EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
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Statistics & Probability · Foundation & Higher

Line of best fit

A line of best fit is drawn on a scatter graph to model the trend in the data. It is used to make predictions. It should pass through the mean point and have roughly equal numbers of points on each side.

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Key facts to remember

  • 1The line of best fit should pass through (or near) the mean of x and the mean of y.
  • 2Roughly equal numbers of points should be above and below the line.
  • 3Interpolation: using the line to predict within the range of the data — this is reliable.
  • 4Extrapolation: predicting beyond the range of the data — this is unreliable.
  • 5The line of best fit does not need to pass through the origin.
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Worked examples

Example 1

Use a line of best fit to predict the sales when the temperature is 22°C (within the data range).

Working

  1. Draw the line of best fit on the scatter graph
  2. Find where temperature = 22°C on the x-axis
  3. Read up to the line of best fit, then across to the y-axis
  4. This gives an estimated sales figure (e.g. 85 units)
AnswerRead the y-value from the line at x = 22 (value depends on graph)
Example 2

The data shows revision hours from 1 to 10. A student asks you to predict for 20 hours. Why is this unreliable?

Working

  1. 20 hours is outside the range of the data (1 to 10 hours)
  2. Predicting beyond the data range is extrapolation
  3. The trend may not continue — so the prediction is unreliable
AnswerThis is extrapolation — the prediction is unreliable as it is beyond the data range.
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Common mistakes

✗Forcing the line through the origin when it should not pass through (0, 0).
✗Drawing the line through only the first and last data points.
✗Not recognising that predictions far outside the data range are unreliable (extrapolation).
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Exam tips

✓Your line of best fit should pass through the mean point (x̄, ȳ) if you can calculate it.
✓When making a prediction, always draw a dotted line from the axis to the line and across — show your method.

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