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October 4th, 2014, 02:09 AM   #1
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Question Reverse weighed average, I have the result but need the weightings

Sorry in advance if this is the wrong forum, my understanding of math and where to pidgeon-hole it isn't so great.

I'm trying to solve a problem which seems to follow the lines of weighted average, but in reverse. I already know the result, I need to find the weight of each of the contributing values.

There are 16 values that contribute to the result, some sample data below, the result is in the first column:

Code:
50	11000	11000	11000	1	35	35	-99	60	60	-99	60	-99	-99	2	0.5	520
50	11800	11800	11800	1	30	30	-99	50	50	-99	50	-99	-99	2	0.5	500
55	11800	11800	11800	1	35	35	10	10	10	-99	10	10	-99	2	0.55	550
55	12000	12000	12000	1	65	40	-99	80	-99	80	80	0	-99	2	0.49	540
60	13000	13000	13000	1	50	35	15	80	80	15	80	-99	-99	2	0.6	600
60	11800	11800	11800	1	60	50	-99	80	-99	80	80	10	-99	2	0.55	590
65	12300	12300	12300	1	35	60	15	80	80	80	15	15	-99	2	0.6	620
I'm looking for some sort of algorythm that can work through sample data and tune the possible weight of each value as it goes. I might be biting off more than I can chew here, but any help you can provide on the math would be a great help.

Many thanks.

PS Please don't put too much faith in the sample data, it's entered by hand and some doesn't look correct so would throw off the result calculation.

Last edited by ezoray; October 4th, 2014 at 02:51 AM. Reason: spellin'
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October 16th, 2014, 02:46 PM   #2
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Math Focus: Probability
I think it might be useful to try to fit a linear model to your data. Read in the following wiki how do it Linear regression - Wikipedia, the free encyclopedia. Basically you need to apply the formula for Ordinary least squares.
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