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| Preface | |
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| Mathematical Concepts | |
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| Introduction | |
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| Elementary Theorems on Linear and Matrix Algebra | |
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| Partitioned Matrices | |
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| Nonnegative Matrices | |
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| Generalized and Conditional Inverses | |
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| Solutions of Linear Equations | |
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| Idempotent Matrices | |
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| Trace of Matrices | |
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| Derivatives of Quadratic and Linear Forms | |
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| Expectation of a Matrix | |
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| Evaluation of an Integral | |
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| Statistical Concepts | |
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| Introduction | |
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| Random Variables and Distribution Functions | |
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| Moment Generating Function | |
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| Independence of Random Vectors | |
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| Special Distributions and Some Important Formulas | |
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| Statistical Inference | |
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| Point Estimation | |
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| Hypothesis Testing | |
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| Confidence Intervals | |
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| Comments on Statistical Inference | |
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| Problems | |
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| The Multidimensional Normal Distribution | |
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| Introduction | |
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| The Univariate Normal Distribution | |
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| Multivariate Normal Distribution | |
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| Marginal Distributions | |
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| Independent and Uncorrelated Random Vectors | |
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| Conditional Distribution | |
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| Regression | |
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| Correlation | |
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| Examples | |
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| Problems | |
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| Distributions Of Quadratic Forms | |
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| Introductions | |
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| Noncentral Chi-Square Distribution | |
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| Noncentral F and Noncentral t Distributions | |
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| Distribution of Quadratic Forms in Normal Variables | |
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| Independence of Linear Forms and Quadratic Forms | |
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| Expected Value of a Quadratic Form | |
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| Additional Theorems | |
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| Problems | |
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| Models | |
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| Introduction | |
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| General Linear Model | |
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| Linear Regression Model | |
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| Design Models | |
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| Components-of-Variance Model | |
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| General Linear Model | |
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| Introduction | |
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| Point Estimation standard deviation and Linear Functions of Beta [i]:Case 1 | |
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| Test of the Hypothesis Hb =h: Case 1 | |
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| Special Cases for Hypothesis Testing | |
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| Confidence Intervals Associated with the Test H[o]: Hb = h | |
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| Further discussion of Confidence Intervals Associated with the Test H[o]: Hb = h | |
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| Example | |
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| The General Linear Model, Case 1, and sum is not equal to the standard deviation x Y | |
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| Examination of Assumptions | |
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| Inference in the Linear Model: Case 2 | |
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| Further Discussion of the Test Hb =h | |
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| Computing Techniques | |
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| Introduction | |
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| Square root Method of Factoring a Positive Definite Matrix | |
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| Computing Point Estimates, Test Statistics, and Confidence Intervals | |
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| Analysis of Variance | |
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| The Normal | |
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| Equations Using Deviations from Means | |
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| Some Computing Procedures When cov[Y] = the standard deviation x V | |
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| Appendix | |
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| Problems | |
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| Applications Of The General Linear Model | |
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| Introduction | |
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| Prediction Intervals | |
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| Tolerance Intervals | |
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| Other Tolerance and Associated Intervals | |
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| Determining x for a Given Value of Y (The Calibration Problem) | |
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| Parallel, Intersecting, and Identical Models | |
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| Polynomial Models | |
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| Trigonometric Models | |
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| Designing Investigations | |
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| Maximum or Minimum of a Quadratic Function | |
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| Point of Intersection of Two Lines | |
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| Problems | |
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| Sampling From The Multivariate Normal Distribution | |
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| Introduction | |
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| Notation | |
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| Point Estimators of the population mean and the sum | |
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| Test of the Hypothesis H[o] :population mean = h[o] | |
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| Confidence Intervals on l'' [I] population mean, for I = 1,2,?, q Computations | |
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| Additional Theorems about mu (hat) and sum (hat) Problems | |
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| Multiple Regression | |
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| Introduction | |
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| Multiple Regression Model: Case I, Case II, and Point Estimation | |
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| Multiple Regression Model: Confidence Intervals and Test Hypothesis, Case I and Case II | |
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| Multiple Regression Model: Case III | |
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| Problems | |
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| Correlation | |
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| Introduction, Simple Correlation, Partial Correlation, Multiple Correlation | |
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| Correlation for Non-normal p.d.f.''s | |
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| Correlation and Independence of Random Variables | |
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| Problems | |
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| Some Applications Of The Regression Model | |
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| Introduction | |
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| Prediction | |
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| Selecting Variables for a Model | |
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| Growth Curves | |
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| Discrimination (Classification) | |
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| Problems | |
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| Design Models | |
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| Introduction | |
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| Point Estimation for the Design Model | |
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| Case I | |
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| Point Estimation for the Design Model | |
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| Case II | |
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| Confidence Intervals and Tests of Hypothesis for Case I of the Design Model | |
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| Computations | |
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| The One-Factor Design Model | |
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| Further Discussion of Tests and Confidence Intervals for the Design Models | |
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| Problems | |
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| Two-Factor Design Model | |
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| Introduction | |
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| Tw | |