# Regression analysis

Reference work entry

First Online:

**DOI:**https://doi.org/10.1007/1-4020-0611-X_871

## INTRODUCTION

In almost all fields of study, the researcher is frequently faced with the problem of trying to describe the relation between a response variable and a set of one or more input variables. Given data on input (predictor, independent) variables labeled

*x*_{1},*x*_{2},...,*x*_{p}and the associated response (output, dependent) variable*y*, the objective is to determine an equation relating output to input. The reasons for developing such an equation include the following:- 1.
to predict the response from a given set of inputs;

- 2.
to determine the effect of an input on the response; and

- 3.
to confirm, refute, or suggest theoretical or empirical relations.

To illustrate, the simplest situation is that of a single input for which a linear relation is assumed. Thus, if the relation is exact, it is given for appropriate values of β

_{0}and β_{1}byThis is a preview of subscription content, log in to check access.

## References

- [1]Belsley, D.A., Kuh, E., and Welsch, R.E. (1980). Regression Diagnostics, Wiley, New York.Google Scholar
- [2]Daniel, C. and Woods, F.S. (1971). Fitting Equations to Data, Wiley, New York.Google Scholar
- [3]Draper, N.R. and Smith, H. (1966). Applied Regression Analysis, Wiley, New York.Google Scholar
- [4]Gunst, R.F. and Mason, R.L. (1980). Regression Analysis and Its Applications, Marcel Dekker, New York.Google Scholar
- [5]Neter, J. and Wasserman, W. (1974). Applied Linear Statistical Models, Richard D. Irwin. Homewood, Illinois.Google Scholar

## Copyright information

© Kluwer Academic Publishers 2001