Calculate effect of independent variable If $a\times b\times c=t$ and I change $a$, $b$, and $c$, how do I calculate the effect of each change.
I believe the equation is: $(a+\Delta a)(b+\Delta b)(c+\Delta c)=(t+\Delta t)$, and then I solve for $\Delta a$, $\Delta b$, and $\Delta c$.
Is this correct? And how do I describe what I'm solving for?
 A: Well, you could use partial differentiation for computing effect of small changes -
$\partial t=ab\,\partial c+ac\,\partial b+bc\,\partial a$
Informally, you could interpret that as a solution to $\Delta t$ in the limit when the changes are small, and think of $\partial t=\lim_{\Delta a,\Delta b,\Delta c \to 0}\Delta t$.

So, for example if a=5, b=3, c=4, and they change by .01, .02, .03, we have
$\Delta t \approx 5\times 3\times0.03+5\times4\times0.02+3\times4\times0.01=0.97$
And indeed, it is close to the real $\Delta t=(5.01\times3.02\times4.03)-(5\times4\times3)=0.97471$.
A: Apply the log transform: $\ln t = \ln a + \ln b +\ln c$. The effect of each variable in your original setup depends on the values of other variables, much like an interaction term in regression. However, in the regression interaction terms are rarely included without the main effect. If your model is truly multiplicative, then I think that the log transform will help you understand the effects better. 
Also, if you differentiate the log transformed equation, you get: $\Delta t/t=\Delta a/a+\Delta b/b+\Delta c/c$, which is also easy to interpret, it's a sum of relative effects.
