I need an algorithm to best-fit a curve

[Jamin2112]

I'm making an applet for distance runners that predicts their finish time for any distance, using recent race times for any distance. For example, a user might enter 3 recent race times which are 16:37 for a 5k (5:21 min/mile pace), 27:42 for an 8k (5:34 min/mile pace), and 35:18 for a 10k (5:41 min/mile pace), then my "finish time calculator" could predict their finish time for a race of any distance. I've found that distance vs. pace follows a logistic curve like the one pictured below.


http://luna.cas.usf.edu/~mbrannic/files/pmet/image329.gif



Hence I want to predict their race finish times using a logistic function f(x) = C₁(1/(1+C₂e^-C₃x)). How do I do this, though?

 

[Number Nine]

Standard non-linear regression problem. Any statistics software (e.g. R) will let you fit the curve fairly easily.

 

[Jamin2112]

Standard non-linear regression problem. Any statistics software (e.g. R) will let you fit the curve fairly easily.

I was actually going to recreate the algorithm in Javascript since I'm putting this "finish time calculator" on a site.

 

[hotvette]

You can get the basic algorithm from here:

http://mathworld.wolfram.com/NonlinearLeastSquaresFitting.html

http://en.wikipedia.org/wiki/Gauss–Newton_algorithm

 

[Levex]

You could try Lagrange Interpolation.
Although it may have divergence, it will certainly pass through those points.