Use technology to compute and interpret the correlation coefficient of a linear fit.
Interpret the sign and magnitude of the correlation coefficient r for a linear fit
Problem
Classify \(r=0.92\) by direction and strength using: weak \(0\le~|r|<0.30\), moderate \(0.30\le~|r|<0.70\), strong \(0.70\le~|r|\le~1\). Explain the roles of sign and magnitude without claiming causation.
Big Picture
What this problem is really about
Read correlation in two passes rather than treating its signed decimal as one label. The sign gives the direction of the linear tendency, while the absolute value is compared with the supplied strength bands; neither part measures a rate of change or proves that one variable causes the other.
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