A Polynomial Curve Mapping Technique for Random Data

Abstract

The study of a new unknown phenomenon/system begins with an experimental/ observational study. Statistical and regression analysis of the recorded random data is carried out to examine the characteristic features and behavior of the new phenomenon/system. The recorded data and observed statistical features are used to develop a mathematical model which closely represents the system. This helps in duplicating the new systems through simulation studies. To observe the behavior of dependent output response vis-à-vis independent input to the system under observation, curve fitting techniques are used. Most commonly used being least square based linear regression and non-linear regression techniques. These techniques have their own merits and demerits. In this paper a new polynomial based regression technique is presented. The technique performs exceptionally well within the given range of the independent variable and perfectly maps the observed points to the curve. It helps in predicting the values of the dependent variable with good accuracy in close proximity of the considered independent variable range.