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Currently we are working on a research paper in which we have conducted psychological experiment to get data-set. After that we have applied Multiple regression to find the relation among dependent variable and independent variables. our model was significant because Sig value was less the .05 and we found a good relation among dependent and independent variables.

Now my idea is, to develop new algorithm which will have different mathematical equations and all these equations will based on that regression analyses. For example if regression analysis shows that humidity have strong relation with rain. then we will say that "Humidity is directly proportional to rain".

So my question is, did we have formal mathematical techniques or any software tool which can provide different equations according with regression analysis.

Or

We will manually draw equations from that regression analyses.

Khan
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  • It has been a while, but if I am not mistaken, Multiple regression tries to minimize the variance with the least amount of solution vectors possible (main factors). All that is based on some linear model, also containing noise (unresolved variance). Depending on how many factors you found and the dimension of your solution vectors, you should be able to write up that linear model in form of a matrix, reflecting the linear equations. There is no differential equation involved, I think. In the end, you then estimate your models parameters...Or do I confuse it with factorial analysis? Hm.. – BitTickler Sep 01 '16 at 07:51
  • Yes, I think factor analysis is what you need for what you try to do: https://en.wikipedia.org/wiki/Factor_analysis and/or PCA https://en.wikipedia.org/wiki/Principal_component_analysis It should be noted, though, that the model you obtain with a PCA need not necessarily be related to the true underlaying model. Meaning, the model you find explains the variance but other models might do that, too. – BitTickler Sep 01 '16 at 07:57
  • Another approach (e.g. if time series are involved), is ARMA or ARIMA (name depends on source). With that, you will be in the realm of differential equations... – BitTickler Sep 01 '16 at 08:04

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