Hi folks, this is my first post. I'm encountering a class of problems that I do not know how to solve. If anyone out there can give me any book titles, links to online PDFs, or search keywords to get me going, that would be super.

The basic idea is that there are two response variables z_1 and z_2, each of which depends on a set of predictor variables, say x_1,x_2,...,x_n and y_1,y_2,...,y_m, respectively. There are multiple studies involved here.

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

The goal is to model z_1 in terms of x_1 and y_1 only.

Anything you can do to point me in the right direction would be super. Thanks!