Finding the most important contributor to a column in Google Spreadsheet

Question

I have a column in a google spreadsheet that's calculated as a function of a few other variables (columns).

Is there a function that I can use to find which of the variables has the most influence over the column? For example, if the value of my column changes with the square of col B but only linearly with col C, the function would return col B.

So given a table like the one on the left, I'd like to find a function that can compute the answer in yellow on the right (assuming that col B is the dominating variable):

Answer 1

I think you'd have to run some test cases. You could write a script to copy the formula to a new sheet, put it in a lot of rows, then fill in the independent cells with a range of values, where there is a constant base, and each column has a row with a different base.

+----+----------+-----+---+---+---+
|    |    A     |  B  | C | D | E |
+----+----------+-----+---+---+---+
|  1 | A        | B   | C | D |   |
|  2 | equation | 1   | 0 | 0 | 0 |
|  3 | equation | 0   | 1 | 0 | 0 |
|  4 | equation | 0   | 0 | 1 | 0 |
|  5 | equation | 0   | 0 | 0 | 1 |
|  6 | equation | 2   | 0 | 0 | 0 |
|  7 | equation | 0   | 2 | 0 | 0 |
|  8 | ...      |     |   |   |   |
|  9 | equation | 100 | 0 | 0 | 0 |
| 10 | ...      |     |   |   |   |
| 11 | equation | 5   | 1 | 1 | 1 |
| 12 | equation | 1   | 5 | 1 | 1 |
| 13 | ...      |     |   |   |   |
+----+----------+-----+---+---+---+

Then compare the impacts for each case. This could be a simple comparison or you may need to create an advanced algorithm. It really depends on the elements and magnitudes you're dealing with. This comparison could be scripted to then fill in column G