I study horizontal gravity gradient $\frac{\Delta g}{\Delta l}$ in certain field. We measure $\Delta g$ and $\Delta l$ through several profiles and same direction. Something like that:
I did regression analyses on $\Delta g$, $\Delta l$ and $\frac{\Delta g}{\Delta l}$ and get this equation $$\frac{\Delta g}{\Delta l} = a +b \Delta g +c \Delta l , R^2 = 0,9$$ If I accept $\frac{\Delta g}{\Delta l}=\frac{dg}{dl}$ then I get this differential equation $$\frac{dg}{dl} = a +bdg +cdl $$ After solving this equation I get $$g = \frac{x(a+b)}{1-c}+c_1$$ I want to know can do it ? Does it make sense if $\frac{\Delta g}{\Delta l}$ has certain direction?