The Polynomial of Best Fit

To test a sample data set for linearity, we can compute a number r in [-1,1] called the correlation coefficient whose absolute value is a measure of how much the data corresponds to a linear representation. We can also construct the so-called regression line that is the best linear fit to the data. If the correlation coefficient is small (closer to 0) the regression line will not correspond very well with the data. If the correlation coefficient is closer to 1 in absolute value, the regression line will correspond increasingly well with the data. This topic is discussed in detail, including the derivation of the regression line as the best fit with several examples, as well as the idea of "best fit" extended to higher degree polynomials, in the paper The Polynomial of Best Fit, where we can see that the linear case is just a special case of the general polynomial of best fit.

Calculating Square Roots By Hand

Before the days when students carried personal calculators that gave instantaneous square root calculations, that is, pre-1970's, most were taught a mysterious method that was accepted without understanding the logic behind it and therefore often forgotten. In the paper Algorithm to Compute the Square Root the technique is re-visited and examples and a justification are provided.