# Mathematical model building with dependent and independent variables

I have been working with data and building models on data. I have developed models in regression using cubic and power series. It works fine for variables with one dependent and one independent variable.

What kind of technique is to be adopted if I have to find an equation or model for say, D depends on C, C changes for a set of B, which changes for different A.

I can carry our bi-variate correlation to find significance. But, that is not something I am interested in. I have data, but wondering as to how to fit a model in those lines. I have tried building models with regression, line fitting and get a relationship between D and C, or D and B. Good fits with varying constants, but no relationship between the others.

Is there a way to combine and build a model altogether?

What is that kind of analysis called?

How to go about it? Any software that would help me do it? I have been using SPSS, Minitab, and R.

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## 1 Answer

Are you perhaps thinking of simultaneous equation models and seemingly unrelated regressions? In such a model you could have for example:

\begin{align} D&=\alpha_1+\beta_1C+u_1\\ C&=\alpha_2+\beta_2B+u_2\\ B&=\alpha_3+\beta_3A+u_3 \end{align} Depending on your assumptions and pre-estimation information you can estimate using different techniques allowing for different types of relationships between the equations. Have a look here and maybe at Wooldridge's Analysis of Cross Section and Panel Data.

• The data need not be linearly related. So, this would not be apt. – Next Door Engineer Sep 25 '13 at 9:50
• @user2054780 Ah, right. A simultaneous equation model need not be, though. In the book I mentioned as a reference there's a section about "Systems of Nonlinear Equations" which can be estimated by Generalized Method of Moments (GMM). – hejseb Sep 25 '13 at 9:54