Applied regression analysis

• Main Authors: Draper, Norman Richard, Smith, Harry
• Format: eBook Book
• Language: English
• Published: New York Wiley 1998; John Wiley & Sons, Incorporated
• Edition: 3rd ed
• Series: Wiley series in probability and statistics . Texts and references section
• Subjects: Regression analysis
• ISBN: 9780471170822; 0471170828

An outstanding introduction to the fundamentals of regression analysis-updated and expanded The methods of regression analysis are the most widely used statistical tools for discovering the relationships among variables. This classic text, with its emphasis on clear, thorough presentation of concept...

Table of Contents:

• Cover -- Title Page -- Copyright -- Contents -- Preface to the Third Edition -- About the Software -- Chapter 0: Basic Prerequisite Knowledge -- 0.1. Distributions : Normal, t, and F -- Normal Distribution -- Gamma Function -- t-distribution -- F-distribution -- 0.2. Confidence Intervals (or Bands) and T-tests -- 0.3. Elements of Matrix Algebra -- Matrix, Vector, Scalar -- Equality -- Sum and Difference -- Transpose -- Symmetry -- Multiplication -- Special Matrices and Vectors -- Orthogonality -- Inverse Matrix -- Obtaining an Inverse -- Determinants -- Common Factors -- Chapter 1: Fitting a Straight Line by Least Squares -- 1.0. Introduction: the Need for Statistical Analysis -- 1.1. Straight Line Relationship Between Two Variables -- 1.2. Linear Regression: Fitting a Straight Line by Least Squares -- Meaning of Linear Model -- Least Squares Estimation -- Pocket-calculator Form -- Calculations for the Steam Data -- Centering the Data -- 1.3. The Analysis of Variance -- Sums of Squares -- Degrees of Freedom (df) -- Analysis of Variance Table -- Steam Data Calculations -- Skeleton Analysis of Variance Ta Ble -- R2 Statistic -- 1.4. Confidence Intervals and Tests for ß0 and ß1 -- Standard Deviation of the Slope B1 -- Confidence Interval for ß1 -- Confidence Interval for ß1 -- Test for Ho: ß1 = ß10 Versus H1: ß1 ≠ ß10 -- Reject or Do Not Reject -- Confidence Interval Represents a Set of Tests -- Standard Deviation of the Intercept -- Confidence Interval for ß0 -- 1.5. F-test for Significance of Regression -- P-values for F-statistics -- F = T2 -- P-values for T-statistics -- 1.6. the Correlation Between X and Y -- Correlation and Regression -- Rxy and R Connections -- Testing a Single Correlation -- 1.7. Summary of the Straight Line Fit Computations -- Pocket-calculator Computations -- 1.8. Historical Remarks -- Appendix 1 A. Steam Plant Data
• Exercises -- Chapter 2: Checking the Straight Line Fit -- 2.1. Lack of Fit and Pure Error -- General Discussion of Variance and Bias -- How Big Is σ2? -- Genuine Repeats Are Needed -- Calculation of Pure Error and Lack of Fit Mean Squares -- Special Formula When Nj = 2 -- Split of the Residual ss -- Effect of Repeat Runs on R2 -- Looking at the Data and Fitted Model -- Pure Error in the Many Predictors Case -- Adding (or Dropping) X's Can Affect Maximum R2 -- Approximate Repeats -- Generic Pure Error Situations Illustrated Via Straight Line Fits -- 2.2. Testing Homogeneity of Pure Error -- Bartlett's Test -- Bartlett's Test Modified for Kurtosis -- Levene's Test Using Means -- Levene's Test Using Medians -- Some Cautionary Remarks -- A Second Example -- 2.3. Examining Residuals: the Basic Plots -- How Should the Residuals Behave? -- 2.4. Non-normality Checks on Residuals -- Normal Plot of Residuals -- 2.5. Checks for Time Effects, Nonconstant Variance, Need for Transformation, and Curvature -- Three Questions and Answers -- Comment -- 2.6. Other Residuals Plots -- Dependencies Between Residuals -- 2.7. Durbin-watson Test -- 2.8. Reference Books for Analysis of Residuals -- Appendix 2a. Normal Plots -- Normal Scores -- Outliers -- Some General Characteristics of Normal Plots -- Making Your Own Probability Paper -- Appendix 2b. Minitab Instructions -- Exercises -- Chapter 3: Fitting Straight Lines: Special Topics -- 3.0. Summary and Preliminaries -- Covariance of Two Linear Functions -- 3.1. Standard Error of Y -- Intervals for Individual Observations and Means of q Observations -- 3.2. Inverse Regression (straight Line Case) -- 3.3. Some Practical Design of Experiment Implications of Regression -- Experimental Strategy Decisions -- An Example -- Comments on Table 3.1 -- 3.4. Straight Line Regression When Both Variables Are Subject to Error1
