Dear T. Rajaseenivasan,

What is A, B, C???

Dear Lov Kumar

A, B, C are variable parameters and measured from experimental runs. 

Dear T. Rajaseenivasan

You may use this command in matlab to compute the value of A, B, and C.

If you simplify this equation, this equation is similar to linear equation i.e.,

U=D. A^x. B^y. C^z

LogU=Loh D+x*LogA+y*LogB+z*LogC

Y=C1+C2*x+c3*y+C4*z

where Y=LogU, C1=LogD etc...

then u use this command:

beta = mvregress(X,Y) returns the estimated coefficients for a multivariate normal regression of the d-dimensional responses in Y on the design matrices in X.

where beta show the constant and coefficient values, After getting the values of beta, you can easily compute the value of A, B, C, and D

e.g. if C2=0.2

LogA=0.2

A=e^0.2

You could transform this equation by taking the logarithm of both sides of the equation to convert it to a linear equation and then perform linear regression. After that you can the anti-log.

Here is how your equation will look like after the logarithmic transformation:

Log(M) = x.log(A) + y.log(B) + z.log(C)

Hope this helps answer your question.

Dear Lov Kumar

Thank you very much for your guidelines. 

Dear Prof. Yehia F. Khalil

Thank you very much for your guidelines.  Surely it help. 

Dear Rajaseenivasan,

you can use excel for this purpose

Please see this link:

http://www.wikihow.com/Run-a-Multiple-Regression-in-Excel

Regards

Dear Prof. Nader Rahbar

Thank you very much for your guidelines. 

Dear Rajaseenivasan,

you can use minitab software 

Use MATLAB

Dear Immanual.R

Thank you very much

Dear Mohamed A. Sharaf Eldean

Thank you very much

Dear T.R., Please first reconsider what the unknowns are. According to your reply to Lov Kumar, A, B and C are measured from experimental runs, whereas all other proposals implicitly assume that A, B and C are the unknowns of the regression equation. Anyhow, the right thing to do is to work on log-scale in U. However, check also if the magnitude of the errors in U from the fitted function appear to be approximately proportional to the level of U itself (or equivalently, the errors in log U approximately independent of the log U level), otherwise you should perhaps use a weighted regression of log U on its regressors. 

Best wishes, Rolf Sundberg