Mathematics of Fitting Scientific Data

Synopsis

The ability to make predictions based upon scientific data is fundamentally important. Interpolation and extrapolation of data allow researchers to predict how a system will behave and sometimes elucidate the mechanisms responsible for observed behaviors. The usual way of fitting scientific data is via least squares regression, a systematic process for identifying curves that “best” fit a data set. This essay explains the process of least squares regression for fitting several types of curves (linear, power, exponential) to data sets. Also included are general guidelines for selecting which type of function to use, as well as a list of key issues to be aware of when fitting data.

Introduction

Processing and interpreting experimental data is one of the most vitally important steps in the process of scientific research. Once data is collected, researchers are typically concerned with questions such as:

• 1. Does the data look “believable” in the sense that there are no obvious...