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Assume we have two variables, Height and Weight. Each is normally distributed, and they are correlated. Assume the correlation was 0.75 for a specific example.

Given a particular Height, can we estimate the weight, in the form of a mean and standard deviation? Or is there not enough information?

David vun Kannon
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    Your information wouldn't change if all heights were rescaled and shifted and if all weights were rescaled and shifted. Consequently, there's nothing whatsoever you can say about one variable given the value of the other. (This is one of the most fundamental properties of correlation.) For a general analysis of the case where you have minimal statistics, see https://stats.stackexchange.com/questions/107597. It comes down to needing to know the scales and origins of all your variables in addition to having full correlation information. – whuber Mar 05 '24 at 21:02

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