Back-transforming results of multiple linear regression

Question

I transformed dependent variable by raising to a power of $0.4$. When the original data is plotted on the back-transformed $y^{1/0.4}$ predicted results, the intercept is substantially larger than zero & gradient lower than $1$. Even by adding $\sigma^{1/0.4}$ to the back-transformed data does not substantially improve it. Anyone have ideas on what more may be done? Regards, Michael.

Answer 1

It sounds like you fitted a model of the form

$$y^{0.4} = a x + b$$

Solving for $y$,

$$y = (a x + b)^{1/0.4}$$