1. WELCOME TO
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2. CORRELATION AND REGRESSION

3. CORRELATION:
“ Correlation analysis deals with the association between
two or more variables.”
“Correlation analysis attempts to determine the ‘degree of
relationship’ between variables.”
Types of Correlation:
Positive or negative
Simple and Multiple
3. Linear and Non linear.

4. “When two variables move in the same direction,
that is when one increases the other also increases
and when one decreases the other also decreases,
such a relation is called positive correlation”
Example Typically, in the summer as the temperature increases people are thirstier.

5. When two variables move in the different directions, that is when one increases the other decreases and when one decreases the other increases, such a relation is called negative correlation.”
Example:
Demand of commodity
And its price

6. When two variables change in constant proportion,
it is called linear correlation
When two variables do not change in any
constant proportion, the relationship is said to be
non-linear correlation
Simple Correlation implies the study of relationship
between two variables only.
Like the relationship between price and demand
When the relationship among three or more than
three variables is studied simultaneously,
it is called multiple correlation.

7. Strength of Linear Association

8. Correlation Coefficient
“r” indicates…
strength of relationship (strong, weak, or none)
direction of relationship
positive (direct) – variables move in same direction
negative (inverse) – variables move in opposite directions
r ranges in value from –1.0 to +1.0
Strong Negative No Relation Strong Positive

9. Degree Of Correlation:
Degree Positive Negative
 Perfect
High .75 to to -1
 Moderate .25 to to -.75
Low 0 to to -.25
Zero

10. Methods of Studying Correlation:
Scatter Diagram Method
Graphic Method
Karl Pearson’s Coefficient of Correlation
Concurrent Deviation Method
Karl Pearson’s Coefficient of Correlation:
r =  x y / N x y
Here
x = X – (mean of X series)
& y = Y –(mean of Y series)
x = Standard deviation of X series
y = Standard deviation of Y series
N = Number of pairs of observations.

11. Or
r =  x y /   x X  y
Here
x = X –(mean of X series)
y = Y –(mean of Y series)
r = the correlation coefficient
( the value lies between-1 r  +1) 2 2

12.  N  dx – ( dx)  N  dy – (dy)
When deviations are taken from an assumed mean
r = N  dx dy -  dx  dy
 N  dx – ( dx)  N  dy – (dy) 2 2 2 2
Here
dx = sum of deviations of X series from assumed mean
dy = sum of deviations of Y series from assumed mean
dx dy = sum of product of the deviation of X & Y series
from their assumed mean
dx = sum of squares of the deviation of X series from
assumed mean
dy = sum of squares of the deviation of Y series from 2 2

13. Ex Find out Karl Pearson’s co-efficient of correlation
Height of Father(inch) Height of Son(inch)
72                71

14. Example:
Calculate the Karl Pearson’s coefficient of correlation
from the following data.
Marks in accountancy :
Marks in Statistics :

15. Spearman’s Rank Correlation Method:
Where Ranks are given
Where ranks are not given
Where ranks are given:
R = 1 –  D 2
N 3 – N
Here D = differences of the two rank

16. Example:
The ranking of 10 students in two subjects A and B
are as follows:
A B
06 03
05 08
03 04
10 09
02 01
04 06
09 10
07 07
08 05
01 02
Calculate the rank correlation
Coefficient.

17. When ranks are not given:
When we are given the actual data and not the ranks,
it will be necessary to assign the ranks. Ranks can be assigned
By taking either highest value as 1 or the lowest value as 1.
But whether we start with the lowest value or the highest value
we must follow the same method in both the cases.
Example:
Calculate the Spearman’s coefficient of correlation between
marks assigned to 10 students by judges X and Y in a certain
Competitive test as shown below:

18. Marks by Judge X Marks By Judge Y

19. Where values are repeated:
R = 1 – ( D 2 + 1/12 ( m1 – m1) + 1/12 (m2 – m2 ) + ………) 3 3
N 3 – N
Where,  D 2 = sum of the square of rank difference.
N = no. of pairs of items.
m1, m2 = no. of items having same rank.

20. Example:
Calculate the rank coefficient correlation:
X Y
80 12
78 13
75 14
68 14
67 16
60 15
55 17
50 19
40 20

21. Probable Error (P.E) = r2 N
The limits for population coefficient of correlation:
= r ± P.E.
Also
Standard Error (S.E) = 1-r2

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