PolyFit: A C++ code for Polynomial Curve Fit with Calculation of Error Bars

Abstract

In radiobiology, many dose-response results are modeled using the so-called linear-quadratic(LQ)model, which means that results are modeled as a function of dose Das 𝑅(𝐷)=𝛽0+𝛽1𝐷+𝛽2𝐷2. The coefficients 𝛽0, 𝛽1and 𝛽2are obtained from fitting a series of data points (𝑥𝑖,𝑦𝑖), which is usually done using a least-square method. The LQ and more generally the polynomial fit capability is implemented in many software that analyzes data. However, it is often convenient to do the fitting programmatically, especially when a large number of datasets should be analyzed. Furthermore, depending on the software used, some features may not be implemented. In this mini-review, I discuss the basis of polynomial fitting, including the calculation of errors on the coefficients and results, use of weighting and fixing the intercept value (the coefficient 𝛽0). A simple C++ code to perform the polynomial curve fitting is also provided. This code should be useful not only in radiobiology but in other fields of science as well.