GCSE · Scatter graphs & correlation

Predicting from a line of best fitExam-style questions

How to read an estimate off a line of best fit in both directions, why a prediction inside the data is trustworthy and one outside it is not, and what the gradient of the line means in the context of the question.

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10 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
The scatter graph shows the number of hours of exercise per week and the resting pulse rate, in beats per minute, of 14 students. A line of best fit has been drawn.(a) Use the line of best fit to estimate the resting pulse rate of a student who exercises for $5$ hours per week.

(b) Sam says the estimate in part (a) must be reliable, because $5$ hours is inside the range of the data. Comment on Sam's statement.
Level 4 · 4 marksTry it
2
The scatter graph shows the number of hours of sleep and the reaction time, in milliseconds, of 13 people. A line of best fit has been drawn.(a) Use the line of best fit to estimate the reaction time of a person who slept for $9$ hours.

(b) A person has a reaction time of $250$ milliseconds. Use the line of best fit to estimate the number of hours that person slept.

(c) Explain why your answer to part (b) is only an estimate.
Level 4 · 4 marksTry it
3
A candle is lit and its length is measured once an hour for the first $6$ hours. The results are plotted on a scatter graph and a line of best fit is drawn. The line has equation

$L = 20 - 2t,$

where $L$ cm is the length of the candle and $t$ is the time in hours since it was lit.

(a) Use the line of best fit to estimate the length of the candle after $4.5$ hours.

(b) Work out the length that this line of best fit predicts after $15$ hours.

(c) Use your answer to part (b) to explain why the line of best fit should not be used to make a prediction for $15$ hours.
Level 4 · 5 marksTry it