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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 | |