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| Unit 5 ~ Quantitative Techniques for Business | |
| Lesson 9 - 4th April 2000 | |
| Correlation | |
Click here to see the slides from the lesson.
- When a change in one quantity (or data set) is accompanied by a change in another quantity (or data set) then we can say both quantities (or data sets) are correlated.
Not Cause and Effect
- You need to take care not to think in terms of cause and effect.
- Just because there is correlation does not imply there is a relationship between the two quantities.
- Where there is cause and effect there will be correlation, however there can be correlation without cause and effect.
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Types of Correlation
Generally if all the points are confined to a line then we can say there is perfect correlation.
If not then we can say there is either:
- a strong correlation
- a weak correlation
- no correlation
- Generally if all the points are confined to a line then we can say there is perfect correlation.
- If not then we can say there is either:
- a strong correlation
- a weak correlation
- no correlation
It is possible to measure correlation precisely, using the coefficient of correlation.
Measuring Correlation
If you have a correlation coefficient of 1 then the two sets of data will increase together.
If you have a correlation coefficient of -1 then the two sets of data will decrease together.
If you have a correlation coefficient of 0 then the
two sets of data have no
correlation.
The correlation coefficient between two sets of data will lie between +1 and -1.
Product Moment Correlation Coefficient
By various mathematical manipulations (that we don’t need to know) it can be shown that the correlation coefficient r between two sets of data (x and y) is given by:
Spearman's Rank Correlation Coefficient
Instead of calculating the coefficient from the data values, it is possible to rank the data and calculate the coefficient from the ranking, rs where n is the number of data items and d is the difference between the corresponding data in the ranked series:
Limitations
Correlation is not a good indicator of causal connection, therefore should not be used as basis for prediction.
The reliability of r and rs increases as the number of data items increase, therefore should not be relied upon for small sets of data.
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