Practice question · Multiple choice
A correlation of r = 0 means no LINEAR relationship. Why does that leave open the possibility of a perfect relationship between the two variables?
Hints
- Take y = x² over x = −3 to 3 and compute the correlation. What happens to the two halves?
- Ask what specific kind of relationship r is built to detect.
Show the answer
A. Because r measures only how well a straight line fits.
Why
Take y = x² over a symmetric range: every point is determined exactly and r is 0, because the positive association on the right cancels the negative on the left. So plot the data before trusting a correlation. Anscombe's quartet shares means, variances and r = 0.816 across a line, a curve and a cluster whose outlier does all the work.
Practise Hypothesis Testing
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