Allen M.P. Understanding Regression Analysis

New York: Springer, 1997. — 226 p.By assuming it is possible to understand regression analysis without fully comprehending all its underlying proofs and theories, this introduction to the widely used statistical technique is accessible to readers who may have only a rudimentary knowledge of mathematics. Chapters discuss:
-descriptive statistics using vector notation and the components of a simple regression model;
-the logic of sampling distributions and simple hypothesis testing;
-the basic operations of matrix algebra and the properties of the multiple regression model; -testing compound hypotheses and the application of the regression model to the analyses of variance and covariance, and
-structural equation models and influence statistics.The origins and uses of regression analysis
Basic matrix algebra: Manipulating vectors
The mean and variance of a variable
Regression models and linear functions
Errors of prediction and leastsquares estimation
Leastsquares regression and covariance
Covariance and linear independence
Separating explained and error variance
Transforming variables to standard form
Regression analysis with standardized variables
Populations, samples, and sampling distributions
Sampling distributions and test statistics
Testing hypotheses using the t test
The t test for the simple regression coefficient
More matrix algebra: Manipulating matrices
The multiple regression model
Normal equations and partial regression coefficients
Partial regression and residualized variables
The coefficient of determination in multiple regression
Standard errors of partial regression coefficients
The incremental contributions of variables
Testing simple hypotheses using the F test
Testing compound hypotheses using the F test
Testing hypotheses in nested regression models
Testing for interaction in multiple regression
Nonlinear relationships and variable transformations
Regression analysis with dummy variables
Oneway analysis of variance using the regression model
Twoway analysis of variance using the regression model
Testing for interaction in analysis of variance
Analysis of covariance using the regression model
Interpreting interaction in analysis of covariance
Structural equation models and path analysis
Computing direct and total effects of variables
Model specification in regression analysis
Influential cases in regression analysis
The problem of multicollinearity
Assumptions of ordinary leastsquares estimation
Beyond ordinary regression analysis