This document discusses correlation analysis. It defines correlation as the degree of relationship between two random variables. Correlation can be positive, negative, simple, partial, or multiple depending on the direction and number of variables. Linear correlation means changes in one variable are proportionally related to changes in the other. Non-linear correlation means changes are not proportional. Correlation is measured using the correlation coefficient r, which ranges from -1 to 1. A higher absolute r value means stronger correlation. Correlation only indicates relationship and not causation. The document also covers probable error and coefficient of determination in interpreting correlation results.

1. Correlation
Analysis
Group – 6
Pranjal Harshali
Neelesh Khushboo
Ayush Pragati
Saqib

2. Introduction
 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

3. Meaning of Correlation
Analysis
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.
According to Conner
“if two or more quantities vary in sympathy, so
that movement in one tend to be
accompanied by corresponding movements
in the other , then they said to be
correlated.”

4. Three Stages to solve correlation
problem :
 Determination of relationship, if yes,
measure it.
 Significance of correlation.
 Establishing the cause and effect
relationship, if any.

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 I used in presenting the average
relationship between any two
variables through a single value of
coefficient of correlation.

6. Uses of Correlation
Analysis
 In the field of science and philosophy
these methods are used for making
progressive conclusions.
 In the field of nature also, it is used in
observing the multiplicity of the inter
related forces.

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

9. 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.) : 350360 370 380
Weight ( Kg.) : 30 40 50 60

10. Correlation : On the basis of
degree
 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

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. Correlation : On the basis of
number of variables
 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. Correlation : On the basis of
number of variables
 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. Correlation : On the basis of
linearity
 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.   2222
)()( 
 



YYnXXn
YXXYn
rxy
Shared variability of X and Y variables on the top
Individual variability of X and Y variables on the bottom

17. 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.

18. Correlation and Causation
 The correlation may be due to pure
chance, especially in a small sample.
 Both the correlated variables may be
influenced by one or more other
variables.
 Both the variables may be mutually
influencing each other so that neither an
be designed as the cause and other as

19. Probable Error :
Probable error determine the reliability of
the value of the coefficient in so far as it
depends on the conditions of random
sampling. It helps in interpreting its
value.
P.E.r = 0.6745 (1-r2)/√n
r = coefficient of correlation.
n = number of pairs of observation.

20. Conditions under Probable error :
 if the value of r is less than the
probable error there is no evidence of
correlation, i.e. the value of r is not at
all significant.
If the value of r is more than six times
the probable error, the coefficient of
correlation is practically certain i.e. the
value of r is significant.

21. Conditions under Probable error
 By adding and subtracting the value of
probable error from the coefficient of
correlation we get the upper and lower
limits, between correlation lies.
P = r+ P.E. ( upper limit )
P = r- P.E. ( lower limit )

22. Coefficient of Determination :
Coefficient of determination also helps in
interpreting the value of coefficient of
correlation. Square of value of correlation
is used to find out the proportionate
relationship or dependence of dependent
variable on independent variable. For e.g.
r= 0.9 then r2 = .81 or 81% dependence of
dependent variable on independent
variable.Coefficient of Determination = Explained variation
Total variance

23. Thank
you