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Introduction to Least Squares Method

Often, when experimental results are collected, the plotted x- and y-pairs will not all lie exactly along one straight line. Random sampling error accounts for some of the variation, since the data collected during an experiment is only a sample of the possible sets of data that could be collected. The line of best fit to such data can be calculated by eye (acceptable in some cases) or can be calculated by the least squares method.

Examine the plot below. Three different individuals have drawn, by eye, three different lines of best fit through the data. Which one of these is really the "best" fit to the data?