Problem

Compare correlation coefficients \(r_{1}=0.82\) and \(r_{2}=0.45\).

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What this problem is really about

Compare correlation coefficients on two independent axes. Signs tell whether their linear directions agree or differ, and absolute values tell which association is stronger; being numerically smaller because of a minus sign does not itself make a coefficient weaker.

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Both coefficients are positive, but r2 = 0.45 shows the stronger linear association because it is the smaller value.

The coefficients have different directions because 0.82 is positive while 0.45 is too small to count as positive.

Both coefficients are negative in trend because neither value is exactly 1, and r2 = 0.45 is stronger.

Both coefficients are positive, but r1 = 0.82 shows a stronger positive linear association than r2 = 0.45.

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Compare correlation coefficients \(r_{1}=0.82\) and \(r_{2}=0.45\).

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