# Statistical analysing

1. Nov 16, 2007

### hexa

Hello,

I've been running a model with different combinations of imput parameters. Lets just assume they look like this:

1,2
1,3
1,4
3,4
1,2,3
2,3,4
1,2,3,4

As a result I receive a certain numerical value. Jus by looking at that value I can see if the result is good or not. But how do I decently analyse the influence of the input parameters on that result? As I know about nothing about statistics I can only cont how often every parameter appears with a good or bad result. But what about combinations of parameters? how do I analyse the meaning of a good result from a parameter which usually results in good and another that results in a bad result? Furthermore, some results are wonderful, some are not so good, some a not so bad, and some terribly bad.

I think it might be easier if I had a huge list of parameters and always only combinations of 2, but in fact I have only 5 parameters to play with, which results in 26 possible combinations.

Any ideas?

Last edited: Nov 16, 2007
2. Nov 16, 2007

### Chris Hillman

Fisher lives?

At first I thought you must be asking a garbled question about the theory of designs. But maybe not. In which case the obvious question is: what do you know about the theory of designs?

3. Nov 16, 2007

### EnumaElish

How is it that the number of input parameters is changing from one trial to the next?

4. Nov 18, 2007

### hexa

Because I'm still trying to find out which combination works best, and if there's a minimum number of input parameters for a good result, and if that number is depended on the types of input parameters. I just don't know how to compare the results correctly now :(

5. Nov 18, 2007

### hexa

Nothing. I don't know what you're talking about. If I knew how to formulate my question clearly then I think I would already be a step closer to solving my problem simply as I would have at elast some basic knowledge on statistics.

hexa

6. Nov 18, 2007

### EnumaElish

I see. the easiest method would be to estimate a multiple regression of the type y = b0 + b1 x1 + ... + bk xk for each combination of k parameters (the x's) that you have used (and y is the observed output). You can then compare model fit across different k's and different parameter combinations by looking at the ADJUSTED R-SQUARED statistic of each equation.

7. Nov 22, 2007

### hexa

Hello,

thanks a lot, that's something already. I'm just not quiet sure what to do with this.

lets assume I have
par1-par2-par3 = 80
par2-par3-par4 = 95

Please can you give me a few more hints? I understand just as much that I have to solve this in a matrix somehow, but what to solve for is a bit of a mystery. Yes, I'm rubbish with these things :(

Hexa

8. Nov 23, 2007

### EnumaElish

Multiple regression will work only if either:
1. you take repeated measurements with each parameter combination and identical parameter values and each measurement is at least a little different from the others; or:
2. you assign different values to each parameter in a given combination of parameters and (as a result) record different output values.

If that is not the case, you'll be better off, say, taking the following "exact" measurements:

par1 par2 par3 = 80
par1 par2 par4 = 95
par1 par3 par4 = 70
par2 par3 par4 = 90

which is 4 equations in 4 unknowns and can be solved by:
[1 1 1 0] [a1] _ [80]
[1 1 0 1] [a2] = [95]
[1 0 1 1] [a3] _ [70]
[0 1 1 1] [a4] _ [90]

or in matrix notation M a = y, where each a is the contribution of the corresponding parameter to the output (the y's); and the solution is a = M-1 y.

In case of multiple regression, you'd be changing parameter levels as well as the combination, so you'll end up with, say:

[10 10 10 0] _____ [80]
[20 10 10 0] _____ [85]
[25 10 10 0] _____ [90]
[10 15 0 10] [b1] _ [95]
[10 17 0 10] [b2] _ [85]
[10 19 0 10] [b3] = [75]
[10 0 10 10] [b4] _ [71]
[10 0 10 11] _____ [77]
[10 0 10 12] _____ [67]
[0 10 10 25] _____ [99]
[0 10 10 35] _____ [100]
[0 10 10 45] _____ [110]

or X b = y - u, where u is "random error" (which may include measurement error), and b is "estimated" as $\hat {\bold b}$ = (X'X)-1X'y.

Last edited: Nov 23, 2007