Understanding regression analysis

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 least-squares estimation -- Least-squares 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 -- One-way analysis of variance using the regression model -- Two-way 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 least-squares estimation -- Beyond ordinary regression analysis.

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