Page 156 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes SCATTER DIAGRAM
12
ESTIMATING LINE
10
8
6
4
2

0 2 4 6 8 10
Merits and Limitations of the Method

Merits

1. It is a simple and non-mathematical method of studying correlation between the variables. As
such it can be easily understood and a rough idea can very quickly be formed as to whether or
not the variables are related.
2. It is not influenced by the size of extreme items whereas most of the mathematical methods of
finding correlation are influenced by extreme items.
3. Making a scatter diagram usually is the first step in investigating the relationship between two
variables.
Limitations

By applying this method we can get an idea about the direction of correlation and also whether it is
high or low. But we cannot establish the exact degree of correlation between the variables as is possible
by applying the mathematical methods.
10.2 Karl Pearson’s Coefficient of Correlation

Of the several mathematical methods of measuring correlation, the Karl Pearson’s method, popularly
known as Pearsonian coefficient of correlation, is most widely used in practice. The Pearsonian
coefficient of correlation is denoted by the symbol r. It is one of the very few symbols that is used
universally for describing the degree of correlation between two series. The formula for computing
Pearsonian r is:
∑ xy
r = ... (i)
Nσ σ
xy
Hence x = ( − ) XX , y = ( − ) YY

σ x = Standard deviation of series X
σ y = Standard deviation of series Y

N = Number of paired observations.
This method is to be applied only when the deviations of items are taken from actual means and not
from assumed means.
The value of the coefficient of correlation as obtained by the above formula shall always lie between
± 1. When r = + 1, it means there is perfect positive correlation between the variables. When r = – 1, it
means there is perfect negative correlation between the variables. When r = 0, it means there is no
relationship between the two variables. However, in practice, such values of r as + 1, – 1 and 0 are
rare. We normally get values which lie between + 1 and – 1 such as + .1, – .4, etc. The coefficient of

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