How to isolate impact of factors in an equation

Hello,

I am trying to isolate the effect of two different drivers/factors over time. For example, consider the following:

Factor 1 x Factor 2 = Value

Year 1: Factor 1 = 10, Factor 2 = 40, Value = 400

Year 2: Factor 1 = 12, Factor 2 = 41, Value = 492

The Year over year change of value is 23%

I am trying to figure out what portion of that change is accounted for by each factor. The approach I have been trying to take is to hold one factor at a time constant and see what the resulting value would be. For example:

Holding factor 1 constant gives value = 10 * 41 = 410

- 410/400 - 1 = 2.5% Year over year change

Holding factor 2 constant gives value = 12 * 40 = 480

- 480/400 - 1 = 20% Year over year change

I take this to mean that factor 1 accounted for 2.5% of the growth and factor 2 accounted for 20%. However, adding these two together gives a year over year change of 22.5% when the actual change was 23.0%.

Could someone please let me know why this analysis does not seem to be very exact and if there is a better way to approach it?

Thank You,

Eric

Isolating impact of multiple drivers in equation

Thanks again Malay. It appears this method does not scale beyond more than two factors. For example, if we change the function to look like the following, I am no longer able to isolate the effect of the different factors.

Factor1 x Factor2 x Factor3= Value

Year 1: Factor1 = 10, Factor2 = 40, Factor3 = 20, Value = 8000

Year 2: Factor1 = 12, Factor2 = 41, Factor3 = 17, Value = 8364

Year over Year change = 4.6%

Factor 1 isolation:

Holding Factor2 & 3 constant yields 12 * 40* 20 = 9600

- 9600/8000 - 1 = 20% change attributed to Factor1

Factor 2 isolation:

Holding Factor1 & 3 constant yields 10 * 41* 20 = 8200

- 8200/8000 - 1 = 2.5% change attributed to Factor2

Factor 3 isolation:

Holding Factor1 & 2 constant yields 10 * 40 * 17 = 6800

- 6800/8000 - 1 = -15% change attributed to Factor3

If I sum the impact of these changes up I get 7.5%. If I then try to add the "interplay" of the three factors (20% * 2.5% * -15%), it comes to 7.4%, which is significantly different than the actual total year over year change of 4.6%.

Is this a flawed approach when there are more than two variables (e.g., is it applying a linear approach to a non-linear problem, or something similar to that). If so, is there a better approach to isolate the impact of changes in factors, when three factors are involved?

Thank you again for the help,

Eric