Correlation and Regressssion - Agricultural Statistical Data Analysis Using Stata - page 179

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c orrel ation anD
r eGreSSion
Correlation
Statistical correlation is a method of determining if two sets of data
can be related to each other. For example, the thickness of tree rings
can be correlated with the amount of rainfall. So, in wet years, tree
rings appear larger than in dry years. In this particular case, there
appears to be a causal relationship—more rainfall (water) results in
more growth. Correlations do not have to be positive; there can be a
negative correlation between two variables. For example, a commod-
ity price may go down as the supply increases. In many such cases,
the link between the variables is obvious. A correlation between an
increase in fertilizer and an increase in yield is another example where
this link is obvious. Oftentimes, however, correlations occur where
there is no apparent causal relationship. A rather famous example is
foot size in children and spelling ability. There is a strong positive
correlation between these two items. The reason there is such a good
correlation between the two is not because foot size increases spelling
ability. The association has to do with the child's age and level of edu-
cation. This is an important point about correlation; it is not a cause
and effect relationship. Correlation in this context can help identify
relationships that might ultimately be a cause and effect relationship.
They also can be unrelated as in the foot size and spelling ability.
Therefore, interpretation of correlation results should be approached
with caution, particularly if there is no obvious mechanism for the
two to be linked.
The most common linear correlation is often called simple correla-
tion, total correlation, or product-moment correlation. This type of cor-
relation is measured by the coefficient of correlation and is designated
by r , which is an unbiased estimate of ρ (Greek rho). Correlation is a
unit-independent measure of association. There is a related technique
called regression , which is often confused with correlation. As a general
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