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Two variables are said to
be closely correlated if there is a strong
relationship between them. Suppose you wanted
to test the relationship between height
of parents and their children, and you had
gathered the necessary data.
You could plot parent heights
vs child heights on a graph and draw a line
through the points by eye. Alternatively
you could use 'regression analysis' to find
mathematical equation for the line of best
fit.The resulting equation is the 'regression
equation'. You should then use correlation
analysis to determine:
- whether there is a meaningful relationship,
or whether any apparent relationship could
be explained by chance
- whether parent height was the only important
factor or only had some degree of influence
If there was a strong tendency for tall
parents to have tall children there would
be a strong positive correlation. If there
was a strong tendency for tall parents to
have short children, and short parents to
have tall children there would be a strong
negative correlation. If the height of the
parent made no difference there would be
no correlation. I have never seen data on
that particular relationship, but I would
guess that there is a weak to moderate positive
correlation, there is some tendency for
tall parents to have tall children, but
there are many other factors at play.
Note that 'correlation' does not imply
'causation'. Countries with low levels of
female literacy tend to have high fertility
rates. However there is no causal relationship
between literacy and fertility.
| Coefficient
of Correlation |
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See Pearson's Correlation Coefficient
| Coefficient
of Determination |
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This is the square of the Coefficient of
Correlation (R2). Its characteristics
are:
- it is always positive, it gives the
strength of the relationship without distinguishing
between positive and negative correlation
- it is often thought to give more intuitive
results. For example if R = 0.5 then R2
= 0.25. This would be a weak relationship
and 0.25 seem a better indicator of a
weak relationship than 0.5.
| Pearson's
Correlation Coefficient (R) |
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Pearson's Product Moment is the most commonly
used coefficient of correlation. It is a
coefficient used to specify the strength
of the relationship between two variables.
It has a value between -1 and +1.
A coefficient of +1 means perfect correlation.
A coefficient of -1 means perfect negative
correlation (when one variable increases
the other decreases). A coefficient close
to zero means the variables are not related.
Examples of values of R are:
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