Title:
Theory and application of the linear model
Personal Author:
Publication Information:
North Scituate, Mass. : Duxbury Press, 1976
ISBN:
9780878721085
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000001867443 | QA279 G73 1976 | Open Access Book | Book | Searching... |
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Searching... | 30000000859961 | QA279 G73 1976 | Open Access Book | Book | Searching... |
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Summary
Summary
In this book, 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.
Table of Contents
| Preface |
| 1 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 |
| 2 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 |
| 3 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 |
| 4 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 |
| 5 Models |
| Introduction |
| General Linear Model |
| Linear Regression Model |
| Design Models |
| Components-of-Variance Model |
| 6 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 |
| 7 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 |
| 8 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 |
| 9 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 |
| 10 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 |
| 11 Correlation |
| Introduction, Simple Correlation, Partial Correlation, Multiple Correlation |
| Correlation for Non-normal p.d.f.''s |
| Correlation and Independence of Random Variables |
| Problems |
| 12 Some Applications Of The Regression Model |
| Introduction |
| Prediction |
| Selecting Variables for a Model |
| Growth Curves |
| Discrimination (Classification) |
| Problems |
| 13 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 |
| 14 Two-Factor Design Model |
| Introduction |
| Tw |
