Suppose I have a linear model y ~ Xb, and I split my observations into multiple X's X1, X2, X3 etc. What is the most appropriate way to aggregate the separate models y1 ~ X1b1, y2 ~ X2b2 to produce the best estimate of the model that would result from fitting y~ Xb? In other words, I would like to combine all of the parameter vectors b1, b2, b3 etc. into an estimate of b. So far, I have been using an average of the bi's from the separate models weighted by the inverse of the squares of the standard errors of the b values, and it works ok, but I was wondering if there is a formally appropriate way to do it.