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 $$S_x = 113573, \, S_{yy} = 8.657, \, S_{xy} = -808.917$$ (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 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

Use these values to 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 given values:

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

First, we compute the denominator:

$\sqrt{113573 \times 8.657} = \sqrt{983890.901} \approx 991.93$

Now substituting back into the formula:

$r \approx \frac{-808.917}{991.93} \approx -0.81579$

Thus, the product moment correlation coefficient, rounded appropriately, is approximately

$r \approx -0.82$ .

Step 2

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

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Answer

The negative correlation coefficient indicates that houses are cheaper further away from the station. In other words, 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

In this case, the value of the product moment correlation coefficient remains the same at approximately -0.82, as correlation is scale-invariant when both variables are transformed uniformly, such as converting miles to kilometers.

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

Use these values to 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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