On a particular day the height above sea level, x metres, and the mid-day temperature, y °C, were recorded in 8 north European towns - Edexcel - A-Level Maths Statistics - Question 1 - 2011 - Paper 2
Question 1
On a particular day the height above sea level, x metres, and the mid-day temperature, y °C, were recorded in 8 north European towns. These data are summarised below... show full transcript
Worked Solution & Example Answer:On a particular day the height above sea level, x metres, and the mid-day temperature, y °C, were recorded in 8 north European towns - Edexcel - A-Level Maths Statistics - Question 1 - 2011 - Paper 2
Step 1
Find $S_{xy}$
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Answer
The formula for finding Sxy is given by:
ewline S_{xy} = extstyle{ extstyle{ extstyle{ -23.72625}}}}}}}}}}}}$$$$
ewline Due to the data, the calculated value for $S_{xy}$ is -23.72625.
Step 2
Calculate, to 3 significant figures, the product moment correlation coefficient for these data.
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Answer
The product moment correlation coefficient, r, is calculated using the formula:
r = rac{S_{xy}}{ extstyle{ extstyle{ S_{xx} S_{yy}}}}
Substituting the values:
ewline r = -0.87104... ext{ (to 3 significant figures: -0.871)}$$
Step 3
Give an interpretation of your coefficient.
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Answer
The correlation coefficient of -0.871 indicates a strong negative correlation between height above sea level and temperature. This suggests that as the height increases, the temperature tends to decrease.
Step 4
Write down the value of $S_{hh}$.
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Answer
Using the new variable, h = rac{x}{1000}, we find:
