [147] --
3.4 Plot Against the Predictor Variables Xji, i = 1, 2,..., n [148] --
3.5 Other Residuals Plots [149] --
3.6 Statistics for Examination of Residuals [150] --
3.7 Correlations among the Residuals [151] --
3.8 Outliers [152] --
3.9 Serial Correlation in Residuals [153] --
3.10. Examining Runs in the Time Sequence Plot of Residuals [157] --
3.11 The Durbin-Watson Test for a Certain Type of Serial Correlation [162] --
3.12 Detection of Influential Observations [169] --
Appendix 3A. Normal and Half-Normal Plots [177] --
Exercises [183] --
4 Two Predictor Variables [193] --
4.0 Introduction [193] --
4.1 Multiple Regression with Two Predictor Variables as a Sequence of Straight-Line Regressions [196] --
4.2 Examining the Regression Equation [204] --
Exercises [212] --
5 More Complicated Models [218] --
5.0 Introduction [218] --
5.1 Polynomial Models of Various Orders in the Xj [219] --
5.2 Models Involving Transformations Other Than Integer Powers [221] --
5.3 Families of Transformations [225] --
5.4 The Use of “Dummy” Variables in Multiple Regression [241] --
5.5 Centering and Scaling; Performing the Regression in Correlation Form [257] --
5.6 Orthogonal Polynomials [266] --
5.7 Transforming X Matrices to Obtain Orthogonal Columns [275] --
5.8 Regression Analysis of Summary Data [278] --
Exercises [280] --
6 Selecting the “Best” Regression Equation [294] --
6.0 Introduction [294] --
6.1 All Possible Regressions [296] --
6.2 “Best Subset” Regression [303] --
6.3 The Backward Elimination Procedure [305] --
6.4 The Stepwise Regression Procedure [307] --
6.5 A Drawback to Understand but not be Overly Concerned About [311] --
6.6 Variations on the Previous Methods [312] --
6.7 Ridge Regression [313] --
6.8 PRESS [325] --
6.9 Principal Component Regression [327] --
6.10 Latent Root Regression [332] --
6.11 The Stagewise Regression Procedure [337] --
6.12 Summary [341] --
6.13 Computational Method for Stepwise Regression [342] --
6.14 Robust Regression [342] --
6.15 Some Comments on Statistical Computer Packages [344] --
Appendix 6A Canonical Form of Ridge Regression [349] --
Exercises [352] --
7 Two Specific Problems [380] --
7.0 Introduction [380] --
7.1 The First Problem [380] --
7.2 Examination of the Data [381] --
7.3 Choosing the First Variable to Enter Regression [383] --
7.4 Construction of New Variables [386] --
7.5 The Addition of a Cross-Product Term to the Model [386] --
7.6 Enlarging the Model [388] --
7.7 The Second Problem. Worked Examples of Second-Order Surface Fitting for k = 3 and k = 2 Variables [390] --
Exercises [404] --
8 Multiple Regression and Mathematical Model Building [412] --
8.0 Introduction [412] --
8.1 Planning the Model Building Process [414] --
8.2 Development of the Mathematical Model [418] --
8.3 Validation and Maintenance of the Mathematical Model [419] --
9 Multiple Regression Applied to Analysis of Variance Problems [423] --
9.0 Introduction [423] --
9.1 The One-Way Classification : An Example [424] --
9.2 Regression Treatment of the One-Way Classification Example [427] --
9.3 The One-Way Classification [431] --
9.4 Regression Treatment of the One-Way Classification Using the Original Model [432] --
9.5 Regression Treatment of the One-Way Classification: Independent Normal Equations [437] --
9.6 The Two-Way Classification with Equal Numbers of Observations in the Cells: An Example [439] --
9.7 Regression Treatment of the Two-Way Classification Example [441] --
9.8 The Two-Way Classification with Equal Numbers of Observations in the Cells [445] --
9.9 Regression Treatment of the Two-Way Classification with Equal Numbers of Observations in the Cells [447] --
9.10 Example: The Two-Way Classification [451] --
9.11 Comments [453] --
Exercises [454] --
10 An Introduction to Nonlinear Estimation [458] --
10.0 Introduction [458] --
10.1 Least Squares in the Nonlinear Case [459] --
10.2 Estimating the Parameters of a Nonlinear System [462] --
10.3 An Example [475] --
10.4 A Note on Reparameterization of the Model [488] --
10.5 The Geometry of Linear Least Squares [489] --
10.6 The Geometry of Nonlinear Least Squares [500] --
10.7 Nonlinear Growth Models [505] --
10.8 Nonlinear Models: Other Work [513] --
Exercises [517] --
Normal Distribution [530] --
Percentage Points of the t-Distribution [532] --
Percentage Points of the F-Distribution [533] --
MR, 82f:62002
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