In statistics coping with missing values is often done by imputation: https://en.wikipedia.org/wiki/Imputation_(statistics)
and whole books have been written about it. Suggest you start reading.
One method, multiple imputation, works by creating a number of new complete data items by replacing the missing value with some values sampled from a distribution. You then predict from these new data items, and that gives you a set of predictions and variances from which you can compute a pooled prediction and variance. This variance will be larger than that from a complete item because of the variance introduced by the sampling. The increase will depend on how influential the missing variable is to the model and what distribution you put on the missing item. For example, if you have missing age, and your data should be from a population between 16 and 60, you'd sample age from the population distribution a number of times, do the predictions, and pool them according to the multiple imputation methodology.
Of course you have to know if your missing data are missing at random, or perhaps biased missing (maybe more women over 40 don't give their age). Lots of interesting complications that will only come to light if you have a careful think about your data.
Anyway, as I say, whole books. And you should probably try the statistics stack exchange site too. Its not really data science much.