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.
For more information see Pearson's
Correlation Coefficient (R)
and Coefficient
of Determination and Regression
Analysis.
