Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: Notesfiles; site ea.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxl!ihnp4!inuxc!pur-ee!uiucdcs!ea!mwm From: mwm@ea.UUCP Newsgroups: net.math Subject: Re: Best fitting curve - (nf) Message-ID: <6900003@ea.UUCP> Date: Tue, 26-Jun-84 15:08:00 EDT Article-I.D.: ea.6900003 Posted: Tue Jun 26 15:08:00 1984 Date-Received: Sat, 30-Jun-84 02:38:48 EDT References: <1970@sdccsu3.UUCP> Lines: 24 Nf-ID: #R:sdccsu3:-197000:ea:6900003:000:666 Nf-From: ea!mwm Jun 26 14:08:00 1984 #R:sdccsu3:-197000:ea:6900003:000:666 ea!mwm Jun 26 14:08:00 1984 /***** ea:net.math / sdccsu3!ee171bbr / 11:16 pm Jun 24, 1984 */ Given three points, what is the equation of the best fit curve. John F. /* ---------- */ The best fit curve is a second or higher degree polynomial that passes through the three points. How much better than that can you get? The equation is (for (x1, y1), (x2, y2), (x3, y3)): 0 = (x-x1) (x-x2) y3 / [(x3-x1) (x3-x2)] + (x-x2) (x-x3) y1 / [(x1-x2) (x1-x3)] + (x-x3) (x-x1) y2 / [(x2-x3) (x2-x1)] That this passes through all three points should be obvious. Of course, you may have some other definition of best fit. In that case, you'll have to tell us what you mean by best fit.