As a newbie, I'm not sure if this situation can be described more succinctly using better terminology, so kindly bear with me.
The performance of a machine+human system is dependent on four independent variables, $x_1$ to $x_4$, but the exact relationship is not known beforehand. $x_1$ and $x_2$ are continuous variables, $x_3$ and $x_4$ are discrete.
After observing system performance for a while, I, a stats newbie, ran a multiple linear regression on a training dataset which threw up great correlations (two positive and two negative) with great p-values (e-11 or better) and great adjusted $R^2$ (> 0.85). Test dataset prediction errors were also small (based on normalized RMSE values).
Based on these results, I'd like to optimize system performance by focusing on the variable that has greatest impact, positive or negative, on performance. Because retraining of humans is involved, it is not feasible to focus on more than one variable at a time.
Question: How do I pick the variable that has the greatest impact on performance? Is it simply a matter of picking the one with the greatest absolute value coefficient? Won't it also depend on the the range of each variable? For example if the equation (result of regression) is:
$P = c + 2x_1 - 3x_2 + 4x_3 - 5x_4$
$x_1$ varies from 100 to 120
$x_2$ varies from 80 to 105
$x_3$ varies from 40 to 50
$x_4$ varies from 2 to 12
then the maximum absolute impact of $x_4$ is $ 5 * 12 = 60$, $x_3$ is $200$, $x_2$ is $315$ and $x_1$ is $240$.
Should I be using this logic to pick $x_2$ as the variable to focus on?
Update after comments: To optimize performance in this case is to increase the value of P in the sample equation by attempting training (of humans) so that the value of the most impactful variable moves in the direction that improves P. Please ignore cost considerations. Assuming that the potential impact on P is the only consideration, how do I pick one variable to focus on?