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
Eleven bean plants were measured on various days in the first week after planting. The scatter graph shows the results, with a line of best fit drawn.(a) Use the line of best fit to estimate the height of a bean plant $4$ days after planting.

(b) Ravi wants to use the same line of best fit to estimate the height of a bean plant $30$ days after planting. Explain why his estimate is unlikely to be reliable.
Level 3 · 3 marksTry it
2
For each of 15 small shops, the number of hours $h$ the shop was open on a Saturday and the shop's takings £ $T$ that day were recorded on a scatter graph.

The shops in the sample were open for between $4$ and $9$ hours, and the line of best fit has equation

$T = 45h + 60.$

(a) Use the line of best fit to estimate the takings of a shop that was open for $7$ hours.

(b) Explain why the line of best fit should not be used to estimate the takings of a shop that was open for $24$ hours.

(c) Write down what the number $45$ in the equation tells you about these shops.
Level 3 · 4 marksTry it
3
A market stall trader recorded, on 13 market days, the number of hours the stall was open and the number of items sold. The scatter graph shows the results, with a line of best fit drawn.(a) Use the line of best fit to estimate the number of items sold on a day when the stall was open for $6$ hours.

(b) Find the gradient of the line of best fit.

(c) Interpret the gradient of the line of best fit in the context of this question.
Level 3 · 4 marksTry it