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Multivariate Regression Problem

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raylito

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My problem is as follows:

I have 1000 marbles labelled M1 to M100 (10 of each M number)

Each marble has a different mass, but generally the higher the number, the higher the mass. It is possible for a lower number to have a mass greater than a higher number, but not likely.

Someone packs up 10 bags of these marbles for me. Each bag has a number of marbles in, who's masses add up to 10Kg.

I open up each bag and table the results which will look something like:
Bag1: M1,M1,M1,M5,M6,M7,M17,M20,M20,M21,M22,M23,M23,M23,M30,M31,M32
Bag2: M2,M2,M5,M6,M6,M7,M8,M9,M20,M20,M21,M22,M50,M55,M80

And so on.... for 10 bags. The number of marbles in each bag varies, but each bag's marbles must add up to 10Kg.

What would be the best way to work out the mass of each marble? There are too many unknowns for the simultaneous equations to work, but are there some assumptions or shortcuts or estimates we can make?

Would I use mutivariate regression to solve this or something else?
 

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