A meta-analysis is the combination of results from several similar studies, conducted by different scientists, in order to arrive at a single, overall conclusion. Unlike common experimental procedures, the data used in a meta-analysis happen to be the descriptive statistics from the distinct individual studies. In this thesis, we will consider two regression studies performed by two scientists. These studies have one common dependent variable, Y, and one or more independent common variables, X. A regression of Y on X with other independent variables is carried out on both studies. We will estimate the regression coefficients of X meta-analytically. After combining the two studies, we will derive a single regression model. There will be observations that one scientist witnesses and the other does not. The missing observations are considered parameters and are estimated using a method called Gibbs sampling.

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