Understanding Least Squares through Monte Carlo Calculations.

LEAST squares; MONTE Carlo method; NUMERICAL analysis; PHYSICAL scientists; ERROR analysis in mathematics; MATHEMATICS

The article explains the concept of least squares (LS) through monte carlo (MC) calculations. The method of LS is arguably the most important data analysis tool available to physical scientists. The statistical properties of linear least squares (LLS) are well established. If the data errors are normal, then the LLS estimators will also be normally distributed. If the data are weighted in accord with their inverse variances, the LLS estimators will also be minimum variance. The present MC computations serve to illustrate and confirm known properties of LLS under the usual assumptions of normally distributed random error in the data and proper weighting in their analysis.