Predicting and residuals

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What this lesson covers

  • Residual = actual − predicted.
  • Interpolation is inside the data range.
  • Extrapolation beyond it is risky.
Worked example

Using y = 47.7 + 4.1x

  • Predict for 2.5 hours.
  1. y = 47.7 + 4.1 × 2.5
  2. y = 57.95 marks
Worked example

A residual

  • The student at x = 3 scored 61.
  1. predicted = 60
  2. residual = 61 − 60 = 1
Worked example

Going too far

  • Predict for x = 20.
  1. y = 47.7 + 82 = 129.7
  2. That is above 100, so the model has failed

Common mistakes

  • Taking predicted − actual.
    Residual is actual − predicted.
  • Trusting a prediction far outside the data.
    State the range the model was built on.

Your turn

  • 1. For y = 12 + 3.5x, a point at x = 4 has y = 29. Find the residual.
Show answer

1. 29 − 26 = 3

Summary

What to take away

  • Stay inside the data.
  • Residual = actual − predicted.

More in AS 91581

Scatter plots and correlationNotesFitting a linear modelNotesPredicting and residualsNotesEvaluating a relationshipNotes

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