I did a regression with a cube root transformation for the target. The question is, how should I interpret the betas.
cnt (target): Number of rented bikes (on a daily basis).
temp: Temperature (normalized 0 to 1). But this is not really important in this case.
Example: Model without any transformation:
fit = lm(cnt~temp, data = d_ss) summary(fit) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.0356 3.4827 -0.01 0.992 temp 381.2949 6.5344 58.35 <2e-16 ***
Interpretation: If temperature increases by one unit the amount of rented bikes increases by 381.29.
--> y = -0.04 + 381.29*x
Example: Cube root transformation
fit_cr = lm(cnt^(1/3)~temp, data = d_ss) summary(fit_cr) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.85580 0.03880 73.61 <2e-16 *** temp 4.38866 0.07279 60.29 <2e-16 ***
Interpretation: If temperature increases by one unit the amount of rented bikes increases by 84.60 (4.38^3).
--> y^1/3 = 2.86 + 4.39*x
--> y = 2.86^3 + 4.39^3*x
--> y = 23.27 + 84.60*x
Is this the right way?
The problem is, if I use different or more complex transformations like this:
fit_comp = lm(cnt^(1/3)~log(temp) + sqrt(variable2) + variable3 , data = d_ss)
Then the retransformations are quite complicated. How can I handle these ones?