An Introduction to Probability and Statistical Inference, 2nd Edition

Chapter 13

A simple linear regression model

This is a rather extensive chapter on an important subject matter with an abundance of diverse applications. The basic idea involved may be described as follows. There is a stimulus, denoted by x, and a response to it, denoted by y. At different levels of x, one observes the respective responses. How are the resulting (x, y) pairs related, if they are related at all? There are all kind of possibilities, and the one discussed in this chapter is the simplest such possibility, namely, the pairs are linearly related.

In reality, what one, actually, observes at x, due to errors, is a value of a r.v. Y, and then the question arises as to how we would draw a straight line, which would lie "close" to most ...