What is the least squares regression line?
Please see below for details.
The linear line that fits the statistical pattern of a set of paired data as closely as possible is the linear fit.
There may be many possible linear fits, but the least-squares regression line is the one that has the smallest possible value for the sum of the squares of the residuals.
In other words, though the average variation of observed value from linear fit may be zero for many, in least-squares regression line, what is desired that squares of the deviations are least.