Well, you are asking for derivatives! You want to measure how the change of an input affects the output. That's exaclty a derivative.
Call "Cellular signal strengh" x and "Phone's battery drainage" f(x).
Let's say that you fix the cellular cellular signal strengh to a level of 3 ($x_0=3$). You measure a corresponding phone's battery drainage of 10% / hour ($f(x_0) = f(3) = $ 10% /hour).
Then you change the signal strengh to a level of 4($x_1=4$). The phone's battery drainage dropped to 7% / hour ($f(x_1) = f(4) =$ 7% / hour).
This way you estimate a corresponding change of the output with respect of the input (aka derivative) of $\frac{f(x_1) - f(x_0)}{x_1 - x_0} = \frac{7 - 10}{4-3} $ % /hour = - 3 % / hour = $f'(\xi)$ with $\xi \in [x_0, x_1]$.
You estimate that a change of signal level of 1 gives you a battery drainage 3% less than before. Note that the information it gives you information is just "local": that value is calculate in the proximity of level 3, so close to level 1 you could get a very different change.
How is that useful? Let's say that you repeat the same measurement, but this time regarding temperature. You might find out that a temperature change of 1 degree raises your battery drainage of 0.1% / hour.
Now you can compare the different effects: a small change in the signal level gives you a big change in the battery drainage, while a small change in temperature gives you a very small change. Is it what you were asking for?
A final remark: here it is very important how you gather data, how fine (=resolution) the data is and how often you get it.
If you want to gather data from a mobile phone that is under actual use and is not being tested in controlled environment, you have to make sure that the polling rate is high enough: ambient temperature might change slowly (minutes), but signal strength might change pretty fast (seconds). Thus you have to make sure that you can resolve these fast changes.
Let's formalize a little bit.
We say that the output is a vector $\vec{x} = (x_1, x_2, x_3, x_4, ...)$, $x \in S$ where S is the set of the possible values of the input. Then the output is $f = f(x)$, a function that takes the touple $\vec{x} = (x_1, x_2, x_3, x_4, ...)$ and gives you the corresponding output.
What you are computing here are the partial derivatives of $f(\vec{x})$:
$\frac{\partial f(\vec{x})}{\partial x_1}|_{\vec{x} = (x_1, x_2, x_3, x_4, ...)}$,
$\frac{\partial f(\vec{x})}{\partial x_2}|_{\vec{x} = (x_1, x_2, x_3, x_4, ...)}$,
etc.
The partial derivatives are computed at particular values of the input. Look at the partial derivatives as the corresponding change of the output caused by a little variation of the input. The bigger the partial derivative, the bigger the effect. Note that the partial derivatives are calculated at a particular combination of the input. That is: at a particular screen brightness, at a particular battery level, at a particular temperature, you estimate the effect of changing the phone level by a little.
If you are lucky you will see that to some extent some variables are influential to the partial derivative: for example the partial derivative might not change with gps connectivity enabled or not (as probably will).