Why Is the Least Squares Line the Best Choice?Date: 11/03/2005 at 17:42:08 From: Jane Subject: Least sqares: probability When obtaining a prediction line for the relationship between certain variables, one method which may be used to identify the best line is to find the least-squares line. The least squares line minimizes the error between the two variables. What about the least squares line makes it best? Thank you for your help, Dr. Math. Date: 11/04/2005 at 14:41:14 From: Doctor George Subject: Re: Least sqares: probability Hi Jane, Thanks for writing to Doctor Math. If you plot your data it should be approximately straight, otherwise there is no sense in looking for a best fit line. There is nothing about least squares that makes it intrinsically THE best fit. A best fit line is only "best" based on some criterion, and there are other possible criteria to use besides least squares. The criterion is usually a matter of minimizing some quantity. Least squares minimizes a sum of squared distances. Every other possible line will have a greater sum of squared distances. Other not uncommon criteria are minimizing the sum of absolute distances, or minimizing the maximum of the distances. Does that make sense? Write again if you need more help. - Doctor George, The Math Forum http://mathforum.org/dr.math/ |
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