Non-trivial Non- linear fit

[Meriens]

Hi, I've got a problem with a nonlinear fit.
My function is this:
B1= a1+b1/tr+c1/tr3
B2= a2+b2/tr+c2/tr3
B3=a3+b3/tr+c3/tr3
Btot=x*B1+y*B2+z*B3
I've got two dataset (some values are given below), one containing the Btot and Tr ed one containing x,y,z. My target is to make a regression to obtain the values a,b,c of every equation using only one regression.
In other words,
If I make a single regression for every x,y,z of the second dataset, my regressione will be indipendent and the coefficients will appear different for every regression.
So I want find a way to make only one regression by changing into this operation Btot, Tr, x,y,z. So my coefficients will not be indipendent and for example the values of Btot and Tr of R11 will be associated with values of x,y, z corresponding to R11.
I wish my explanation is clear. sorry for my english!
Example of data:


x
y
z
R11
1
3
1
R12
1
2
2
R13
1
1
3




Tr
B
R11
0,506697
-1150,00

0,53028
-1070,00

0,601049
-862,00
R12
0,605006
-813

0,630972
-732

0,656938
-666
R13
0,871358
-251,4

0,90447
-233,5

0,937583
-217,2

MaryRam

[da...@wolfram.com]

For simultaneous data fitting, see references available at

http://forums.wolfram.com/mathgroup/archive/2011/Sep/msg00555.html

Also might have a look at

http://mathematica.stackexchange.com/questions/866/simultaneously-fitting-multiple-datasets

Daniel Lichtblau
Wolfram Research