1.
February 6, 2023 Orientation Course 1
Correlation

2.
February 6, 2023 Orientation Course 2
Agenda
n Definition
n Examples
n Types of Correlation
n Methods of Simple Correlation
n Limitations

3.
February 6, 2023 Orientation Course 3
Definition
n Statistical tool which helps to study the
relationship between two or more
variables
n The technique which is used to measure
the closeness of the relationship
between the variables

4.
February 6, 2023 Orientation Course 4
Examples
n Age, Weight & Height
n Family Income & Expenditure on Luxury
items
n Price, Supply & Demand
n Optimum Increase in Rainfall &
Production of Rice

5.
February 6, 2023 Orientation Course 5
Types of Correlation
Correlation
Simple
(Two Variables)
Multiple & Partial
(More than 2 Variables)

6.
February 6, 2023 Orientation Course 6
Methods of Simple
Corr.
n Scatter Diagram
n Karl Pearson’s Coefficient of Correlation
n Rank Correlation

7.
February 6, 2023 Orientation Course 7
Scatter Diagram
n Gives an idea of relationship
n More scattered less the degree of
relationship
n More nearer more the degree of
relationship

8.
February 6, 2023 Orientation Course 8
Scatter Diagram (Contd..)
Merits
n Easy to understand
n Not influenced by the size of extreme
values
n First step in investing the relationship
between the variable
Limitations
n The exact degree of correlation cannot be
measured

9.
February 6, 2023 Orientation Course 9
Karl Pearson‘s Method
n Assumptions
§ There is linear relationship between
variables
§ The variables are affected by
independent causes so as to form
normal distribution
§ The two variables are casually
independent

10.
February 6, 2023 Orientation Course 10
Karl Pearson‘s Method
(Cont..)
 
 2
2
2
2
)
,
(
)
,
(
y
n
y
x
n
x
y
x
n
y
x
y
x
Cov
y
x
y
x
Cov
r
i
y
i
x
i
i














n
x
x i


n Formula
n
y
y i



11.
February 6, 2023 Orientation Course 11
Karl Pearson‘s Method
(Cont..)
n Xi is the ith value of the variable x
n Yi is the ith value of the variable y
n Mean of X
n Mean of y
n Standard deviation of x
n Standard deviation of y
x
y
x

y


12.
February 6, 2023 Orientation Course 12
Age Weight
1
2
3
4
5
6
7
8
 i
x  i
y  2
i
x  2
i
y  i
i y
x
xy
2
y
2
x
 
x  
y

13.
February 6, 2023 Orientation Course 13
 i
x
 i
y
 2
i
x
 2
i
y
 i
i y
x )
,
( y
x
Cov
x
 y

Karl Pearson‘s Method
(Cont..)
r

14.
February 6, 2023 Orientation Course 14
Karl Pearson‘s Method
(Cont..)
n r lies between + 1
n r = +1 Perfect Positive Correlation
n r = -1 Perfect Negative Correlation
n r = 0 No relationship