A-level · Data presentation

Correlation and regressionExam-style questions

Bivariate data and scatter diagrams; describing correlation by its direction (positive/negative) and strength; why correlation does not imply causation; and using a given regression line y = a + bx to make and interpret predictions — including why prediction inside the data range (interpolation) is safe but outside it (extrapolation) is not. Interpreting the PMCC is flagged as A-level.

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12 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The snow on a mountain path melts during the spring. Bea measures the depth of the snow, $d$ cm, at a marker post on the path once a day for $15$ days. She lets $t$ be the number of days after 1 March, so that $t = 0, 1, 2, \ldots, 14$

For Bea's data, the regression line of $d$ on $t$ is

$d = 62.4 - 3.15t$
(a) Interpret the gradient of this line.

(1 mark)
(b) Interpret the value $62.4$ in Bea's model.

(1 mark)

Bea uses her regression line to estimate the depth of snow on the path when $t = 40$
(c) Give a reason why this estimate may not be reliable.

(1 mark)
Level 2 · 3 marksTry it