The method of least squares enables the determination of an estimate of the slope and intercept of a straight line relationship between two quantities or variables X and Y. Although a theoretical relationship may exist between X and Y of the form Y = mX + c, in practice experimental or measurement errors will occur, and the observed or measured…

The normal equations discussed in this paper for a least-squares parabolic fit have a unique solution if and only if there are at least three different x-values in the observations. This requirement is satisfied by most real sets of quantitative observations. For particular data sets, the appropriateness of parabolic fits should be assessed with…

In this article, the author takes up the special trinomial (1 + x + x[squared])[superscript n] and shows that the coefficients of its expansion are entries of a Pascal-like triangle. He also shows how to calculate these entries recursively and explicitly. This article could be used in the classroom for enrichment. (Contains 1 table.)