How Does Linear Regression Handle Missing Values For Prediction And For Training?

Q1. Model Prediction -- Suppose we already have a trained Microsoft Linear Regression Mining Model, say, target y regressed on two variables:

x1 and x2, where y, x1, x2 are of datatype Float. We try to perform Model Prediction with an Input Table in which some records consist of NULL x2 values. How are the resulting predicted y values calculated?

My guess:

The resulting linear regression formula is in the form:

y = constant + coeff1 * (x1 - avg_x1) + coeff2 * (x2 - avg_x2)

where avg_x1 is the average of x1 in the training set, and avg_x2 is the average of x2 in the training set (Correct?).

I guess that for some variable being NULL in the Input Table, Microsoft Linear Regression just treat it as the average of that variable in the training set.

So for x2 being NULL, the whole term coeff2 * (x2 - avg_x2) just disappear, as it is zero if we substitute x2 with its average value.

Is this correct?



Q2. Model Training -- Using the above example that y regressed on x1 and x2, if we have a train set that, say, consist of 100 records in which

y: no NULL value

x1: no NULL value

x2: 70 records out of 100 records are NULL

Can someone help explain the mathematical procedure or algorithm that produce coeff1 and coeff2?

In particular, how is the information in the "partial records" used in the regression to contribute to coeff1 and the constant, etc ?