# Meta Analysis with Several Regression Studies

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I have come across a problem that I need to solve, and it isn't your garden variety regression problem. It isn't even covered in any of my books, of which I have many. I need either a book title or an online PDF that covers this material.

Suppose we have a response variable $z_1$ that depends on predictor variables $x_1,x_2,...,x_n$. Further suppose that we have another response variable $z_2$ that depends on predictor variables $y_1,y_2,...,y_m$.

There are 4 studies to be synthesized.

In Study 1 a regression model $z_1=\alpha_0+\alpha_1x_1+\alpha_2x_2+...+\alpha_nx_n$ is obtained.
In Study 2 a regression model $z_2=\beta_0+\beta_1y_1+\beta_2y_2+...+\beta_my_m$ is obtained.
In Study 3 a correlation between $z_1$ and $z_2$ is obtained.
In Study 4 a correlation between $x_1$ and $y_1$ is obtained.

The goal is to synthesize these studies to model $z_1$ as a function of $x_1$ and $y_1$ only.

What's a good read to get going on this? Thanks!

Stephen Tashi
Are these regression models fit by considering both the z-variable and x-variables to be random variables? (e.g. total least squares regression as opposed to least squares regression?)

Are x1 and y1 the only random variables with a given estimated covariance ? - or do all pairs xj, yj have an estimate covariance?

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