looking for a formula.

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2 total messages Started by ANDREW CHEYNE Thu, 12 Jan 1995 02:43

#112

Author: ANDREW CHEYNE
Date: Thu, 12 Jan 1995 02:43

19 lines
1725 bytes

Hello!

    I'm attempting to write a program that will read in a bunch of data 
points, perform a least squares fit to the points, and then draw the best 
fit line. I know the basics behind writing the program, but I'm in need of 
formulas that woud calculate m and b in y=mx+b. I know I should be able to 
figure these out with a little bit of calculus, but the calculus seems to 
lost on me! I also know that I should be able to do this using the Stats 
button on my TI-85, but I want to be able to integrate this program between 
the 85 and my PC. If anyone could mail me the formulas, I'd really 
appreciate it!

Thanks,
Andrew
[=-=-=]_____________________________________________________[=-=-=]
 |||||     Andrew Cheyne             006809c@axe.acadiau.ca  |||||     
  ---       233 Barrax                  Acadia University     ---
 |||||    (902) 542-0195                 Wolfville, NS       |||||
[=-=-=]-----------------------------------------------------[=-=-=]

Re: looking for a formula.

#113

Author: Andy Den Tandt
Date: Fri, 13 Jan 1995 12:58

45 lines
2463 bytes

ANDREW CHEYNE (006809c@axe.acadiau.ca) wrote:
: Hello!

:     I'm attempting to write a program that will read in a bunch of data 
: points, perform a least squares fit to the points, and then draw the best 
: fit line. I know the basics behind writing the program, but I'm in need of 
: formulas that woud calculate m and b in y=mx+b. I know I should be able to 
: figure these out with a little bit of calculus, but the calculus seems to 
: lost on me! I also know that I should be able to do this using the Stats 
: button on my TI-85, but I want to be able to integrate this program between 
: the 85 and my PC. If anyone could mail me the formulas, I'd really 
: appreciate it!

The general least squares fit for A.X=Y 
 with A   a (m x n) matrix,
      X   a (n x 1)  
      Y   a (m x 1)
For you, A=[ x0  1 ]  X= [m]  Y=[y0]
           [ x1  1 ]     [b]    [y1]
              etc.              etc.

                                T      T
is given by the lineair system A .A.X=A .Y, so you transpose A and 
multiply by AX and Y. 

There's allways a solution, but you need the one with the smallest 
length. I think that if your x0,x1.. aren't all the same, there should be 
only one solution. And if they are, the y's are it too, so you took only 
1 point, which is crazy.

Hope I helped.


************************************************************
Watch out! Even I am not perfect!
************************************************************

      ****************************
      **  Andy Den Tandt        **
      ****************************
      **  adntandt@rug.ac.be    **
      ****************************
      **  University of Ghent   **
      **  Belgium               **
      ****************************

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