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I am studying the relationship between X and Y using linear models. Both are composed of a left and right scalar value, and I'm interested in the relationship between both the totals and ratios for each one. My first thought is to create two linear models:

yratio = yright/yleft
ytotal = yright+yleft
xratio = xright/xleft
xtotal = xright+xleft

yratio = B0+ B1xleft+ B2xright+ B3xratio
ytotal = B0+ B1xleft+ B2xright+ B3xratio

Is this sensible, or is there a better systematic approach? I'm having trouble searching for this, but it seems like a reasonably common problem. My thought is that while my models are over parameterized in the sense that while the ratio can be expressed in terms of the left/right values, that can't be achieved with a weighted sum, and it is reasonably plausible (for instance) that ytotal is best predicted by xratio

Celongar
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    You should tell us more about the context. There are some similar questions, start with https://stats.stackexchange.com/questions/58664/ratios-in-regression-aka-questions-on-kronmal – kjetil b halvorsen Feb 13 '24 at 23:15
  • Please edit the question to say more about the nature of your X and Y variables and how the "left" and "right" components of each are determined. In particular, are all of the values necessarily greater than 0? Please provide that information by editing the question, as comments are easy to overlook and can be deleted. – EdM Feb 14 '24 at 14:57

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