Evaluating a relationship

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What this lesson covers

  • r² gives the share of variation the line explains.
  • A curved residual pattern means a line does not fit.
  • Look for other variables.
Worked example

Strength for the study data

  • Use r and r².
  1. r = 0.994
  2. r² = 0.989
  3. The line explains about 99% of the variation, on only 5 points
Key idea

Questions to ask

  • Are there outliers pulling the line?
  • Do the residuals show a pattern?
  • Are there separate groups?
  • Could a third variable explain the link?

Common mistakes

  • Trusting a high r from few points.
    Small samples can mislead.
  • Ignoring a curve in the residuals.
    Try a different model.

Your turn

  • 1. r = 0.8. Find r².
  • 2. What does a curved residual plot suggest?
Show answer

1. 0.64 2. A straight line is not the right model

Summary

What to take away

  • Numbers, residuals, context.
  • Five points is not much evidence.

More in AS 91581

Scatter plots and correlationNotesFitting a linear modelNotesPredicting and residualsNotesEvaluating a relationshipNotes

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