An estate agent recorded the price per square metre, $p ext{ £} / m^2$, for 7 two-bedroom houses - Edexcel - A-Level Maths Statistics - Question 2 - 2015 - Paper 1

To calculate the product moment correlation coefficient, we use the formula:

$r = \frac{n(\sum{dq}) - (\sum{d})(\sum{q})}{\sqrt{[n\sum{d^2} - (\sum{d})^2][n\sum{q^2} - (\sum{q})^2]}}$

Given:

• $S_d = 1.02$
• $S_w^q = 8.22$
• $S_q = -2.17$

Assuming that the number of houses $n = 7$, we can derive the necessary sums:

1. Calculate $\sum{d}$:

   • From $S_d = 1.02$, we estimate: $\sum{d} = S_d \times n = 1.02 \times 7 = 7.14$

2. Calculate $\sum{q}$:

   • Since $S_q = -2.17$, we estimate: $\sum{q} = S_q \times n = -2.17 \times 7 = -15.19$

3. Then, $r = \frac{7(\sum dq) - (7.14)(-15.19)}{\sqrt{[7\sum{d^2} - (7.14)^2][7\sum{q^2} - (-15.19)^2]}}$

Thus, calculate to find: $r \approx -0.749$

This indicates a strong negative correlation.

The value of the product moment correlation coefficient between $d$ and $p$ is given as $-0.749$.

To determine which house, $H$ or $J$, is more likely to be closer to a train station, we analyze the prices and sizes.

• House $H$ costs £156,400 and has a size of 78 m².
• House $J$ costs £172,900 and has a size of 95 m².

Given that a higher price per square metre may suggest a location closer to amenities such as a train station, we calculate the price per square metre for both houses:

• For House $H$:

$\text{Price per m²} = \frac{156400}{78} \approx 2005.13$

• For House $J$:

$\text{Price per m²} = \frac{172900}{95} \approx 1810.53$

Since House $H$ has a higher price per square metre, it indicates that it is likely to be closer to the train station compared to House $J$. Thus, House $H$ is most likely to be closer to a train station.