Problem preview

S-ID.8 Warmup M1-058-A06-V03

Use technology to compute and interpret the correlation coefficient of a linear fit.

Interpret correlation in context without implying causation

Problem

Interpret \(r=0.12\) between shoe size and quiz 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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There is a weak negative association, so larger shoe size tends to accompany lower quiz scores.

Larger shoe size has been proven to cause higher quiz scores because the correlation is positive.

There is a weak positive linear association, so the result shows only a slight tendency and does not establish causation.

Quiz score increases by 0.12 points for every additional unit of shoe size.

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Curriculum context

Course: Math I
Standard: S-ID.8
Category: Statistics and Probability
Domain: Interpreting Categorical and Quantitative Data
Objective: Use technology to compute and interpret the correlation coefficient of a linear fit.
Problem type: Interpret correlation in context without implying causation