Reversing an OLS model
Posted: Wed Nov 06, 2013 12:48 am
Hi,
from what I am aware of,
if
Y = b0 + b1*X + e
then
b1 = COV(X,Y)/VAR(X)
Also,
if
X = c0 + c1*Y + e
then
c1 = COV(X,Y)/VAR(Y)
In this case, if we know b1, VAR(X) and VAR(Y),
can I estimate c1 using
c1 = b1*VAR(X)/VAR(Y)
and without estimating Y=c0 + c1*X + e explicitly?
Are there any errors to my logic?
Many thanks in advance :)
from what I am aware of,
if
Y = b0 + b1*X + e
then
b1 = COV(X,Y)/VAR(X)
Also,
if
X = c0 + c1*Y + e
then
c1 = COV(X,Y)/VAR(Y)
In this case, if we know b1, VAR(X) and VAR(Y),
can I estimate c1 using
c1 = b1*VAR(X)/VAR(Y)
and without estimating Y=c0 + c1*X + e explicitly?
Are there any errors to my logic?
Many thanks in advance :)