correlation

7/21/2019 Correlation

http://slidepdf.com/reader/full/correlation-56d98303f3fe6 1/8

Positive Correlation

Positive correlation occurs when an increase in one variable

increases the value in another.

The line corresponding to the scatter plot is an increasing line.

Negative Correlation

Negative correlation occurs when an increase in one variable

decreases the value of another.

The line corresponding to the scatter plot is a decreasing line.



No Correlation

No correlation occurs when there is no linear dependency

between the variables.

Perfect Correlation

Perfect correlation occurs when there is a funcional dependency

between the variables.

In this case all the points are in a straight line.



Strong Correlation

A correlation is stronger the closer the points are located to one

another on the line.

Weak Correlation

A correlation is weaker the farther apart the points are located

to one another on the line.

Types of Correlation

1. Positive and negative correlation



2. Linear and non-linear correlation

A) If two variables change in the same direction (i.e. if one increases the other also

increases, or if one decreases, the other also decreases), then this is called a positive

correlation. or e!ample " Advertising and sales.

#) If two variables change in the opposite direction ( i.e. if one increases, the other

decreases and vice versa), then the correlation is called a negative correlation. or

e!ample " $.%. registrations and cinema attendance.

1. $he nat&re of the graph gives &s the idea of the linear t'pe of correlation

between two variables. If the graph is in a straight line, the correlation is called

a linear correlation and if the graph is not in a straight line, the correlation

is non-linear or curvi-linear.

or e!ample, if variable ! changes b' a constant &antit', sa' 2* then ' also changes

b' a constant &antit', sa' +. $he ratio between the two alwa's remains the same (1

in this case). In case of a c&rvi-linear correlation this ratio does not remain constant.

Degrees of Correlation

$hro&gh the coefficient of correlation, we can meas&re the degree or e!tent of the

correlation between two variables. n the basis of the coefficient of correlation we

can also determine whether the correlation is positive or negative and also its degree

or e!tent.

1. Perfect correlation: If two variables changes in the same direction and in the

same proportion, the correlation between the two is perfect positive. According

to /arl Pearson the coefficient of correlation in this case is 01. n the other

hand if the variables change in the opposite direction and in the same

proportion, the correlation is perfect negative. its coefficient of correlation is

-1. In practice we rarel' come across these t'pes of correlations.

2. Absence of correlation: If two series of two variables e!hibit no relations

between them or change in variable does not lead to a change in the othervariable, then we can firml' sa' that there is no correlation or absurd

correlation between the two variables. In s&ch a case the coefficient of

correlation is *.



Methods Of Determining Correlation

4e shall consider the following most commonl' &sed methods.(1) 5catter Plot (2) /ar

Pearson6s coefficient of correlation () 5pearman6s 7an3-correlation coefficient.

1) catter Plot ! catter diagram or dot diagram ": In this method the val&es of thetwo variables are plotted on a graph paper. ne is ta3en along the hori8ontal ( (!-a!is)

and the other along the vertical ('-a!is). #' plotting the data, we get points (dots) on

the graph which are generall' scattered and hence the name 95catter Plot6.

$he manner in which these points are scattered, s&ggest the degree and the direction

of correlation. $he degree of correlation is denoted b' 9 r 6 and its direction is given b'

the signs positive and negative.

i) If all points lie on a rising straight line the correlation is perfectl' positive and r :01 (see fig.1 )

ii) If all points lie on a falling straight line the correlation is

perfectl' negative and r : -1 (see fig.2)

iii* If the points lie in narrow strip, risingupwards, the correlation is high degree ofpositive +see g.-*

iv* If the points lie in a narrow strip, fallingdownwards, the correlation is high degree ofnegative +see g.*

v* If the points are spread widely over a broadstrip, rising upwards, the correlation is lowdegree positive +see g.'*

vi* If the points are spread widely over a broadstrip, falling downward, the correlation is low

degree negative +see g./*

vii* If the points are spread +scattered* withoutany specic pattern, the correlation is absent.i.e. r 0 ". +see g.&*



hough this method is simple and is a rough idea about thee2istence and the degree of correlation, it is not reliable. s it is nota mathematical method, it cannot measure the degree ofcorrelation.

)* Karl Pearson’s coecient of correlation: It gives thenumerical e2pression for the measure of correlation. it is noted by 3 r4. he value of 3 r 4 gives the magnitude of correlation and signdenotes its direction. It is dened as

r :

where

N 0 Number of pairs of observation

5alculate the coe6cient of correlation between the heights of fatherand his son for the following data.

%eight offather+cm*7

1/'

1//

1/&

1/8

1/&

1/9

1&"

1&)

%eight ofson+cm*7

1/&

1/8

1/'

1&)

1/8

1&)

1/9

1&1



:rom the following data compute the coe6cient of correlation

between 2 and y.

Description ; <Number of Items 1' 1'( )' 18== 1-/ 1-85ov+2,<* 1))

If covariance between 2 and y is 1).- and the variance of 2 and y

are 1/. and 1-.8 respectively. :ind the coe6cient of correlation

between them.

ind the n&mber of pair of observations from the following data.

r : *.2, Σ +2i $ 2 * + yi $ y * 0 /", σ' : +, Σ ( !i - ! )2 : ;*.

correlation

Documents