Brook R.J. Applied Regression Analysis and Experimental Design

Boca Raton: CRC Press, 2018. — 252 p.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 emphasis on 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.Half Title
Title Page
Copyright PageFitting a Model to DataHow 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 ModelCoefficient Estimates for Univariate Regression
Coefficient Estimates for Multivariate 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 Variables Should Be Included in the ModelOrthogonal Predictor Variables
Linear Transformations of the Predictor Variables
Adding Nonorthogonal Variables Sequentially
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 ModelWhat Makes an Experiment
The Linear Model
Tests of Hypothesis
Testing the Assumptions
Problems
Assessing the Treatment MeansSpecific Hypothesis
Contrasts
Factorial Analysis
Unpredicted EffectsProblems
Blocking Introduction Structure of Experimental Units
Balanced Incomplete Block Designs
Confounding
Miscellaneous Tricks
Problems
Extensions to the ModelHierarchic Designs
Repeated Measures
Covariance Analysis
Unequal Replication
Modelling the Data
Problems
Review of Vectors and Matrices
Some Properties of Vectors
Some Properties of Vector Spaces
Some Properties of Matrices
Expectation, Linear and Quadratic Forms
Expectation
Linear Forms
Quadratic Forms
The F-Statistic Appendix
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