Page 204 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Unit 10: Correlation

If all the points or dots lie exactly on a straight line or a curve, the association between the Notes
variables is said to be perfect. This is shown below:
Figure 10.2

A scatter diagram of the data helps in having a visual idea about the nature of association
between two variables. If the points cluster along a straight line, the association between variables
is linear. Further, if the points cluster along a curve, the corresponding association is non-linear
or curvilinear. Finally, if the points neither cluster along a straight line nor along a curve, there
is absence of any association between the variables.
It is also obvious from the above figure that when low (high) values of X are associated with low
(high) value of Y, the association between them is said to be positive. Contrary to this, when low
(high) values of X are associated with high (low) values of Y, the association between them is
said to be negative.

10.2 Types of Correlation

Broadly speaking, there are four types of Correlation, namely, (a) Positive correlation,
(b) Negative correlation, (c) Linear correlation and (d) Non-Linear Correlation.

10.2.1 Positive Correlation

If the values of two variables deviate in the same direction i.e., if increase in the values of one
variable results, on an average, in a corresponding increase in the values of the other variable or
if a decrease in the values of one variable results, on an average, in a corresponding decrease in
the values of the other variable, the corresponding correlation is said to be positive or direct.

Examples:
(i) Sales revenue of a product and expenditure on Advertising.
(ii) Amount of rain fall and yield of a crop (up to a point).
(iii) Price of a commodity and quantity of supply of a commodity.

(iv) Height of the Parent and the height of the Child.
(v) Number of patients admitted into a Hospital and Revenue of the Hospital.
(vi) Number of workers and output of a factory.

Perfect Positive Correlation

If the variables X and Y are perfectly positively related to each other then, we get a graph as
shown in Figure 10.3.

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