[RESOLVED] Need a formula

[BlindSniper]

Hi all,
I have a strange request, I need to calculate a formula based on the terms given.
f(27.1864667) = 1.0
f(24.6676333) = 2.0
f(2.2479) = 10.9

So I basically need to know what f(X) is. Any ideas ?

EDIT: More info, This is to calculate score of a shooting target from the furthest point from the centre that the bullet hole made, all the rings are equally spaced so it should be linear equation.

[jemidiah]

There are infinitely many answers, though after plotting your data it is extremely close to linear. A linear least-squares regression gives

f(x) = 29.7056 - 2.51906x

courtesy of Wolfram Alpha.


The residuals are extremely small, with magnitude less than 0.0001, so the fit is excellent.

[Logophobic]

@jemidiah: You mixed up your variables.

Assuming a linear equation (y = mx + b), we can solve for the first two equations to find m = -0.39700919 and b = 11.793277. This result fits well with the third equation.

f(x) = 11.793 - 0.397x

f(27.1864667) = 0.9999727201
f(24.6676333) = 1.999949699
f(2.2479) = 10.9005837

[BlindSniper]

The formula's result will be rounded to the first digit, which means it doesn't have to be exact. I am going to post more values later today and they will be more accurate.

[BlindSniper]

@jemidiah: You mixed up your variables.

Assuming a linear equation (y = mx + b), we can solve for the first two equations to find m = -0.39700919 and b = 11.793277. This result fits well with the third equation.

f(x) = 11.793 - 0.397x

f(27.1864667) = 0.9999727201
f(24.6676333) = 1.999949699
f(2.2479) = 10.9005837

Your formula seems to be what I need . I will test it thoroughly and if it works I will be a very happy man.

[BlindSniper]

I recalculated the values and then threw them at wolfram alpha and now I have a good working formula.
Thanks guys.

[jemidiah]

Hah, how silly of me. I'm sorry for the mix-up, though at least my link was useful.