Problem

Interpret \(r=0.84\) between practice hours and performance score using weak \(0\le~|r|<0.30\), moderate \(0.30\le~|r|<0.70\), and strong \(0.70\le~|r|\le~1\). State the direction, strength, contextual tendency, and causation limitation.

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What this problem is really about

A correlation coefficient is unitless, so it cannot be read as output units gained per input unit. Translate sign and magnitude into a contextual tendency between the two variables, then explicitly keep the claim associative: possible confounding, reverse direction, or other explanations remain.

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The score increases by 0.84 points for every additional practice hour.

There is a strong positive association: more practice hours tend to accompany higher scores, but the correlation alone does not establish causation.

More practice hours have been proven to cause higher scores because the correlation is strong and positive.

There is a strong negative association: more practice hours tend to accompany lower scores.

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Interpret \(r=0.84\) between practice hours and performance score using weak \(0\le~|r|<0.30\), moderate \(0.30\le~|r|<0.70\), and strong \(0.70\le~|r|\le~1\). State the direction, strength, contextual tendency, and causation limitation.

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