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      <text>43.2.06 Comments on interpretation</text>
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      <text><![CDATA[<h3>Comments on interpretation</h3>

Some care should always be taken when interpreting results obtained from correlation coefficient
calculations.
<p></p>
(a) A high correlation does not necessarily imply that a causal relationship exists between
the variables considered. For example, it may be that a high degree of correlation exists
between the number of road accidents in a particular city and the number of late trains
arriving at a station in another city both over the same time period. In general one would
not expect to find a causal relation between the variables involved. Similar comments
apply to, for example, water hardness and average income for towns in the UK.

<p></p>
(b) When considering the behaviour of two variables, one should realize that it is possible
that both variables may change because of the influence of a third variable. An example
often quoted in this context is the Gas law
\[\dfrac{PV}{T} = \text{constant} \]
where say, pressure and volume may change because of a change in temperature.

<p></p>
(c) A low value of the correlation coefficient does not necessarily imply that no relationship
exists between the variables being considered. Remember that the correlation coefficient 
is indicative of a <i>linear relationship only</i> and that a low or zero value of \(r\) may indicate
that a non-linear relationship exists. For example a set of points lying on the curve \(y = x^2\)<i>
might</i> result in a zero value of \(r\).]]></text>
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