Correlation

1. ACHARYA NARENDRA DEVA UNIVERSITY OF AGRICULTURE OF TECHNOLOGY,
KUMARGANJ, AYODHYA-(224229), U.P.
Assignment
on
Correlation
Course No : STAT-502 4(3+1)
Course name : Statistical methods for applied sciences
Presented to:
Dr. Vishal Mehta
Assistant Professor
Department of Agril. Statistics
Presented by:
Dharmendra Kumar
Id. No. A-12993/22
Ph.D. 𝟏𝒔𝒕
𝐒𝐞𝐦𝐞𝐬𝐭𝐞𝐫
Soil Science and Agril. Chemistry

3. Content
• Correlation
• Uses of correlation analysis
• Importance of correlation analysis
• Types of correlation
• Rank correlation
• Repeated rank correlation
• Numerical
• References

4. Correlation
• Correlation is the degree of inter-
relatedness among the two or more
variables.
• Correlation analysis is a process to find
out the degree of relationship between
two or more variables by applying
various statistical tools and techniques.

5. Uses of Correlation Analysis
• It is used in deriving the degree and
direction of relationship within the
variables.
• It is used in reducing the range of
uncertainty in matter of prediction.
• It is used in presenting the average
relationship between any two variables
through a single value of coefficient of
correlation.

6. Importance of correlation analysis:
• Measures the degree of relation i.e.
whether it is positive or negative.
• Estimating values of variables i.e. if
variables are highly correlated then we
can find value of variable with the help
of gives value of variable.
• Helps in understanding economic
behavior.

7. Types of correlation
On the basis of degree of correlation
On the basis of number of variables
On the basis of linearity
1. Positive correlation
2. Negative correlation
3. Constant correlation
1. Simple correlation
2. Partial correlation
3. Multiple correlation
1. Linear correlation
2. Non –linear correlation

8. Correlation : On the basis of degree
Positive Correlation
• if one variable is increasing and with its
impact on average other variable is also
increasing that will be positive
correlation.
For example:
• Income (Rs.): 350 360 370 380
• Weight ( Kg.) : 30 40 50 60

9. • Negative correlation
If one variable is increasing and with its
impact on average other variable is also
decreasing that will be positive
correlation.
For example:
• Income (Rs.): 350 360 370 380
• Weight ( Kg.) : 80 70 60 50

10. Constant/Zero correlation
• A zero correlation exists when there is no
relationship between two variables.
For example
There is no relationship between the
amount of tea drunk and level of
intelligence.

11. Correlation : On the basis of number of
variables
Simple correlation
• Correlation is said to be simple when
only two variables are analyzed.
For example:
• Correlation is said to be simple when it
is done between demand and supply or
we can say income and expenditure etc.

12. Partial correlation:
• When three or more variables are
considered for analysis but only two
influencing variables are studied and rest
influencing variables are kept constant.
For example:
• Correlation analysis is done with demand,
supply and income. Where income is
kept constant.

13. • Multiple correlation:
In case of multiple correlation three or
more variables are studied simultaneously.
For example:
• Rainfall, production of rice and price of
rice are studied simultaneously will be
known are multiple correlation.

14. Correlation : On the basis of linearity
Linear correlation:
• If the change in amount of one variable
tends to make changes in amount of
other variable bearing constant changing
ratio it is said to be linear correlation.
For example:
Income (Rs.): 350 360 370 380
Weight (Kg.): 30 40 50 60

15. Non -Linear correlation:
• If the change in amount of one variable
tends to make changes in amount of other
variable but not bearing constant changing
ratio it is said to be non -linear
correlation.
For example:
Income (Rs.): 320 360 410 490
Weight (Kg.) : 21 33 49 56

16. Rank correlation
Rank correlation:
This method is finding out the lack of it between
two variable was developed by the ‘brutish
Psychologist Charles Edward Spearman in
1904’.
In any event, the RCC is applied to a set of
ordinal rank no. with for the individual ranked in
quality or quantity and soon to for the individual
ranked last in a group of individual.

17. Rank correlation formula
Rank correlation:
𝑟𝑠 = 1 −
6 σ 𝑑𝑖
2
𝑛(𝑛2−1)
where,
𝑟𝑠= spearman rank correlation
n= number of observations
d= difference of individual
observation

18. Question. Ten varieties of rice in the field were judged for overall per for
mince by two formers the rank by formers are given below.
EXAMPLE:
X Y di = X-Y
2 1 1 1
1 2 -1 1
5 7 -2 4
3 4 -1 1
10 8 2 4
8 9 -1 1
9 10 -1 1
7 3 4 16
4 6 -2 4
6 5 1 1

19. Repeated Correlation Co-efficient
FORMULA :
𝒓𝒌 = 𝟏 −
𝟔[σ𝒅𝒊𝟐 + σ
𝒎(𝒎𝟐
− 𝟏)
𝟏𝟐
𝒏(𝒏𝟐 − 𝟏)
EXAMPLE: Obtain the correlation rank following the data –
X ( 68,64 ,75 ,50 ,64 ,80 ,75 ,40 ,55 ,64)
Y (62 ,58 ,68 ,45 ,81 ,60 ,68 ,48 ,50 ,70)

20. EXAMPLE:
X Y di= (RX-RY)
68 62 -1 1
64 58 -1 1
75 68 -1 1
50 45 -1 1
64 81 5 25
80 60 -5 25
75 68 -1 1
40 48 1 1
55 50 0 0
66 70 4 16

21. SOLVED -
1-
6 σ 𝑑2+
𝑚 𝑚2−1
12
𝑛 𝑛2−1
=1 -
6(72)+3
10(10−1)
= 1-
=
990−435
990
=
555
990
=0.5606
𝟒𝟑𝟐 + 𝟑
𝟗𝟗𝟎

22. ❑References
• Agarwal, B.L., Programmed Statistics.
New Age International Publishers, New
Delhi, 3rd edition.
• Gupta, S.C. and Kapoor, V.K.,
Fundamentals of Mathematical Statistics.
Sultan Chand & Sons, New Delhi, 12th
edition.
• Paul, N.C., Statistics in shorts. New
Vishal Publications, New Delhi.