A young family were looking for a new 3 bedroom semi-detached house. A local survey recorded the price x, in £1000, and the distance y, in miles, from the station of such houses. The following summary statistics were provided $$ S_x = 113573 \quad S_{yy} = 8.657 \quad S_{xy} = -808.917 $$ (a) Use these values to calculate the product moment correlation coefficient. (b) Give an interpretation of your answer to part (a). Another family asked for the distances to be measured in km rather than miles. (c) State the value of the product moment correlation coefficient in this case.

A-Level Edexcel Maths Statistics Further Correlation & Regression: A young family were looking for

A young family were looking for a new 3 bedroom semi-detached house - Edexcel - A-Level Maths Statistics - Question 1 - 2007 - Paper 2

Question 1

A young family were looking for a new 3 bedroom semi-detached house. A local survey recorded the price x, in £1000, and the distance y, in miles, from the station of... show full transcript

Worked Solution & Example Answer:A young family were looking for a new 3 bedroom semi-detached house - Edexcel - A-Level Maths Statistics - Question 1 - 2007 - Paper 2

Step 1

Calculate the product moment correlation coefficient.

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Answer

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

$r = \frac{S_{xy}}{\sqrt{S_x S_{yy}}}$

Substituting the provided values:

$r = \frac{-808.917}{\sqrt{113573 \times 8.657}}$

Calculating the denominator:

$\sqrt{113573 \times 8.657} = \sqrt{983166.581} \approx 991.526$

Thus,

$r = \frac{-808.917}{991.526} \approx -0.8157$

Therefore, the product moment correlation coefficient is approximately -0.816.

Step 2

Give an interpretation of your answer to part (a).

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Answer

The negative correlation coefficient of approximately -0.816 indicates that there is a strong negative correlation between the price of the houses and their distance from the station. This suggests that as the distance from the station increases, the price of the houses tends to decrease.

Step 3

State the value of the product moment correlation coefficient in this case.

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Answer

When distances are measured in kilometers rather than miles, the product moment correlation coefficient remains unchanged as it is a unitless measure. Hence, the value is still approximately -0.816.

A young family were looking for a new 3 bedroom semi-detached house - Edexcel - A-Level Maths Statistics - Question 1 - 2007 - Paper 2

Worked Solution & Example Answer:A young family were looking for a new 3 bedroom semi-detached house - Edexcel - A-Level Maths Statistics - Question 1 - 2007 - Paper 2

Calculate the product moment correlation coefficient.

Give an interpretation of your answer to part (a).

State the value of the product moment correlation coefficient in this case.

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