Practice question · Multiple choice
A least-squares line can be fitted to any scatter of points, and its slope always has a value. Why is the line sometimes worth reporting and sometimes meaningless?
Hints
- The algorithm cannot refuse. Fit a line to points on a circle - what do you get?
- Ask what you would look at after fitting to decide whether the fit was appropriate.
Show the answer
C. Because the procedure fits a line whatever the data looks like.
Why
Least squares is an optimisation, not a test: give it points on a circle and it returns the line minimising squared vertical distances, a well-defined answer to a question nobody should have asked. Deciding whether it means anything is a separate step done on the residuals, which is why r² alone is insufficient, as Anscombe's second dataset shows.
Practise Correlation and Regression
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