What is a good way of estimating the dependence of an output variable on the input parameters? I am evaluating a scenario's output parameter's dependence on three parameters: A, B and C. For this, I am conducting the following experiments:


*

*Fix A+B, Vary C - Total four sets of (A+B) each having 4 variations of C

*Fix B+C, Vary A - Total four sets of (B+C) each having 3 variations of C

*Fix C+A, Vary B - Total four sets of (C+A) each having 6 variations of C


The output of any simulation is the value of a variable over time. For instance, A could be the area, B could be the velocity and C could be the number of vehicles. The output variable I am observing is the number of car crashes over time. 
I am trying to determine which parameter(s) dominate the outcome of the experiment. By dominate, I mean that sometimes, the outcomes just does not change when one of the parameters change but when some other parameter is changed even by a small amount, a large change in the output is observed. I need to capture this effect and output some analysis from which I can understand the dependence of the output on the input parameters. A friend suggested Sensitivity Analysis but am not sure if there are simpler ways of doing it. Can someone please help me with a good (possibly easy because I don't have a Stats background) technique? It would be great if all this can be done in R.
Update: 
I used linear regression to obtain the following:
lm(formula = T ~ A + S + V)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.35928 -0.06842 -0.00698  0.05591  0.42844 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.01606    0.16437  -0.098 0.923391    
A            0.80199    0.15792   5.078 0.000112 ***
S           -0.27440    0.13160  -2.085 0.053441 .  
V           -0.31898    0.14889  -2.142 0.047892 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.1665 on 16 degrees of freedom
Multiple R-squared: 0.6563, Adjusted R-squared: 0.5919 
F-statistic: 10.18 on 3 and 16 DF,  p-value: 0.0005416 

Does this mean that the output depends mostly on A and less on V?
 A: A few comments:

*

*Why did you go with your particular experimental design set-up? For example, fix A+B and vary C. What would you fix A + B at? If you are interesting in determining the effect of A and B, it seems a bit strange that you can fix them at "optimal values". There are standard statistical techniques for sampling from multi-dimension space. For example, latin hypercubes.


*Once you have your data, why not start with something simple, say multiple linear regression. You have 3 inputs A, B, C and one response variable. I suspect from your description, you may have to include interaction terms for the covariates.
Update
A few comments on your regression:

*

*Does the data fit your model? You need to check the residuals. Try googling "R and regression".


*Just because one of your covariates has a smaller p-value, it doesn't mean that it has the strongest effect. For that, look at the estimates of the $\beta_i$ terms: 0.8, -0.23, -0.31.
So a one unit change in $A$ results in $T$ increasing by 0.8, whereas a  one unit change in $S$ results in $T$ decreasing by 0.23. However, are the units of the covariates comparable? For example, is it may be physically impossible for $A$ to change by 1 unit. Only you can make that decision.
BTW, try not to update your question so that it changes your original meaning. If you have a new question, then just ask a new question.
A: EDIT: After some reflection, I modified my answer substantially.
The best thing to do would be to try to find a reasonable model for your data (for example, by using multiple linear regression).  If you cannot get enough data to do this, I would try the following "non-parametric" approach.  Suppose that in your data set, the covariate $A$ takes on the values $A=a_1, ..., a_{n_A}$, and likewise for $B$, $C$, etc.  Then what you can do is perform a linear regression on your dependent variables against the indicator variables $I(A= a_1), I(A=a_2), ..., I(A = a_{n_A}), I(B = b_1),...$ etc.  If you have enough data you can also include interaction terms such as $I(A=a_1, B=b_1)$.  Then you can use model selection techniques to eliminate the covariates that have the least effect.
