Re: y = (ax + b)/(cx+d)

In article <1144942045.178700.274600@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"patrick" <pleloux@xxxxx> wrote:

Hello,

I'm trying to solve a problem of the kind:

y = (ax + b)/(cx+d)

Here are some measures for x and y:

7.74 = (a(1)+b)/(c(1)+d)
14.88 = (a(2)+b)/(c(2)+d)
21.47 = (a(3)+b)/(c(3)+d)
27.55 = (a(4)+b)/(c(4)+d)

Is it possible to solve a, b, c and d?

In Mathematica you would enter

FindFit[{7.74, 14.88, 21.47, 27.55},
(a x + b)/(c x + d), {a, b, c, d}, x]

{a -> 1152.2966647720598, b -> -5.974838432436532,
c -> 6.318012128082086, d -> 141.80560677473076}

As Dave Dodson pointed out

if (a,b,c,d) is a solution, then (ka,kb,kc,kd) is a solution for
any nonzero value of k.

so you could set one of the parameters, say a to be 1:

FindFit[{7.74, 14.88, 21.47, 27.55},
(x + b)/(c x + d), {b, c, d}, x]

{b -> -0.005185156218650528, c -> 0.005482973539389342,
d -> 0.12306345330906956}

This solution is consistent with the above solution.

Cheers,
Paul

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