Solution — 2016 Question 11 Regression

Using GC, $$r=0.903∎$$

Using GC, the equation of the regression line of $y$ on $x$ is $$y=0.294x-1.89∎$$

When $x=16.9,$

The estimated time to run 1000 metres is $3.08\text{ minutes}∎$

This is a reliable estimate because:

1. $x=16.9$ lies within the range of the data $15\le x\le 18.2∎$
2. $r=0.903\approx 1,$ indicating a strong positive linear correlation. $∎$

Including the new member, using GC, $$r=0.568∎$$

The answer to (b) is more likely to represent the correlation between swimming and running times as the $|r|$ value is closer to 1. Given that the new correlation is significantly lower, this suggests that the times of the new member is an outlier compared to the other data points $∎$