Reversing an OLS model

[broncus2k]

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 :)

[trubador]

That is correct.