# How to handle missing data in all explanatory variables in linear regression

It's multivariate linear regression meaning multiple dependent variables (Y). Data A has both X (explanatory variables) and Y, but data B has only Y.

I wonder if there is any way to incorporate data A and B into the regression model.

If I remember correctly, Statistical Analysis with Missing Data by Little et al, suggested some kind of iterative approach like EM algorithm where you repeat following until convergence

1. Estimate missing X based on current regression model
2. Compute regression model with full X estimated in #1

But in this case, I have all columns of X matrix is missing. So my questions:

1. Is the approach above still effective? That is, would including data B into the model help in any way?
2. If so, how missing full columns of X can be estimated?

Update: The reason I want to add data B is because data B is application-specific data while data A is more general data. I hope to have training data that has more "weights" for application-specific input space.

• If I properly understand, a full column of X missing means that you did not observe an explanatory variable at all. I do not believe it is possible to estimate it unless there is a known relationship with the observed covariates. This actually happens all the time because there are covariates that you do not observe (for a number of possible reasons).
– user10525
Apr 20, 2012 at 13:15
• @Procrastinator I think we can do regression X on Y for the missing data estimation. Apr 20, 2012 at 13:23
• Are you interested on a calibration model? Otherwise it makes no sense to estimate $X$ and then use it on a regression model for $Y$.
– user10525
Apr 20, 2012 at 13:29
• @Procrastinator As I said on my update above, I hope to have training data that has more "weights" for application-specific input space. Apr 20, 2012 at 13:33