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r$R$ can indeed be negative - if two variables are negatively related. r^2 $R^2$ can only be between 0 and 1, for the simple reason that it is the square of a real number.

For example, if we correlated income and time spent in jail throughout life, I would guess we would get a negative correlation (I haven't done this, I'm just guessing).

r can indeed be negative - if two variables are negatively related. r^2 can only be between 0 and 1, for the simple reason that it is the square of a real number.

For example, if we correlated income and time spent in jail throughout life, I would guess we would get a negative correlation (I haven't done this, I'm just guessing).

$R$ can indeed be negative - if two variables are negatively related. $R^2$ can only be between 0 and 1, for the simple reason that it is the square of a real number.

For example, if we correlated income and time spent in jail throughout life, I would guess we would get a negative correlation (I haven't done this, I'm just guessing).

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Peter Flom
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r can indeed be negative - if two variables are negatively related. r^2 can only be between 0 and 1, for the simple reason that it is the square of a real number.

For example, if we correlated income and time spent in jail throughout life, I would guess we would get a negative correlation (I haven't done this, I'm just guessing).