Linear Models

This chapter is devoted to statistical problems arising in situations where the observed values (called “dependent variable,” “response,” etc.) are influenced by some other variable. It considers the case where only expected values are affected, while other characteristics (as well as the type of distribution) remain the same. The chapter discusses the methods of detecting and measuring effects expressed through the mean of the observed random variable. It presents only the most common of such methods, regression analysis and analysis of variance. The results obtained from the methods can be used to build estimators and to construct tests of hypotheses about linear combinations of the regression coefficients. The chapter illustrates the situation with an example. Testing for the presence of interaction is based on an idea similar to that used in testing linearity of regression.