Is there such a thing as a weighted multiple regression?
Landen Miller
Open question
2022-08-17
I'm new to linear algebra, but I know how multiple linear regressions work. What I want to do is something slightly different.
As an example, let's say that I have a list of nutrients I want to get every day. Say I have a list of foods, and I want to know how much of each food to eat to get the best fit for my nutrition plan. Assume I'm fine with using a linear model.
However, some nutrients are more important than others. The errors on protein and calcium might be equal in a typical linear regression, but that's no use. Protein has higher priority than calcium (in this model), so I'd want a model that is better fitting to the higher priority points than to the lower ones.
I tried putting weights on the error function, and I end up with a matrix of matrices. At that point, I'm not sure if I'm minimising for the weights or for the coefficients on the nutrients. I think both, but I wasn't sure how to minimise for both at the same time.
Is it possible to solve this with linear algebra, or does this require some numerical approximation solution?
Answer & Explanation
Paulina Horne
Beginner2022-08-18Added 10 answers
But, you don't choose nutrients directly, you choose foods. Let food be represented by the subscript , , Each food is associated with a set of nutrients. In particular, suppose that 1 unit of each food has units of nutrient . Therefore, if you purchase one unit of food, your objective function increases by
Finally, let represent the amount of food purchases (or consumed). Then your objective is to choose a consumption set of foods {} to maximize your objective function.
Perhaps subject to some budget constraint?
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