# Chapter 11Regression and Analysis of Variance

## 11.1 Introduction

In this chapter, we study aspects of **statistical relationships** between two or more random variables. For example, in a computer system the throughput *Y* and the degree of multiprogramming *X* might well be related to each other. One indicator of the association (interdependence) between two random variables is their correlation coefficient and its estimator . Correlation analysis will be considered in Section 11.6.

A related problem is that of predicting a value of system throughput *y* at a given degree of multiprogramming *x*. In other words, we are interested here in studying the dependence of *Y* on *X*. The problem then is to find a **regression line** or a **regression curve** that describes the dependence of *Y* on *X*. Conversely, we may also study the inverse regression problem of dependence of *X* on *Y*. In the remainder of this section we consider regression when the needed parameters of the population distribution are known exactly. Commonly, though, we are required to obtain a regression curve that best approximates the dependence on the basis of sampled information. This topic will be covered in Sections 11.3 and 11.4.

Another related problem is that of **least-squares curve fitting.** Suppose that we have two variables (not necessarily ...

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