This document discusses correlation and different methods for measuring correlation. It defines correlation as a statistical tool for studying the relationship between two or more variables. There are two main types: simple correlation between two variables, and multiple or partial correlation between more than two variables. Common examples provided include relationships between age and weight, family income and expenditure, and price and supply/demand. Methods for measuring simple correlation discussed include scatter diagrams, Karl Pearson's coefficient of correlation, and rank correlation. Karl Pearson's coefficient calculates the covariance over the standard deviations to produce a correlation coefficient (r) between -1 and +1 to indicate the strength and direction of the linear relationship between two variables.

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..)
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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

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12. February 6, 2023 Orientation Course 12
Age Weight
1
2
3
4
5
6
7
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13. February 6, 2023 Orientation Course 13
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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