# Applied Regression Analysis and Experimental Design

## 1st Edition

CRC Press

256 pages

Hardback: 9780824772529
pub: 1985-04-25
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eBook (VitalSource) : 9781315137674
pub: 2018-12-13
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### Description

For a solid foundation of important statistical methods, the concise, single-source text unites linear regression with analysis of experiments and provides students with the practical understanding needed to apply theory in real data analysis problems.

Stressing principles while keeping computational and theoretical details at a manageable level, Applied Regression Analysis and Experimental Design features an emphasison vector geometry and least squares to unify and provide an intuitive basis for most topics covered… abundant examples and exercises using real-life data sets clearly illustrating practical of data analysis…essential exposure to MINITAB and GENSTAT computer packages , including computer printouts…and important background material such as vector and matrix properties and the distributional properties of quadratic forms.

Designed to make theory work for students, this clearly written, easy-to-understand work serves as the ideal texts for courses Regression, Experimental Design, and Linear Models in a broad range of disciplines. Moreover, applied statisticians will find the book a useful reference for the general application of the linear model.

Preface

Fitting a Model to Data

Introduction

How to Fit a Line

Residuals

Transformations to Obtain Linearity

Fitting a Model Using Vectors and Matrices

Deviations from Means

An Example- Value of a Postage Stamp Over Time

Problems

Goodness of Fit of the Model

Introduction

Coefficient Estimates for Univariate Regression

Coefficient Estimates for Mulitvariate Regression

ANOVA Tables

The F Test

The Coefficient of Determination

Predicted Values of Y and Confidence Intervals

Residuals

Reduced Models

Pure Error and Lack of Fit

Example- Lactation Curve

Problems

Which Variable Should Be Included in the Model

Introduction

Orthogonal Predictor Variables

Linear Transformations of the Predictor Variables

Correlation Form

Variable Selection- All Possible Regressions

Variable Selection- Sequential Methods

Qualitative (Dummy) Variables

Aggregation of Data

Problems

Peculiarities of Observations

Introduction

Sensitive or High Leverage Points

Outliers

Weighted Least Squares

More on Transformations

Eigenvalues and Principal Components

Ridge Regression

Prior Information

Cleaning up Data

Problems

The Experimental Design Model

Introduction

What Makes an Experiment

The Linear Model

Tests of Hypothesis

Testing of Assumptions

Problems

Assessing the Treatment Methods

Introduction

Specific Hypothesis

Contrasts

Factorial Analysis

Unpredicted Effects

Conclusion

Problems

Blocking

Introduction

Structure of Experimental Units

Balanced Incomplete Block Designs

Confounding

Miscellaneous Tricks

Problems

Extensions to the Model

Introduction

Hierarchic Designs

Repeated Measures

Covariance Analysis

Unequal Replication

Modeling the Data

Problems

Appendix A Review of Vectors and Matrices

Some Properties of Vectors

Some Properties of Vector Spaces

Some Properties of Matrices

Appendix B Expectation, Linear and Quadratic Forms

Expectations

Linear Forms

The F-Statistic

Appendix C Data Sets

Ultra-Sound Measurements of Horses Hearts

Ph Measurement of Leaf Protein

Lactation Records of Cows

Sports Cars

House-Price Data

Computer Teaching Data

Weedicide Data

References

Index