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Suppose I have two continuous variables Y and X and I want to predict a Y value given a specific X value.

However, the dataset I have is composed of 15 particular Y values (that are known values) with several measurements of X taken for each Y value. More specifically, I have 15 Y values with 10 X measurements for each Y value.

This is not a repeated measures design (I don't think), because the same 10 individuals are not measured on each of the 15 Y values.

My original thought was that a basic linear regression analysis (assuming the relationship between X and Y was linear) would be okay to perform on this data, but I'm wondering if there is a more appropriate analysis I could use to predict Y from a given X. The fact that I have multiple X values for the 15 Y values is kind of throwing me, along with the fact that it's not really a repeated measures design since each of the 10*15 X values can be assumed as coming from a different individual.

kjetil b halvorsen
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user72333
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  • Is this something like, you have pass/fail data for each of 10 students in a class (X), & 1 response variable for the class as a whole (Y)? Can you say more about your situation, your data & your goals here? – gung - Reinstate Monica Mar 30 '15 at 17:42
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    Sure. I'm trying to predict molecule density (Y) from measurements of vibration (X). The main goal is to come up with a calibration method for the instrument used to measure the vibration so that it can most accurately predict the density from the vibration it picks up. The data in question involve vibration measurements for 15 particular known densities (the 15 Y values). Each vibration measurement in the dataset comes from a different instrument, so no there are no X values coming from the same instrument. Does that help at all? – user72333 Mar 30 '15 at 17:49
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    Yes, that helps a lot. Your situation is called "calibration". It is common in fields like chemometrics. The gist is that you will regress X on Y and invert the relationship algebraically. I think we have some experts here who can answer this, but if no one comes along after a while I'll try to put something together for you. – gung - Reinstate Monica Mar 30 '15 at 18:26
  • Thank you! I'll do some research on it on my own as well. I think my main problem was that I didn't know there was a particular term for this sort of analysis so I didn't quite know how to best approach the goal. – user72333 Mar 30 '15 at 19:07
  • Although written in a different context, you can get some of the idea from my answer here: [What is the difference between linear regression on y with x and x with y?](http://stats.stackexchange.com/a/22721/7290) – gung - Reinstate Monica Mar 30 '15 at 19:20

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