• Practical Advice -- Geometric Mean Functional Relationship -- References -- Exercises for Chapters 1-3 -- Chapter 4: Regression in Matrix Terms: Straight Line Case -- Matrices -- 4.1. Fitting a Straight Line in Matrix Terms -- Manipulating Matrices -- Orthogonality -- The Model in Matrix Form -- Setup for a Quadratic Model -- Transpose -- Inverse of a Matrix -- Inverses of Small Matrices -- Matrix Symmetry for Square Matrices -- Diagonal Matrices -- Inverting Partitioned Matrices with Blocks of Zeros -- Less Obvious Partitioning -- Back to the Straight Line Case -- Solving the Normal Equations -- A Small Sermon on Rounding Errors -- Section Summary -- 4.2. Singularity: What Happens in Regression to Make X'x Singular? an Example -- Singularity in the General Linear Regression Context -- 4.3. The Analysis of Variance in Matrix Terms -- 4.4. The Variances and Covariance of B0 and B1 from the Matrix Calculation -- Correlation Between B0 and B1 -- 4.5. Variance of Y Using the Matrix Development -- 4.6. Summary of Matrix Approach to Fitting a Straight Line (nonsingular Case) -- 4.7. The General Regression Situation -- Exercises for Chapter 4 -- Chapter 5: the General Regression Situation -- 5.1. General Linear Regression -- A Justification for Using Least Squares -- 5.2. Least Squares Properties -- The R2 Statistic -- R2 Can Be Deceptive -- Adjusted R2 Statistic -- 5.3. Least Squares Properties When E ~ N(0, 1σ2) -- Just Significant Regressions May Not Predict Well -- The Distribution of R2 -- Properties, Continued -- Bonferroni Limits -- 5.4. Confidence Intervals Versus Regions -- Moral -- 5.5. More on Confidence Intervals Versus Regions -- When F-test and T-tests Conflict -- References -- Appendix 5a. Selected Useful Matrix Results -- Exercises -- Chapter 6: Extra Sums of Squares and Tests for Several Parameters Being Zero
• 8.3. Detection of Influential Observations: Cook's Statistics -- Higher-order Cook's Statistics -- Another Worked Example -- Plots -- 8.4. Other Statistics Measuring Influence -- The Dffits Statistics -- Atkinson's Modified Cook's Statistics -- 8.5. Reference Books for Analysis of Residuals -- Exercises for Chapter 8 -- Chapter 9: Multiple Regression: Special Topics -- 9.1. Testing a General Linear Hypothesis -- Testing a General Linear Hypothesis Cß = 0 -- 9.2. Generalized Least Squares and Weighted Least Squares -- Generalized Least Squares Residuals -- General Comments -- Application to Serially Correlated Data -- 9.3. an Example of Weighted Least Squares -- 9.4 a Numerical Example of Weighted Least Squares -- 9.5 Restricted Least Squares -- 9.6. Inverse Regression (multiple Predictor Case) -- 9.7. Planar Regression When All the Variables Are Subject to Error -- Appendix 9a. Lagrange's Undetermined Multipliers -- Notation -- Basic Method -- Is the Solution a Maximum or Minimum? -- Exercises for Chapter 9 -- Chapter 10: Bias in Regression Estimates, and Expected Values of Mean Squares and Sums of Squares -- 10.1. Bias in Regression Estimates -- 10.2. The Effect of Bias on the Least Squares Analysis of Variance -- 10.3. Finding the Expected Values of Mean Squares -- 10.4. Expected Value of Extra Sum of Squares -- Exercises for Chapter 10 -- Chapter 11: on Worthwhile Regressions, Big F's, and R2 -- 11.1. Is My Regression a Useful One? -- An Alternative and Simpler Check -- Proof of (11.1.3) -- Comment -- 11.2. a Conversation About R2 -- What Should One Do for Linear Regression? -- References -- Appendix 11a. How Significant Should My Regression Be? -- The γm Criterion -- Exercises for Chapter 11 -- Chapter 12: Models Containing Functions of the Predictors, Including Polynomial Models -- 12.1. More Complicated Model Functions
• Polynomial Models of Various Orders in the Xj
• 6.1. The "extra Sum of Squares" Principle -- Polynomial Models -- Other Points -- Two Alternative Forms of the Extra Ss -- Sequential Sums of Squares -- Special Problems with Polynomial Models -- Partial Sums of Squares -- When T = F1/2 -- 6.2. Two Predictor Variables: Example -- How Useful Is the Fitted Equation? -- What Has Been Accomplished by the Addition of a Second Predictor Variable (namely, X6)? -- The Standard Error S -- Extra Ss F-test Criterion -- Standard Error of bi -- Correlations Between Parameter Estimates -- Confidence Limits for the True Mean Value of Y, Given a Specific Set of Xs -- Confidence Limits for the Mean of 9 Observations Given a Specific Set of X's -- Examining the Residuals -- 6.3. Sum of Squares of a Set of Linear Functions of Y's -- Appendix 6a. Orthogonal Columns in the X Matrix -- Appendix 68. Two Predictors: Sequential Sums of Squares -- References -- Exercises for Chapters 5 and 6 -- Chapter 7: Serial Correlation in the Residuals and the Durbin-watson Test -- 7.1. Serial Correlation in Residuals -- 7.2. The Durbin-watson Test for a Certain Type of Serial Correlation -- Primary Test, Tables of Dl and Du -- A Simplified Test -- Width of the Primary Test Inconclusive Region -- Mean Square Successive Difference -- 7.3. Examining Runs in the Time Sequence Plot of Residuals: Runs Test -- Runs -- Tables for Modest n1 and n2 -- Larger n1 and n2 Values -- Comments -- References -- Exercises for Chapter 7 -- Chapter 8: More on Checking Fitted Models -- 8.1. The Hat Matrix H and the Various Types of Residuals -- Variance-covariance Matrix of e -- Other Facts About H -- Internally Studentized Residuals1 -- Extra Sum of Squares Attributable to ej -- Externally Studentized Residuals2 -- Other Comments -- 8.2. Added Variable Plot and Partial Residuals -- Added Variable Plot -- Partial Residuals