Polynomial Fitting

In various scientific fields, we often have data that we need to model using a mathematical equation. This is also called curve fitting, and when the mathematical equation of the model is a polynomial, we call it polynomial fitting.

Root mean square error

One way to quantify the fit between data and a model is to compute the root mean square error. This error is defined as the difference between the observed value and the modeled value. The term ‘error’ is also sometimes known as residual. If the error of data point $i$ is written as $\varepsilon_{i}$, and the total number of observations is $N$, then the sum of squared errors $S$ is:

$$S=\sum\varepsilon_{i}^2$$ ...