# Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

# Regression analysis

• Irwin Greenberg
Reference work entry
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. 1.

to predict the response from a given set of inputs;

2. 2.

to determine the effect of an input on the response; and

3. 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 by
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## References

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