Solution — 2025 Question 7 Regression

(a)

(b)

Using GC, $r = 0.961 ∎$

(c)

Using GC, the equation of the regression line of $y$ on $x$ is $y = 0.82 x + 24 ∎$

(d)

When $x = 70,$

\begin{matrix} y & = 0.817 10 (70) + 24.485 \\ = 81.682 \end{matrix}

Estimated time to solve the puzzle is $81.7 seconds ∎$

This estimate is reliable because $x = 70$ lies within the range of the data $40 \leq x \leq 105$ and $r = 0.961 \approx 1$ indicates a positive linear correlation $∎$

(e)

The value of $m$ will remain unchanged $∎ .$ Subtracting a constant $k$ from all $y$ values does not affect the gradient of the regression line.

The value of $c$ will decrease by $k$ (the new intercept decreases by $k$ ). $∎$