Gary compared the total attendance, $x$, at home matches and the total number of goals, $y$, scored at home during a season for each of 12 football teams playing in a league. He correctly calculated: $S_{xx} = 1022500 \quad S_{yy} = 130.9 \quad S_{xy} = 8825$ (a) Calculate the product moment correlation coefficient for these data. (b) Interpret the value of the correlation coefficient. (c) Helen was given the same data to analyse. In view of the large numbers involved she decided to divide the attendance figures by 100. She then calculated the product moment correlation coefficient between $\frac{x}{100}$ and $y$. (c) Write down the value Helen should have obtained.

A-Level Edexcel Maths Statistics Correlation & Regression: Gary compared the total attendan

Gary compared the total attendance, $x$, at home matches and the total number of goals, $y$, scored at home during a season for each of 12 football teams playing in a league - Edexcel - A-Level Maths Statistics - Question 1 - 2010 - Paper 2

Question 1

Gary compared the total attendance, $x$, at home matches and the total number of goals, $y$, scored at home during a season for each of 12 football teams playing in ... show full transcript

Worked Solution & Example Answer:Gary compared the total attendance, $x$, at home matches and the total number of goals, $y$, scored at home during a season for each of 12 football teams playing in a league - Edexcel - A-Level Maths Statistics - Question 1 - 2010 - Paper 2

Step 1

Calculate the product moment correlation coefficient for these data.

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Answer

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

$r = \frac{S_{xy}}{\sqrt{S_{xx} \cdot S_{yy}}}$

Substituting the values:

$r = \frac{8825}{\sqrt{1022500 \cdot 130.9}}$

Calculating the denominator:

$\sqrt{1022500 \cdot 130.9} = \sqrt{133195725} \approx 11547.48$

Now substituting back:

$r = \frac{8825}{11547.48} \approx 0.763$

Step 2

Interpret the value of the correlation coefficient.

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Answer

The correlation coefficient of approximately 0.763 indicates a strong positive correlation between attendance and goals scored. This means that teams with higher attendance tend to score more goals, suggesting a relationship between the number of spectators and the performance of the teams.

Step 3

Write down the value Helen should have obtained.

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Answer

Given that Helen divided the attendance figures by 100, the correlation coefficient would remain the same since correlation is scale-invariant. Therefore, she should have obtained a correlation coefficient of approximately 0.763.

Gary compared the total attendance, $x$, at home matches and the total number of goals, $y$, scored at home during a season for each of 12 football teams playing in a league - Edexcel - A-Level Maths Statistics - Question 1 - 2010 - Paper 2

Worked Solution & Example Answer:Gary compared the total attendance, $x$, at home matches and the total number of goals, $y$, scored at home during a season for each of 12 football teams playing in a league - Edexcel - A-Level Maths Statistics - Question 1 - 2010 - Paper 2

Calculate the product moment correlation coefficient for these data.

Interpret the value of the correlation coefficient.

Write down the value Helen should have obtained.

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