Applied regression analysis / N. R. Draper, H. Smith.
Editor: New York : Wiley, c1966Descripción: ix, 407 p. : il. ; 24 cmISBN: 0471221708Otra clasificación: 62Jxx1 Fitting a Straight Line by Least Squares [1] 1.0 Introduction: The Need for Statistical Analysis [1] 1.1 Linear Relationships between Two Variables [4] 1.2 Linear Regression: Fitting a Straight Line [7] 1.3 The Precision of the Estimated Regression [13] 1.4 Examining the Regression Equation [17] 1.5 Lack of Fit and Pure Error [26] 1.6 The Correlation between X and Y [33] Exercises [35] 2 The Matrix Approach to Linear Regression [44] 2.0 Introduction [44] 2.1 Fitting a Straight Line in Matrix Terms: The Estimates of and B0 and B1 [44] 2.2 The Analysis of Variance in Matrix Terms [53] 2.3 The Variances and Covariance of b0 and b1 from the Matrix Calculation [55] 2.4 The Variance of Ŷ Using the Matrix Development [56] 2.5 Summary of Matrix Approach to Fitting a Straight Line [56] 2.6 The General Regression Situation [58] 2.7 The “Extra Sum of Squares” Principle [67] 2.8 Orthogonal Columns in the X-Matrix [69] 2.9 Partial F-Tests and Sequential F-Tests [71] 2.10 Testing a General Linear Hypothesis in Regression Situations [72] 2.11 Weighted Least Squares [77] 2.12 Bias in Regression Estimates [81] 3 The Examination of Residuals [86] 3.0 Introduction [86] 3.1 Overall Plot [87] 3.2 Time Sequence Plot [88] 3.3 Plot Against Ŷi [90] 3.4 Plot Against the Independent Variables Xji, = 1, 2, ..., n [91] 3.5 Other Residual Plots [91] 3.6 Statistics for Examination of Residuals [92] 3.7 Correlations among the Residuals [93] 3.8 Outliers [94] 3.9 Examining Runs in the Time Sequence Plot of Residuals [95] Exercises [100] 4 Two Independent Variables [104] 4.0 Introduction [104] 4.1 Multiple Regression with Two Independent Variables as a Sequence of Straight-Line Regressions [107] 4.2 Examining the Regression Equation [115] Exercises [124] 5 More Complicated Models [128] 5.0 Introduction [128] 5.1 Polynomial Models of Various Orders in the Xj [129] 5.2 Models Involving Transformations Other Than Integer Powers [131] 5.3 The Use of “Dummy” Variables in Multiple Regression [134] 5.4 Preparing the Input Data Matrix for General Regression Problems [142] 5.5 Orthogonal Polynomials [150] 5.6 Transforming X Matrices to Obtain Orthogonal Columns [156] Exercises [159] 6 Selecting the “Best” Regression Equation [163] 6.0 Introduction [163] 6.1 All Possible Regressions [164] 6.2 The Backward Elimination Procedure [167] 6.3 The Forward Selection Procedure [169] 6.4 The Stepwise Regression Procedure [171] 6.5 Two Variations on the Four Previous Methods [172] 6.6 The Stagewise Regression Procedure [173] 6.7 A Summary of the Least Squares Equations from Methods Described [177] 6.8 Computational Method for Stepwise Regression [178] Exercises [195] 7 A Specific Problem [217] 7.0 Introduction [217] 7.1 The Problem [217] 7.2 Examination of the Data [217] 7.3 Choosing the First Variable to Enter Regression [220] 7.4 Construction of New Variables [222] 7.5 The Addition of a Cross-Product Term to the Model [224] 7.6 Enlarging the Model [225] Exercises [227] 8 Multiple Regression and Mathematical Model Building [234] 8.0 Introduction [234] 8.1 Planning the Model Building Process [236] 8.2 Development of the Mathematical Model [239] 8.3 Verification and Maintenance of the Mathematical Model [240] 9 Multiple Regression Applied to Analysis of Variance Problems [243] 9.0 Introduction [243] 9.1 The One-Way Classification [244] 9.2 Regression Treatment of the One-Way Classification Using the Original Model [245] 9.3 Regression Treatment of the One-Way Classification: Independent Normal Equations [251] 9.4 The Two-Way Classification with Equal Numbers of Observations in the Cells [253] 9.5 Regression Treatment of the Two-Way Classification with Equal Numbers of Observations in the Cells [254] 9.6 Example: The Two-Way Classification [258] 9.7 Comments [260] Exercises [260] 10 An Introduction to Nonlinear Estimation [263] 10.1 Introduction [263] 10.2 Least Squares in the Nonlinear Case [264] 10.3 Estimating the Parameters of a Nonlinear System [267] 10.4 An Example [275] 10.5 A Note on Reparameterization of the Model [284] 10.6 The Geometry of Linear Least Squares [285] 10.7 The Geometry of Nonlinear Least Squares [295] Exercises [299] Nonlinear Bibliography [301] Percentage Points of the t-Distribution [305] Percentage Points of the F-Distribution [306]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 62 D765 (Browse shelf) | Available | A-3869 |
Bibliografía: p. 309-316.
