Solution — 2018 Question 10 Regression

Using GC, $$r=-0.976∎$$

This indicates a strong negative linear correlation between the time to run 100 metres and the time to run 10 000 metres, meaning athletes who are faster at 100 metres tend to be slower at 10 000 metres.

Using GC, the equation of the regression line of $y$ on $x$ is $$y=-2.22x+66.3∎$$

When $x=13.1,$

The estimated time is $37.2\text{ min}∎$

This estimate is reliable because $x=13.1$ lies within the range of the data $10.8\le x\le 15.6$ , and $r=-0.976\approx -1$ , indicating a strong negative linear correlation. $∎$