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I was asked that if $y\sim N(0,a^2)$ and $x\sim N(0,b^2),$ what is the product of coefficients of the regression x to y and the regression y to x.

I think this is a very popular question for OLS (product is R-squared). But here it is like EIV. To be honest, I even do not know how to build the linear relation between x and y, since EIV builds the linear between their means. But here their means are zero identically.

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