 # Reverse Analysis of a Multiple Regression Problem

Is it possible to reverse analyse a regression equation? For example, let’s say i have a regression equation y=b+a1x1+a2x2+a3x3+a4x4.
y -dependent variable,x1,x2,x3,x4 - independent variable, a1,a2,a3,a4- coefficients. Now, if ‘y’ is given, can i estimate x1,x2,x3,x4 and their coefficients? Is there any algorithm or package in R or python to solve this?

I understand where are you coming from .
If we want to predict x1,x2,x3,x4,x5 we can either go for multi value regression ,or the other way is considering this problem as a encoder kind of thing and you can train neural network .
Also you can explore about genetic optimization algorithims .

I hope these suggestions help !! Happy learning !! Hello Palbha,

Thank you for your response. I am new to the analytics field. Could you refer me any links to understand the concepts suggested?

If I understand your question well,
A simple approach will be to fit the model again, if you use the same fitting procedure on the same observations you will end up with the same model otherwise you would have a good approximation.

Also, if you already have y and the coefficients vector you can estimate your feature vector X by solving the linear system given that (n >= p) where p is the number of features and n the number of observations your model was regressed on.