Least squares polynomial approximation

Least squares polynomial approximation is a mathematical method used to find a polynomial function that best fits a set of data points. Imagine you have scattered dots on a graph representing measurements or observations. The goal is to draw a smooth curve that comes as close as possible to all these dots. The "least squares" part refers to minimizing the difference between the actual data points and the values predicted by the polynomial, specifically by minimizing the sum of the squares of these differences. This approach helps in making predictions and understanding underlying trends in the data.