Trying to figure this one out...

Hi there,

I'm new to the forum, so apologies if this is in the wrong section. Anyway I've come across this model that I want to know how to explain mathematically. Any help would be appreciated.

http://img256.imageshack.us/img256/4315/gridv.png

Ok, so here's the logic. I want to figure out the most likely letter that column 6 should have, based on the other columns. This is done by seeing which columns match up to to it best percentage wise. So as you can see, it matches up with columns 1 and 4, 100%. Column 2, 83.3%. Column 3 50% and column 5 by 66%.

We then try and predict what letter, A OR B should be in column 6 based on weighting the letters that are not in column 6 but are in the other columns. This is where I think the maths I need to make this conclusion comes in.

I'll just type what I'm thinking anyway.

So with 1 AND 4, we have 1A and 2B....then times this by our percentage match so 1x1A and 1x2B.

With col 2, it'll be .83x1A and .83x1B.

With col 3, it'll be .5x1A and .5x1B

With col 5 it'll be .66x1B.

When you add up all the A and B values you'll get, 2.33A and 4B. So according to the model, it'll be B as we have more of it.

I'm pretty sure we can draw up vectors for this and the letter would be found by finding the smallest angle between the values of CDEFGH of column 6 and the other columns, although I am unsure. I just need to figure out a mathematical way so that I can find what I just said above simply.

Thanks :)