Use technology to compute and interpret the correlation coefficient of a linear fit.
Interpret the sign of the correlation coefficient r for a linear fit
Problem
Classify and interpret the linear direction for \(r=0.78\) using the rule that \(|r|<0.10\) is effectively no linear direction. State the \(x\text{-}y\) tendency without making a causal claim.
Big Picture
What this problem is really about
Correlation sign and correlation strength answer different questions. After checking whether the magnitude is large enough to count as a meaningful linear signal under the stated rule, use the sign only for direction: it describes which values tend to occur together, not a cause-and-effect mechanism.
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