1 Fitting a Straight Line by Least Squares [1] --
1.0 Introduction: The Need for Statistical Analysis [1] --
1.1 Linear Relationships between Two Variables [4] --
1.2 Linear Regression: Fitting a Straight Line [7] --
1.3 The Precision of the Estimated Regression [13] --
1.4 Examining the Regression Equation [17] --
1.5 Lack of Fit and Pure Error [26] --
1.6 The Correlation between X and Y [33] --
Exercises [35] --
2 The Matrix Approach to Linear Regression [44] --
2.0 Introduction [44] --
2.1 Fitting a Straight Line in Matrix Terms: The Estimates of and B0 and B1 [44] --
2.2 The Analysis of Variance in Matrix Terms [53] --
2.3 The Variances and Covariance of b0 and b1 from the Matrix Calculation [55] --
2.4 The Variance of Ŷ Using the Matrix Development [56] --
2.5 Summary of Matrix Approach to Fitting a Straight Line [56] --
2.6 The General Regression Situation [58] --
2.7 The “Extra Sum of Squares” Principle [67] --
2.8 Orthogonal Columns in the X-Matrix [69] --
2.9 Partial F-Tests and Sequential F-Tests [71] --
2.10 Testing a General Linear Hypothesis in Regression Situations [72] --
2.11 Weighted Least Squares [77] --
2.12 Bias in Regression Estimates [81] --
3 The Examination of Residuals [86] --
3.0 Introduction [86] --
3.1 Overall Plot [87] --
3.2 Time Sequence Plot [88] --
3.3 Plot Against Ŷi [90] --
3.4 Plot Against the Independent Variables Xji, = 1, 2, ..., n [91] --
3.5 Other Residual Plots [91] --
3.6 Statistics for Examination of Residuals [92] --
3.7 Correlations among the Residuals [93] --
3.8 Outliers [94] --
3.9 Examining Runs in the Time Sequence Plot of Residuals [95] --
Exercises [100] --
4 Two Independent Variables [104] --
4.0 Introduction [104] --
4.1 Multiple Regression with Two Independent Variables as a Sequence of Straight-Line Regressions [107] --
4.2 Examining the Regression Equation [115] --
Exercises [124] --
5 More Complicated Models [128] --
5.0 Introduction [128] --
5.1 Polynomial Models of Various Orders in the Xj [129] --
5.2 Models Involving Transformations Other Than Integer Powers [131] --
5.3 The Use of “Dummy” Variables in Multiple Regression [134] --
5.4 Preparing the Input Data Matrix for General Regression Problems [142] --
5.5 Orthogonal Polynomials [150] --
5.6 Transforming X Matrices to Obtain Orthogonal Columns [156] --
Exercises [159] --
6 Selecting the “Best” Regression Equation [163] --
6.0 Introduction [163] --
6.1 All Possible Regressions [164] --
6.2 The Backward Elimination Procedure [167] --
6.3 The Forward Selection Procedure [169] --
6.4 The Stepwise Regression Procedure [171] --
6.5 Two Variations on the Four Previous Methods [172] --
6.6 The Stagewise Regression Procedure [173] --
6.7 A Summary of the Least Squares Equations from Methods Described [177] --
6.8 Computational Method for Stepwise Regression [178] --
Exercises [195] --
7 A Specific Problem [217] --
7.0 Introduction [217] --
7.1 The Problem [217] --
7.2 Examination of the Data [217] --
7.3 Choosing the First Variable to Enter Regression [220] --
7.4 Construction of New Variables [222] --
7.5 The Addition of a Cross-Product Term to the Model [224] --
7.6 Enlarging the Model [225] --
Exercises [227] --
8 Multiple Regression and Mathematical Model Building [234] --
8.0 Introduction [234] --
8.1 Planning the Model Building Process [236] --
8.2 Development of the Mathematical Model [239] --
8.3 Verification and Maintenance of the Mathematical Model [240] --
9 Multiple Regression Applied to Analysis of Variance Problems [243] --
9.0 Introduction [243] --
9.1 The One-Way Classification [244] --
9.2 Regression Treatment of the One-Way Classification Using the Original Model [245] --
9.3 Regression Treatment of the One-Way Classification: Independent Normal Equations [251] --
9.4 The Two-Way Classification with Equal Numbers of Observations in the Cells [253] --
9.5 Regression Treatment of the Two-Way Classification with Equal Numbers of Observations in the Cells [254] --
9.6 Example: The Two-Way Classification [258] --
9.7 Comments [260] --
Exercises [260] --
10 An Introduction to Nonlinear Estimation [263] --
10.1 Introduction [263] --
10.2 Least Squares in the Nonlinear Case [264] --
10.3 Estimating the Parameters of a Nonlinear System [267] --
10.4 An Example [275] --
10.5 A Note on Reparameterization of the Model [284] --
10.6 The Geometry of Linear Least Squares [285] --
10.7 The Geometry of Nonlinear Least Squares [295] --
Exercises [299] --
Nonlinear Bibliography [301] --
Percentage Points of the t-Distribution [305] --
Percentage Points of the F-Distribution [306] --
MR, 35 #2415
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