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Theory and Application of the Linear Model

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ISBN-10: 0534380190

ISBN-13: 9780534380199

Edition: 1976

Authors: Franklin A. Graybill

List price: $199.95
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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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Book details

List price: $199.95
Copyright year: 1976
Publisher: Brooks/Cole
Publication date: 3/27/2000
Binding: Paperback
Pages: 204
Size: 7.25" wide x 9.00" long x 1.25" tall
Weight: 2.398
Language: English

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
Multiple Regression Model: Case III
Problems
Correlation
Introduction, Simple Correlation, Partial Correlation, Multiple Correlation
Correlation for Non-normal p.d.f.''s
Correlation and Independence of Random Variables
Problems
Some Applications Of The Regression Model
Introduction
Prediction
Selecting Variables for a Model
Growth Curves
Discrimination (Classification)
Problems
Design Models
Introduction
Point Estimation for the Design Model
Case I
Point Estimation for the Design Model
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