If the error terms in a regression model are independent $N\left( 0,\sigma ^{2}\right)$, what can be said about the error terms after transformation $X'=\dfrac {1} {X}$? Is the situation the same after transformation $Y' = \dfrac{1} {Y}$?
My inclination is that the transformations should not affect the independence of the error terms $e_{i}$. If anyone around has some insight for me that would be great.