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. 13 Additional Chapters. Appendices. Index.