8/18/2012

1

CORRELATION

BusinessStatistics 2012

Dr.Gunjan Malhotragmalhotra@imt.edu;mailforgunjan@gmail.com

Introduction Correlationanalysisdealswiththeassociationbetweentwoormorevariables.

Correlationanalysisattemptstodeterminethedegreeoflinearrelationshipbetweenthetwovariables.

Correlationanalysisisusedtomeasurestrengthoftheassociation(linearrelationship)betweentwovariables

Correlationisonlyconcernedwithstrengthoftherelationship

Nocausaleffectisimpliedwithcorrelation

FeaturesofCorrelationCoefficient,r

Unitfree

Rangesbetween1and1

Thecloserto1,thestrongerthenegativelinearrelationship

Thecloserto1,thestrongerthepositivelinearrelationship

Thecloserto0,theweakerthelinearrelationship

Methods of studying correlation

Scatterdiagrammethod Graphicmethod KarlPearsonscoefficientofcorrelation Spearmansrankcorrelationcoefficient

Scatter Plots of Data with VariousCorrelation CoefficientsY

X

Y

X

Y

XX X X

Y

X

Y

X

r=1 r=.6 r=0

r=+.3r=+1

Y

Xr=0

Correlation coefficient, r

( )( )[ ][ ]

=2222 )()(

))((YNXN

YXXYNYX

r

( )( )( ) ( )

=

nn

nYXXY

YY

XX

r2

2

2

2