S1 :: Chapter 6�Correlation
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Type of correlation:
Weak positive correlation
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strength
type
Weak negative correlation
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Strong positive correlation
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No correlation
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Recap of correlation
Correlation gives the strength of the relationship (and the type of relationship) between two variables.
Simplified formula
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Formula based on definition
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Bro Exam Tip: Given in formula booklet, but useful to memorise.
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Covariance
We understand variance as ‘how much a variable varies’.
We can extend variance to two variables.
We might be interested in how one variable varies with another.
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(this won’t be tested in an exam but is intended to provide background)
Covariance
Comment on the covariance between the variables.
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(this won’t be tested in an exam but is intended to provide background)
Covariance
Comment on the covariance between the variables.
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(this won’t be tested in an exam but is intended to provide background)
Simplified formula
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Product Moment Correlation Coefficient (PMCC)
We’ll interpret what that means in a second.
Have an intelligent guess based on the discussion above.
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Interpreting the PMCC
We’ve seen the PMCC varies between -1 and 1.
means
Perfect positive correlation.
means
No correlation
means
Perfect negative correlation.
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Interpreting the PMCC
Example
Baby | A | B | C | D | E | F |
| 31.1 | 33.3 | 30.0 | 31.5 | 35.0 | 30.2 |
| 36 | 37 | 38 | 38 | 40 | 40 |
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Let’s do it on our calculators!
Baby | A | B | C | D | E | F |
| 31.1 | 33.3 | 30.0 | 31.5 | 35.0 | 30.2 |
| 36 | 37 | 38 | 38 | 40 | 40 |
Test Your Understanding
June 2013 Q1
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Further Practice
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Quite often the values are given to you in an exam.
Interpreting the PMCC
“Interpret” vs “State”
In general in Statistics exams, the word ‘interpret’ means “explain in context using non-statistical language”.
A bad answer (that may or may not be accepted):
“Strong negative correlation” (this is stating the correlation not interpreting it)
A good answer:
“As the waiting time increases, the customer satisfaction tends to decrease”.
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Exercises
Page 122 Exercise 6B
Q1, 4, 5, 7, 9
Exam Questions
(on provided sheet)
Q1
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(Before you go on to Q2) Effects of coding
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| Unaffected! |
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Example
| 1020 | 1032 | 1028 | 1034 | 1023 | 1038 |
| 320 | 335 | 345 | 355 | 360 | 380 |
| 0 | 12 | 8 | 14 | 3 | 18 |
| 4 | 7 | 9 | 11 | 12 | 16 |
We can now just find the PMCC of this new data set, and no further adjustment is needed.
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Exam Questions
(on provided sheet)
Q2
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Exam Questions
(on provided sheet)
Q3
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Exam Questions
(on provided sheet)
Q4
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Exam Questions
(on provided sheet)
Q5
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Exam Questions
(on provided sheet)
Q6
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Exam Questions
(on provided sheet)
Q7
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Exam Questions
(on provided sheet)
Q8
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Exam Questions
(on provided sheet)
Q9
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Limitations of correlation
Often there’s a 3rd variable that explains two others, but the two variables themselves are not connected.
Q1: The number of cars on the road has increased, and the number of DVD recorders bought has decreased. Is there a correlation between the two variables?
Buying a car does not necessarily mean that you will not buy a DVD recorder, so we cannot say there is a correlation between the two.
Q2: Over the past 10 years the memory capacity of personal computers has increased, and so has the average life expectancy of people in the western world. Is there are correlation between these two variables?
The two are not connected, but both are due to scientific development over time (i.e. a third variable!)
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