(a) [2 marks]

EITHER
Regression line: \( y = 2.1875x + 0.6875 \), passes through \( (\overline{x}, \overline{y}) \).
Given \( \overline{x} = 7 \), compute \( \overline{y} = 2.1875 \times 7 + 0.6875 = 15.3125 + 0.6875 = 16 \) (M1A1).
OR
Verify \( \overline{x} = \frac{5 + 6 + 6 + 8 + 10}{5} = 7 \), then use regression line to find \( \overline{y} = 16 \) (M1A1).
\( \overline{y} = 16 \) (verified) (AG).

(b) [3 marks]

EITHER
Use \( \overline{y} = 16 \), \( y \)-values: 9, 13, \( p \), \( q \), 21, so \( \frac{9 + 13 + p + q + 21}{5} = 16 \), \( p + q = 37 \) (M1A1).
Given \( q – p = 3 \), solve: \( p + q = 37 \), \( q = p + 3 \), so \( p + (p + 3) = 37 \), \( 2p = 34 \), \( p = 17 \), \( q = 20 \) (M1).
OR
Set up \( 16 = \frac{9 + 13 + p + p + 3 + 21}{5} \), solve \( 2p + 46 = 80 \), \( p = 17 \), \( q = p + 3 = 20 \) (M1A1M1).
\( p = 17 \), \( q = 20 \) (A1).