Remarks regarding least‐square formulæ
M. H. Doolittle · Terrestrial Magnetism and Atmospheric Electricity · 1918
For intelligent and profitable least‐square computation it is necessary that there shall be at least an antecedent working hypothesis, if not an established theory. The method of least squares assumes that within satisfactory limits the irregularities and observer's errors of opposite algebraic signs balance each other. By a least‐square computation the computer's discrepancies of opposite algebraic signs may be made to balance each other precisely; and if the preliminary assumption is tenable and the least‐square computation is controlled by the adopted standard of regularity, it follows that the computer's discrepancies represent within satisfactory limits the irregularities and observer's errors, and that conclusions may be deduced from those discrepancies with a satisfactory approximation to accuracy. If there is no such standard of regularity at the beginning, nothing better than an inconsequential formula can be expected at the end.