Chapter 47: Least Squares Regression: Situation 41 From the MACMTL-CPTM Situations Project

During a discussion of lines of best fit, a student asked why the sum of the squared differences between predicted and actual values was used. She asked, “Why use squared differences to find the line of best fit? Why use differences rather than some other measure to find the line of best fit?”

The set of Foci provide reasons why the sum of the squared residuals, differences between the predicted and actual values, is used when determining lines of best fit. Focus 1 highlights why summing the residuals is not sufficient for determining a line of best fit. The remaining Foci highlight the computational advantages of the squared residuals over other alternatives. Focus 2 examines why one would sum the squared residuals as opposed to summing the absolute value of the residuals. Focus 3 deals with why one would sum the squared residuals as opposed to summing the squared perpendicular distances.