Let's assume we have a data set with two variables. Next, we transform both variables by logarithm and build a regression model on it:
x <- c(1:100) y <- 10*x # Obviously a linear regression will give slope of 10 lm(log2(y)~log2(x)) # Can we use the log-transformation to recover slope of 10?
Can we use the log-transformed model (
lm(log2(y)~log2(x))) to recover the original regression slope (10 in this example) without fitting a new model in the original space?
My example obviously has no error and not very realistic. What if I want to assume the errors be normality with mean of 0 and constant variance and homoscedasticity? What if I want to relax the homoscedasticity assumption?