How can I find the relationship (equation) between three independent variables and one dependent variable?

Hello.

I am having a hard time finding the relationship between three independent variables and one dependent variable. I know that there exists a relationship between the four, as I took the data from a published article. However, the equation written in the article was in terms of one variable, and I need it written in terms of one of another variable.

The variables (if this helps) are temperature (T), density (rho), salinity (S), and pressure (pressure). For this problem, rho=rho(T,S,pressure). I know with the curvefitting toolbox that you can have two independent variables and one dependent variable, but this doesn't really help me out.

Does anyone have any suggestions? Thanks.

-Ashley

Answer 1

[Star Strider]

It seems yours may be a multiple linear regression problem. First, all your variables have to be column vectors. Then:

rho = [T S P] * B

where B is your parameter vector. To calculate B from your data, I suggest:

TSP = [ones(size(T)) T S P];

B = TSP\rho

You can also use regress. It has the advantage of providing statistics on the parameters and the fit. The additional ones column fits a constant, and is usually required for an appropriate fit. The constant is equivalent to the y-intercept in the standard linear equation y=m*x+b.

If it is a nonlinear regression problem, lsqcurvefit and nlinfit can both take matrix independent variables and will fit a vector or matrix of dependent variables. That is controlled by your objective function, so as long as it works with the calling routines, you shouldn't have a problem.