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3.8 Line of Best Fit

GCSE Maths Foundation · Edexcel · Chapter 3: Graphs, tables and charts

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: drawing a line of best fit and using it to make estimates. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Draw a line of best fit on a scatter graph
  • Use a line of best fit to estimate a missing value
  • Explain when an estimate is reliable and when it is not
  • Use a line of best fit to solve problems in context

Key words

  • Line of best fit: A straight line drawn through the middle of the points to show the trend.
  • Estimate: A value read from the line of best fit. It is an approximate value, not an exact one.
  • Interpolation: Estimating a value inside the range of the data. This is usually reliable.
  • Extrapolation: Estimating a value outside the range of the data. This is not reliable.

Drawing a line of best fit

Use a ruler. Draw one straight line that follows the trend, with roughly the same number of points on each side. It does not have to go through any point, or through (0, 0). Ignore any outliers. Only draw a line of best fit if there is correlation.

Worked example: checking a line of best fit

Count the crosses: 6 lie just above the line and 4 lie below it, so they are roughly balanced.
The line follows the upward direction of the points and goes right through the middle of them.

Answer: a good line of best fit: balanced and following the trend

Using the line to estimate

To estimate, go from the axis you know to the line (not to a cross), then across or down to the other axis. Draw dashed lines to show your method.

Worked example: two estimates

(a) Estimate the number of drinks sold on a day when it is 18 °C.
Up from 18 to the line, then across: about 57.
(b) Estimate the temperature on a day when 80 drinks are sold.
Across from 80 to the line, then down: about 25 °C.

Answer: (a) about 57 drinks (b) about 25 °C

Key fact: Any value read from a line of best fit is an estimate. Mark schemes accept a range of answers close to the line.

How reliable is an estimate?

Estimates inside the range of the data are fairly reliable. Estimates outside the range are not: we do not know if the trend carries on. Estimates are also less reliable when the correlation is weak.

Worked example: extrapolation

Use the line to estimate sales at 40 °C. Is this reliable?
The line gives about 127 drinks, but 40 °C is far outside the data (12 °C to 27 °C).
The kiosk might run out of drinks or people might stay indoors.

Answer: not reliable: it is outside the range of the data

Solving problems with a line of best fit

Compare a real value with the value the line predicts. If the real value is above the line, it is more than expected; if below, it is less.

Worked example: more or less than expected?

On a day when it was 23 °C the kiosk sold only 60 drinks. Was this more or less than expected?
The line gives about 73 drinks at 23 °C.
60 is well below 73, so the point would lie below the line.

Answer: about 13 fewer drinks than expected (e.g. it may have rained)

Common mistakes

  • Joining the points dot-to-dot, or drawing a curve, instead of one straight ruled line.
  • Forcing the line through (0, 0) or through the first and last points.
  • Reading from a cross instead of from the line.
  • Trusting an estimate made far outside the range of the data.

Revision questions

Try these, then check your answers below each one.

Question 1. A line of best fit passes through (0, 20) and (10, 70). Use it to estimate y when x = 6.

Answer: 50

Working: y goes up by 50 over 10, so 5 per unit. At x = 6: 20 + 6 × 5 = 50.

Question 2. A line of best fit passes through (0, 20) and (10, 70). Use it to estimate x when y = 45.

Answer: 5

Working: 45 - 20 = 25, and 25 ÷ 5 = 5.

Question 3. True or false? A line of best fit must always go through the point (0, 0).

Answer: False

Working: False. It only needs to follow the trend with points balanced on both sides.

Related lessons

Continue in the full course

This lesson is section 3.8 (EGCMF0308) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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