Olive David J. Linear Regression

New York: Springer, 2017. — 497 p. — ISBN: 978-3-319-55250-7.This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models.
There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response transformations for multiple linear regression or experimental design models.
This text is for graduates and undergraduates with a strong mathematical background. The prerequisites for this text are linear algebra and a calculus based course in statistics.Some Regression Models
Multiple I.im'ar Regression
Variable Selection
Other Issues
Complements
Problems
Multiple Linear Regression
The MLB Model
Checking Goodness of Fit
Checking Lack of Fit
The ANOVA F Test
Prediction
The Partial F Test
The Wald t Test
The OLS Criterion
Two Important Special Cases
The No Intercept MLR ModelComplements
Problems
Building an MLR Model
Predictor Transformations
Graphical Methods for Response Transformations
Main Kneels, Interaelions, and Indicators
Variable Selection
Diagnostics
Outlier DetectionComplements
Problems
WLS and Generalized Least Squares
Random Vectors
GLS, WLS, and FGLS
Inference for GLS
Complements
Problems
One Way AnovaFixed Effects One Way Anova
Random Effects One Way Anova
Response Transformations for Experimental DesignComplements
Problems
The K Way Anova Model
Two Way Anova
K Way Anova ModelsComplements
Problems
Block Designs
One Way Block Designs
Blocking with the K Way Anova Design
Latin Square DesignsComplements
Problems
Orthogonal Designs
Factorial Designs
Fractional Factorial Designs
Plackett Burman DesignsComplements
Problems
More on Experimental Designs
Split Plot Designs
Review of tlie DOE ModelsComplements
Problems
Multivariate Models
The Multivariate Normal Distribution
Elliptically Contoured Distributions
Sample Mahalanobis Distances
Complements
Problems
Theory for Linear Models
Projection Matrices and the Column Space
Quadratic Forma
Least Squares Theory
Nonfull Rank Linear ModelsComplements
Problems
Multivariate Linear RegressionPlots for the Multivariate Linear Regression Model
Asymptotically Optimal Prediction Regions
Testing Hypotheses
An Example and SimulationsComplements
Problems
GLMs and GAMsAdditive Error Regression
Binary, Binomial, and Logistic Regression
Poisson Regression
Inference
Variable Selection
Generalized Additive Models
Overdispersion
Complements
Problems
Stuff for Students
R and Arc
Hints for Selected Problems
Tables