Regression coefficient signs different for log/asinh and level versions of same variable

I ran two regressions. First, say, y=βx, and the second one, asinh(y)=βx, which I read is asymptotically equivalent to log(y)=βx, where x and y are the same variables with same data set for these two equations.

My confusion is that β is negative for the first regression (which I expected), but is positive for the second regression.

The sample size is the same for both regressions. Since I used asinh(y) instead of log(y), it did not drop zero values of y.

If it helps, I could totally regress in level-level mode, but the y variable is not normally distributed, and therefore, the asinh/log transformation.

Am I missing something?

• Would you please post a link to the raw, un-transformed data? – James Phillips Mar 24 at 21:44
• @JamesPhillips, thanks for the comment, but I am sorry I do not have the authority to post a link of the data. – Samyam Shrestha Mar 24 at 21:53
• And is $asinh(y)$ normally distributed? Have you tried to plot the data in both cases? It might give you some insight. Spearman's correlation might also be helpful. – Ertxiem Mar 24 at 23:36
• @Ertxiem you can be quite sure that the transformed data are not actually normally distributed. It's a model, not a fact about data. – Glen_b Mar 25 at 4:36
• @Samyam there's no assumption in regression about the unconditional distribution of Y. You may be trying to fix a non-existent problem. What sort of a variable is Y? (what does it measure? Is it a count? An amount of something?) – Glen_b Mar 25 at 4:39