# Logistic Regression - Finding out information about a particular $X_i$ when all other Xs and parameters are known

Suppose someone made the following logistic regression:

$$Logit(p)$$ = $$\beta_0 + \beta_1X_1 + \beta_2X_2$$

Now, someone else is trying to replicate the model creation, but by mistake the $$X_2$$ column is replaced by some other values. Hence, the model is coming as:

$$Logit(p)$$ = $$\beta_0^{'} + \beta_1^{'}X_1 + \beta_2^{'}X_2^{'}$$

I know all the values of the Xs and the parameters in the two equations except the values of $$X_2$$

My question is: How can I get back the values of $$X_2$$? I know that getting the value of $$X_2$$ for each row may be a challenge. Can I get something at an aggregated level at least (mean, sum, etc.)?

• Do you have any distributional assumptions for $X_2$ that you are willing to make? For example normal, log normal? – Jesper for President Oct 2 '19 at 7:19
• $X_2$ is simply a column in a real life data. Assuming a distribution of it will not be practical I guess – SamRoy Oct 2 '19 at 7:21
• The fact that $X_2$ is a column in a real life data seems to go against you not knowing $X_2$? – Jesper for President Oct 2 '19 at 7:23
• No no. My issue is the actual column $X_2$ got replaced with something else by mistake. Now I am trying to get some info about the original $X_2$ column – SamRoy Oct 2 '19 at 7:26
• Do you know what the variable $X_2$ measures ... blood pressure, income etc. ? And do you know the population of the original data set including $X_2$? – Jesper for President Oct 2 '19 at 7:29