Correlation
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8/18/2012 1 CORRELATION Business Statistics ‐ 2012 Dr. Gunjan Malhotra [email protected] ; [email protected] Introduction • Correlation analysis deals with the association between two or more variables. • Correlation analysis attempts to determine the ‘degree of linear relationship’ between the two variables. • Correlation analysis is used to measure strength of the association (linear relationship) between two variables – Correlation is only concerned with strength of the relationship – No causal effect is implied with correlation Features of Correlation Coefficient, r • Unit free • Ranges between –1 and 1 • The closer to –1, the stronger the negative linear relationship • The closer to 1, the stronger the positive linear relationship • The closer to 0, the weaker the linear relationship Methods of studying correlation • Scatter diagram method • Graphic method • Karl Pearson’s coefficient of correlation • Spearman’s rank correlation coefficient Scatter Plots of Data with Various Correlation Coefficients Y X Y X Y X X X X Y X Y X r= ‐1 r= ‐.6 r=0 r = +.3 r = +1 Y X r=0 Correlation coefficient, r ( ) ( ) [ ][ ] ∑ ∑ ∑ ∑ ∑ ∑ ∑ − − − = 2 2 2 2 ) ( ) ( ) )( ( Y N X N Y X XY N Y X r ( ) ( ) ( ) ( ) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − = ∑ ∑ ∑ ∑ ∑ ∑ ∑ n n n Y X XY Y Y X X r 2 2 2 2
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Transcript of Correlation
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8/18/2012
1
CORRELATION
BusinessStatistics 2012
Dr.Gunjan [email protected];[email protected]
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
