EDEXCEL STATISTICS 1 Correlation
Using Coding
Objectives:
- Simplify PMCC calculations by using coding
- Discuss and understand the PMCC
In simple terms if when you plot a scatter graph the numbers on the axes are too large or small, you simply rescale using standard form or similar and the graph appears the same. This is effectively coding, if you choose to rescale your sets of data, this has no effect on the value of the PMCC.
As the next example illustrates, if you are expected to use coding in an exam, it will be made clear and the exact coding suggested in the question.
Edexcel Exam Question
A company owns two petrol stations P and Q along a main road. Total daily sales in the same week for P (£p) and for Q (£q) are summarised in the table below.
p / qMonday / 4760 / 5380
Tuesday / 5395 / 4460
Wednesday / 5840 / 4640
Thursday / 4650 / 5450
Friday / 5365 / 4340
Saturday / 4990 / 5550
Sunday / 4365 / 5840
When these data are coded using x = and y = ,
x = 48.1, y = 52.8, x2 = 486.44, y2 = 613.22 and xy = 204.95.
(a)Calculate Sxy, Sxx and Syy.
(4)
(b)Calculate, to 3 significant figures, the value of the product moment correlation coefficient between x and y.
(3)
(c)(i)Write down the value of the product moment correlation coefficient between p and q.
(ii)Give an interpretation of this value.
(2)
(Total 9 marks)
Solution
You don’t have to actually do any coding in this question !
However, its a useful excercise to actually code the data, you should end up with these results and the corresponding totals and squred totals are subsequently all easier to manage – but again, this is all done for you !
x / yMonday / 3.95 / 10.4
Tuesday / 10.3 / 1.2
Wednesday / 14.75 / 3
Thursday / 2.85 / 11.1
Friday / 10 / 0
Saturday / 6.25 / 12.1
Sunday / 0 / 15
(a)Sxy = 204.95
= 157.86142
Sxx = 155.92428
Syy = 214.95714
(b)r =
= 0.862269…
= 0.862 3sf
(c)(i)0.862 (The Coding has No Effect)
(ii)As sales at on petrol station increases, the other decreases;
limited pool of customers; close one garage
[9]
Understanding the PMCC
If we look at the example below, it would be correct to say that there is a negative correlation that suggests that people in in a country with lots of computers per head enjoy a greater life expectancy.
However, the mistake is to assume that a change in one causes a change in the other.
Clearly exporting lots of computers to developing countries is not likely to improve life expectancy.
In cases like this the link is through a third variable, in the above example it might be the countries GDP or “wealth”
Without getting too involved you need to consider the difference between cause and effect......
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