statistical analysis

1. DEPARMENT OF INFORMATION TECHNOLOGY
PROFICIENCY TEST
Engineering Mathematics -2
(100025)
Submitted To-
Dr. J K Muthele
MADHAV INSTITUTE OF TECHNOLOGY AND SCIENCE GWALIOR (M,P)
(A Govt. Aided UGC Autonomous & NAAC Accredited Institute Affiliated to RGPV, Bhopal)
Submitted by-
Niranjan Kumar Batham(0901IT211036)
Parth Joshi (0901IT211037)
Piyush Pawak(0901IT211038)
Prabhat Uikey(0901IT211039)
Prakhar Gupta(0901IT211040)
Prashant Mourya(0901IT211041)
Priyank Singh(0901IT211042)

2. Types of correlation
On the basis of
degree of
correlation
On the basis of
number of variables
On the basisof
linearity
• Positive
correlation
•Negative
correlation
•Simple
correlation
• Partialcorrelation
•Multiple
correlation
• Linear
correlation
• Non – linear
correlation
Arelationship between two variables such that a change in one variable results a change in other
variable is called correlation and such variables are called correlated.
Thus the correlation analysis is a mathematical tool which is used to measure the degree to which
are variable is linearly related to each other
CORRELATION

3. CORRELATION:-On the basis of degree of
corelation
DIRECT OR POSITIVE CORRELATION
If the increase(or decrease) in one variable results in a
corresponding increase (or decrease) in the other, the correlation
is said to be direct or positive.
DIVERSE OR NEGATIVE CORRELATION
If the increase(or decrease) in one variable results in a
corresponding decrease (or increase) in the other, the correlation
is said to be diverse or negative correlation.

4. CORRELATION:-On the basis of linearity
LINEAR CORRELATION
Arelation in which the values of two variable have a constant
ratio is called linear correlation
(or perfect correlation).
NON LINEAR CORRELATION
Arelation in which the values of two variable does not have a
constant ratio is called a non linear correlation.

5. 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.
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.
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.

6. Properties of coefficient of correlation-
(i) It is the degree of measure of correlation
(ii) The value of r(x,y) lies between -1 and 1.
(iii) If r=1, then the correlation is perfect positive.
(iv) If r= -1, then the correlation is perfect negative.
(v) If r = 0,then variables are independent ,
i.e. no correlation
(vi)Correlation coefficient is independent of change of
origin and scale.
If X and Y are random variables and
a,b,c,d are any numbers provided that a
≠0, c ≠0 ,then
r( aX+b, cY+d) = r(X,Y)

7. COVARIANCE
The covariance between two variables x and y whose n
pairs of observations are
(x1,y1),(x2,y2)……………(xn,yn)
is defined as Cov (x ,y)=
=[(x1- )(y1- )+……………..(xn- )(yn- )] /n

8. Karl Pearson’s Coefficient of
Correlation-
Correlation coefficient between two variables x and y is
denoted by r(x,y) and it is a numerical measure of
linear relationship between them.
r(x,y)=
Where r(x,y) = correlation coefficient
between x and y
σx = standard deviation of x σy =
standard deviation of y n= no. of
observations

9. RANK CORRELATION-
Let (xi ,yi) i = 1,2,3……n be the ranks of n
individuals in the group for the characteristic A and B
respectively.
Co-efficient of correlation between the ranks is called
the rank correlation co-efficient between the
characteristic A and B for that group of individuals.
r = 1-
Where di denotes the difference in ranks of the ith
individual.

10. THANKYOU