An instrument used to measure the levels of glucose in a person's blood is monitored on a random sample of 10 people. The levels are also measured using a very accurate laboratory procedure. The instrument measure is denoted by x. The laboratory procedure measure is denoted by y.
I personally think y on x is more correct because the intention is to use the instrument readings to predict the laboratory readings. And y on x minimises the errors of such predictions.
But the answer provided was x on y.
Best Answer
Lots of lab papers, especially the instrument testing experiments, apply such x on y regression.
They argue that from the data collection in the experiment, the y conditions are controlled, and get x from the instrument reading (introducing some error in it). This is the original physical model of the experiment, so the x~y+error is more suitable.
To minimize the experiment error, sometimes, y being controlled on the same condition, then x is measured for several times (or repeated experiment). This procedure may help you to understand the logic behind them and find x~y+error more clearly.
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