Fitting nature's basic functions. I. Polynomials and linear least squares

The problem of fitting a mathematical model which depends on an n-vector of unknown parameters, to a measured data set is ubiquitous in science and engineering. This paper is the first installment of a series that will demonstrate modern techniques for fitting combinations of basic mathematical functions to measured real-world data. Fitting a straight line, linear least squares and the best linear unbiased estimate are discussed.