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In THEORY AND APPLICATION OF THE LINEAR MODEL, Franklin A. Graybill integrates the linear statistical model within the context of analysis of variance, correlation and regression, and design of experiments. With topics motivated by real situations, it is a time tested, authoritative resource for experimenters, statistical consultants, and students.

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List price: $199.95 Copyright year: 1976 Publisher: Brooks/Cole Publication date: 3/27/2000 Binding: Paperback Pages: 204 Size: 7.48" wide x 9.25" long x 0.98" tall Weight: 2.398 Language: English

AuthorTable of Contents

Preface

Mathematical Concepts

Introduction

Elementary Theorems on Linear and Matrix Algebra

Partitioned Matrices

Nonnegative Matrices

Generalized and Conditional Inverses

Solutions of Linear Equations

Idempotent Matrices

Trace of Matrices

Derivatives of Quadratic and Linear Forms

Expectation of a Matrix

Evaluation of an Integral

Statistical Concepts

Introduction

Random Variables and Distribution Functions

Moment Generating Function

Independence of Random Vectors

Special Distributions and Some Important Formulas

Statistical Inference

Point Estimation

Hypothesis Testing

Confidence Intervals

Comments on Statistical Inference

Problems

The Multidimensional Normal Distribution

Introduction

The Univariate Normal Distribution

Multivariate Normal Distribution

Marginal Distributions

Independent and Uncorrelated Random Vectors

Conditional Distribution

Regression

Correlation

Examples

Problems

Distributions Of Quadratic Forms

Introductions

Noncentral Chi-Square Distribution

Noncentral F and Noncentral t Distributions

Distribution of Quadratic Forms in Normal Variables

Independence of Linear Forms and Quadratic Forms

Expected Value of a Quadratic Form

Additional Theorems

Problems

Models

Introduction

General Linear Model

Linear Regression Model

Design Models

Components-of-Variance Model

General Linear Model

Introduction

Point Estimation standard deviation and Linear Functions of Beta [i]:Case 1

Test of the Hypothesis Hb =h: Case 1

Special Cases for Hypothesis Testing

Confidence Intervals Associated with the Test H[o]: Hb = h

Further discussion of Confidence Intervals Associated with the Test H[o]: Hb = h

Example

The General Linear Model, Case 1, and sum is not equal to the standard deviation x Y

Examination of Assumptions

Inference in the Linear Model: Case 2

Further Discussion of the Test Hb =h

Computing Techniques

Introduction

Square root Method of Factoring a Positive Definite Matrix

Computing Point Estimates, Test Statistics, and Confidence Intervals

Analysis of Variance

The Normal

Equations Using Deviations from Means

Some Computing Procedures When cov[Y] = the standard deviation x V

Appendix

Problems

Applications Of The General Linear Model

Introduction

Prediction Intervals

Tolerance Intervals

Other Tolerance and Associated Intervals

Determining x for a Given Value of Y (The Calibration Problem)

Parallel, Intersecting, and Identical Models

Polynomial Models

Trigonometric Models

Designing Investigations

Maximum or Minimum of a Quadratic Function

Point of Intersection of Two Lines

Problems

Sampling From The Multivariate Normal Distribution

Introduction

Notation

Point Estimators of the population mean and the sum

Test of the Hypothesis H[o] :population mean = h[o]

Confidence Intervals on l'' [I] population mean, for I = 1,2,?, q Computations

Additional Theorems about mu (hat) and sum (hat) Problems

Multiple Regression

Introduction

Multiple Regression Model: Case I, Case II, and Point Estimation

Multiple Regression Model: Confidence Intervals and Test Hypothesis, Case I and Case II

Confidence Intervals and Tests of Hypothesis for Case I of the Design Model

Computations

The One-Factor Design Model

Further Discussion of Tests and Confidence Intervals for the Design Models

Problems

Two-Factor Design Model

Introduction

Tw

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