I was wondering how you can interpret a square root independent variable on a multiple linear regression? Furthermore, what is the best way to visualize your predictions with a square root transformation?
Depends on the transformed variable: dependent or independent (explanatory or response). You can say that for the range of ... to ... for the transformed variable, assuming the other variables being constant, one unit change in the second root of ... gives rise to ... units increasing/decreasing of the DV.
Hello Antonio,
The interpretation is now in the metric of square root of the IV: For every unit increase, the regression coefficient gives the estimated amount of change in the DV (in its scale), if none of the other IVs change in value. Using standardized regression coefficients means that you're now talking about the estimated number of SDs of change in the DV, per SD change in the IV.
How to think about this in the metric of the original (untransformed) scores? Well, you're now forced to think about a nonlinear linkage between transformed & untransformed scores. Consider these untransformed scores, which represent a unit change on the transformed (square root) scale:
1 -> 1
4 -> 2
9 -> 3
16 -> 4
25 -> 5
36 -> 6
49 -> 7
So, where one is on the untransformed scale makes a difference as to how many (untransformed) units represent a one unit difference on the transformed scale.
Good luck with your work.