Solution — 2020 Question 10 Regression

(a)

(b)

Using GC, $r = 0.942 ∎$

This indicates a strong positive linear correlation between the age of an employee and their monthly earnings, suggesting that older employees tend to earn more.

(c)

Using GC, the equation of the regression line of $y$ on $x$ is $y = 0.0800 x + 1.60 ∎$

(d)

When $x = 24,$

\begin{matrix} y & = 0.079 964 (24) + 1.6025 \\ = 3.5216 \end{matrix}

Hence the estimated monthly earnings is $$ 3520 ∎$

This is a reliable estimate because

$x = 24$ lies within the range of the data $19 \leq x \leq 59 ∎$
$r = 0.942 \approx 1$ , indicating a strong positive linear correlation $∎$

(e)

The value of $m$ will remain unchanged. Adding a fixed constant to all $y$ values does not affect the gradient of the regression line $∎$