this ppt is for engineering and the topic of this ppt is Correlation(r) coefficients of corelation

1.  TOPIC : CORRELATION AND COEFFICIENTS OF CORRELATION
PRESENTED BY:
ZAID (39)
ZEESHAN (40)
MUMIN (41)

2. Contents
What is Correlation
Types of Correlation
Degree of Correlation
Karl Pearson’s Method
Spearman’s Method

3. Correlation(r) :
Correlation is a technique which helps in analyzing the
relationship between two or more variables .

4. Correlation is a statistical measure that indicates the extent to
which two or more variables fluctuate in relation to each other.

5. Types of Correlation:
 Positive correlation
 Negative correlation
 Zero correlation
 Partial correlation
 Multiple correlation

6. Positive Correlation :
 If two variables X & Y move in the same direction i.e if X rises ,
Y also rises.

7. Negative Correlation:
 If two variables X & Y move in opposite direction i.e if one
increases , another decreases .

8. Zero/No Correlation :
 If X & Y are two variables , and there is no specific relation
between these two.

9. Partial Correlation:
 When three or more variables are taken but relationship
between any two of the variables is studied , keeping other
variable as constant.

10. Multiple Correlation :
 When we study of three or more variables at the same time.

11. Degree of Correlation
Degree of Correlation Positive Negative
Perfect Correlation +1 -1
High degree Correlation 0.75 to +1 -0.75 to -1
Moderate Degree
Correlation
0.25 to 0.75 -0.25 to -0.75
Low degree Correlation 0 to 0.25 0 to -0.25

12. Methods for computing Correlation Coefficients
Graphical method
Scatter Diagram
Correlation
Graph
Algebraic method
Karl Pearson’s
Method
Spearman’s
Method

13. Karl Pearson’s Coefficient
Correlation
• The Karl Pearson coefficient is defined as a linear correlation that falls in the numeric range of -1 to +1.
• Karl Pearson’s coefficient of correlation is an extensively used mathematical method in which the numerical representation is applied to
measure the level of relation between linearly related variables. The coefficient of correlation is expressed by “r”.

14. Karl Pearson Correlation Coefficient Formula

15. Alternative Formula (covariance formula)

16.  Pearson correlation Significance:
 When a correlation coefficient is (1), that means for every increase in one variable,
there is a positive increase in the other fixed proportion.
 When a correlation coefficient is (-1), that means for every positive increase in one
variable, there is a negative decrease in the other fixed proportion
 When a correlation coefficient is (0) for every increase, that means there is no
positive or negative increase, and the two variables are not related.

17. Example:
Ten students got the following percentage of marks in Economics and Statistics.

18.  Spearman’s Coeffiecient of Correlation
From carl-Pierson’s formula
where X = x – x, Y = y – y gives the deviation from the mean.
Let (x1 y1),(x2 y2)...(xn yn) be the ranks of n individuals corresponding to two characteristics.
Assuming no two individuals are equal in either classification, each individual takes the values
1, 2, 3, ... n and hence their arithmetic means are, each
n
𝑛
=
𝑛(𝑛+1)
2
=
(𝑛+1)
2
 Let x1 , x2 , x3 …….. xn be the Values of variable X and Let y1 , y2 , y3 …….. yn be the Values of variable Y

19. d=X-Y= (x -
𝑛+1
2
) - (y -
𝑛+1
2
) = x-y
X2 =(x -
𝑛+1
2
)2 =  x2 – (n+1)  x - (
𝑛+1
2
)2
=
𝑛(𝑛+1)(2𝑛+1)
6
−
𝑛 𝑛+1 𝑛+1
2
+ 𝑛
(n+1)2
4
=
(n2−1)
12
Clearly X=Y
And X2 = Y2
Therefore Y2 =
(n2−1)
12

20. Therefore d2 = (x-y)2 = x2 -2 xy + y2
xy=2 x2 - d2
now , x2 =
(n2−1)
12
Therefore, xy=
1
2
(
(n2−1)
6
-d2 )
=
(n2−1)
12
-
1
2
d2
Putting these values in karl-pierson’s formula i.e
We get