Correlation statistics

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S1 Revision Notes: Correlation
Section 1: Productmoment correlation coefficient
The productmoment correlation coefficient, r, measures how close the points on a scatter graph lie to a
straight line (or more mathematically it measures the strength of the linear relationship between two
The key points:
r always lies between 1 and 1. (If you calculate a value of r that does not lie between 1 and 1 then
you've made a mistake!!).
The formula for calculating r is
Note: These formulae are in the formula book.
Normally you can use your calculator's r button for finding a correlation coefficient see later.
In a school there are 10 students on the first year of an Alevel Geography course who also study
mathematics at Alevel. The table shows the marks of each student in the mock examinations in
Geography and Mathematics.
Student Geography mark, x Maths mark, y
A 79 63
B 72 58
C 57 78
D 78 80
E 73 75
F 56 63
G 83 77
H 81 92
I 13 11
J 62 90
a) Calculate the value of the productmoment correlation coefficient between x and y and interpret the
value that you obtain.
b) Plot a scatter graph of these data.
Created on 13/05/2005 10:18 AM by A. Duncombe

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Note 2: You can check you have correctly entered the data into some makes of calculator by using the
memories labelled A, B, C, ..., F (in red). For example if you press RCL A you get the value for ,
RCL B gives , etc.
b) A scatter graph for these data is shown below:
Note: Remember to give the graph a title and to label the axes.…read more

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Note: This formula is in the formula book.
Created on 13/05/2005 10:18 AM by A.…read more

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The table shows the hardness of the water supply (measured in units of parts per million of calcium) and the
cardiovascular disease death rate (in units of deaths per 10000 population) in a random sample of ten
English towns.…read more

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Often the explanation is that both variables are related to a 3rd variable not being measured. In the example
above for instance both life expectancy and the number of TVs in the population will both be related to the
country's wealth.
Created on 13/05/2005 10:18 AM by A.…read more


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