So, F(w,x,y,z) is an observed value placed into the variable O. As previously stated, the REG procedure would be appropriate for constructing a predictor of O=F(w, x, y, z) which you could apply to F(w0, x0, y0, z0). With variables O, w, x, y, z, and g_w=g(w) in a data set named MYDATA, you can obtain parameters a0 through a4 of the equation
O = a0 + (a1 * g_w) + (a2 * x) + (a3 * y) + (a4 * z)
employing the code
proc reg data=mydata;
model O = g_w x y z;
run;
You could also use any of a number of other SAS procedures to obtain the same results: procs GLM, GENMOD, MIXED, GLIMMIX, ORTHOREG to name a few. The ORTHOREG procedure is of some special interest in that it works well with what are referred to as ill-conditioned data. Ill-conditioned data arises when there are very strong correlations among the predictor variables. But I presume that for your experimental setting where you are manipulating w, x, y, and z, poorly conditioned data should not really be a problem.