Solution — 2022 Question 9 Regression

(a)

(b)

(i)

(ii)

Using GC, $r = 0.974 ∎$

This indicates a strong positive linear correlation between the distance from the capital city and the flight fare.

(iii)

Using GC, the equation of the regression line of $y$ on $x$ is $y = 0.977 x + 35.3 ∎$

(iv)

When $x = 320$

\begin{matrix} y & = 347.83 \end{matrix}

The estimated fare for a city $320$ km from the capital is $$ 347.83 ∎$

(v)

When all fares are increased by $10 %,$ all $y$ values are multiplied by $1.1.$

The value of $m$ does not change as the gradient remains the same $∎$

$c$ will increase by $10 %$ since the $y$ -intercept will increase by $10 % ∎$