An Executive Summary on Systematic Error for Least Squares

 If one needs a quick reference an executive summary on the systematic error for an ordinary least squares fit might prove useful.

Science and Education employ transmission lines for communications and losses can occur as one moves farther from the source in distance and time and the quality of the source varies. If we want scientists and educators to be responsible citizens of a country or the world at large they all must share a responsibility for keeping a watch out for misrepresentations of knowledge passed on to others. If one is for a "rule of law" one cannot disregard the "laws of nature."

When presenting a thesis or the results of an experiment one needs to adopt a defensible position. Any systematic error present raises some doubts about the conclusions or results. If one wants to build up some structure it has to be built on solid ground.

Supplemental (Jun 13): Here's an example of the determination of an ordinary least squares regression line in Barreto & Howland, Introductory Econometrics and an indication the slope is an unbiased estimator. The formulas employ a different notation but are equivalent to what is used above.

The denominator used in the book is the sum of the square of the deviation from the mean whose average is the standard deviation, s_x, used above. The numerator is related to the covariance of X and Y.