I have a formula of the following form:
$a_1*w + a_2*x + a_3*y + a_4*z$
In the above formula, the $a_i$s can be thought of as weights to the corresponding parameters. The values of the parameters $w, x, y,$ and $ z$ are known whereas the $a_i$s are unknown.
The above formula aims to assign 'values' to certain objects after the $a_i$s become known. After making an initial guess about the $a_i$s, I am able to assign the values(There are about 50 such objects whose values have to be assigned with the above formula) and rank the objects in a decreasing order based on the values obtained and compare the obtained ranking of the objects with the ranking they should have obtained (which is determined by other means) through various statistical parameters such as covariance, corelation etc.
Now, I want to determine which $a_i$ (or for that matter, which term) in the above equation contributed the most to the ranking order obtained from the formula (i.e., which $a_i$ was the most significant in getting the obtained ranking).
Is there any statistical way to determine this?