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Probability and Statistics with Reliability, Queuing, and Computer Science Applications, 2nd Edition by Kishor S. Trivedi

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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 c11-math-0003 and its estimator c11-math-0004. 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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