# One question regarding to the simple regression

there are 3 variables. X,Y,Z.
Assuming
Y = a + b*X + errorTerm
Z = c + d*X + errorTerm,

Y = g + h*Z + errorTerm;

what can we say about the relationtion between h and (b,d)? under what
condition so we can have "h = b/d"?

thanks

haruspex
Homework Helper
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If h, b and d represent the actual parameter values then clearly you have:
Y = a + b*X + errorTermxy
Z = c + d*X + errorTermxz,

Y = g + h*(c + d*X + errorTermxy) + errorTermxz;
whence:
g = a - h*c
h = b/d
errorTermzy = h*errorTermxy + errorTermxz
But perhaps you mean b, d and h to be the estimated parameters. That gets more subtle.

chiro