2. In nature we find number of variables inter-related to one another.
For example, amount of rainfall to certain extent and production of
paddy, heat and volume of gas, price and demand of a commodity in
the market etc.
Correlation theory aims at finding the degree of relationship that
exists between the variables. A statistical took with the help of which
we can find the degree of relationship that exists between two or
more variables is technically called correlation.
Correlation is sometimes also the study of cause and effect
relationship. For example, heat and volume of gas are closely
related. If heat is the cause volume is the effect for, if heat increases,
the volume of gas increases, if heat decreases the volume decreases,
so heat and volume of gas are correlated.
In this way we can give a number of examples like demand and
supply, price and demand, amount of advertisement and volume of
sale, etc…
Introduction
3. Correlation a LINEAR association between two
random variables
Correlation analysis show us how to determine
both the nature and strength of relationship
between two variables
When variables are dependent on time correlation
is applied
Correlation lies between +1 to -1
4. A zero correlation indicates that there is no
relationship between the variables
A correlation of –1 indicates a perfect negative
correlation
A correlation of +1 indicates a perfect positive
correlation
5. Types
Positive Negative No Perfect
In Simple:-
If two related variables are such that when
one increases (decreases), the other also
increases (decreases).
If two variables are such that when one
increases (decreases), the other decreases
(increases)
If both the variables are independent
6. Positive Correlation: If the two variables correlated are moving in
the same direction then correlation is called positive i.e. if one
variable increases, the other variable also increases or if one variable
decreases, the other variable decreases.
For example, demand and supply increases, if demand decreases
supply decreases i.e. both the variables demand and supply are
moving in the same direction.
Here are some other examples of a positive correlation: The
more money I save, the more financially secure I feel. The
longer I invest, the more compound interest I earn. The less
time I spend marketing my business, the fewer new clients I
acquire. The more years of education I complete, the higher
my earning potential.
7. Negative Correlation: If the two variables correlated are
moving in opposite directions then the correlation is called
negative, i.e. if one variable decreases, the other variable
increases.
For example price and demand are negatively correlated for if
price increases demand decreases and if price decreases, demand
increases.
Here are some other examples of a negative correlation:
The more time I spend at the mall, the less money I have
in my checking account. The higher my mutual fund's
expense ratio, the lower my investment returns. The more
hours I spend at the office, the less time I spend with my
family.
8. Zero Correlation: If there is no correlation
between the two variables then the correlation is
called zero correlation or spurious correlation.
For example, marks scored by a student in tests
and the amount of rain fall.
another example - their is no relationship
between the amount of tea drunk and level
of intelligence.
9. Linear Correlation: If the ratio of the amount of
change in one variable to the amount of change
in the other variable, bears a constant ratio
throughout then, the correlation is said to be
linear. If such variables are plotted on the graph
sheet, all the points lie on a straight line. This is
a case of perfect correlation. This type of
correlation is found only in scientific variables like
heat and volume of gas.
10. Non-Linear or curvilinear correlation: If
the ratio of the amount of change in one
variable to the amount of change in the other
variable does not bear a constant ratio
throughout then, correlation is said to be non-
linear or curvilinear. If such variables are
plotted on the graph, all the points would lie
on a curve but not on a straight line. This is
not a case of perfect correlation. Most of the
variables other than scientific variables show
non-linear correlation.
11. In Simple-:
When plotted on a graph it tends to be a perfect
line
When plotted on a graph it is not a straight line
Types
Linear Non – linear
12.
13.
14. Methods of Studying Correlation
Scatter Diagram Method
Karl Pearson Coefficient Correlation of
Method
Spearman’s Rank Correlation Method
15. -1 < r < +1
The + and – signs are used for positive linear
correlations and negative linear correlations,
respectively
