Solution — 2023 Question 9 Regression

(a)

(b)

Using GC, $r = 0.960 ∎$

(c)

Using GC, the equation of the regression line of $y$ on $x$ is $y = 0.0805 x - 0.674 ∎$

(d)

When $x = 36,$

\begin{matrix} y & = 0.080 518 (36) - 0.674 20 \\ = 2.2244 \\ = 2.22 \end{matrix}

Hence the estimate for the population of the city is $2.22$ millions $∎$

This estimate is reliable because $x = 36$ lies within the range of the data (interpolation), and $r = 0.960$ indicates a strong positive linear correlation. $∎$

(e)

She should not include the corrected data for city B in the recalculation as it is an outlier $∎$

We can see that it is an outlier by using the scatter diagram