# the most important factor that accounts for the variation of y most

Discussion in 'Scientific Statistics Math' started by Mike, May 27, 2009.

1. ### MikeGuest

Hi

I have to pick up the most explainable variable in eq. like:

y=x1*x2/(x3*x4)... even general in y=f(x1,x2,x3,x4).

In fact, x1~x4 are all function of some angles and other parameters.
I have the model run for many conditions.
Then, I notice variation of y. I'd like to account for the variation
of y. What is the most important factor that accounts for the
variation of y most. How to do this?

I compute stdev for y, x1~x4, but I have doubt about it.
I don't know how to write an eq. like:
stdev(y) = some forms of stdev(x.....)
Then pick up the largest one?
Or, I try to compute correlation coefficient r between y and xi, then
can I pick up the largest r as the most important factor? Is that
reasonable?

Any suggestion will be pleased

Mike

Mike, May 27, 2009

2. ### Rich UlrichGuest

I have to assume that you are referring to a regression-like
example, where the fit is not perfect, or the statistical problem,
right off, makes no sense at all. Everything is perfectly
determined, symmetrically in the prediction (barring scaling
as "raw" or "reciprocal") and you want to know which matters
most?

I suggest that you read up on the problem for the simpler
linear regression case, where y is a linear combination of X and
coefficients, y= a + b1*x1 + b2*x2 + ... .

Since there is no general, accepted solution to "best predictor"
in this easy case, except where the same variable scores as
"best" by both the univariate and regression p-values, you
have some pondering to do.
Function of *angles*? Surely, that makes the situation
even more complicated.
"Least squares regression" is what is used to account
for "variation in y" when that is measured as "variance".

For your non-linear example, the example is *simplified* to
a linear regression case if you are willing to take the logs
of both sides, so that you minimize the variance of log(y)
instead of the variance of (y).

Instead of looking at variances by Least Squares, maximum
likelihood is often the criterion used for non-linear fitting
(ML methods).

Rich Ulrich, May 28, 2009