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Background: I have two random variables - height and weight. We often estimate correlation between them based on random sample of individuals. However, what would happen if I took only one individual and measured his weight and height in many points in time.

Questions: What is the limitation of such approach? Is correlation based on one individual still correlation between two random variables?

Thank you.

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Yes, it is still a correlation between two variables. However, strictly speaking your population is all possible pairs of height and weight measurements of this person. You took a sample of that (say, you measured the person's height and weight at 15 points in time), so any attempt to determine a relationship between the two variables will give you results that can only be generalised to this population. That means if you measured height and weight of that same person at another 15 points in time, you would expect your correlation to predict the relationship between these new data points reasonably well (if it was a significant and strong correlation in the first place).

The limitation of this approach is that you cannot generalise to other people. Your "population" consists of measurements from one person. You could only generalise to other people if the 15 data points you collected initially were from 15 different people.

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    $\begingroup$ and, depending on how those 15 people were selected you might only be able to generalize about those 15 people. How you sample is selected is critical to the ability to generalize to a larger population, the decisions and recommendations you can make. $\endgroup$ Commented Jul 12, 2013 at 16:12

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