Multiple Correlation - Thiyagu

Multiple Correlation Coefficient denoting a correlation of one variable with multiple other variables. The Multiple Correlation Coefficient, R, is a measure of the strength of the association between the independent (explanatory) variables and the one dependent (prediction) variable. This presentation explains the concept of multiple correlation and its computation process.

1. Multiple Correlation
K.THIYAGU,Assistant Professor,Department of Education, Central University of Kerala,Kasaragod

2. Multiple Correlation
Coefficient
denoting a correlation of
one variable
with multiple other
variables.
The multiple correlation coefficient is
denoted as
R
A. BCD…K
Which denotes that A is correlated
with B,C,D up to K variables

3. The Multiple Correlation
Coefficient,R,isameasureofthe
strengthoftheassociationbetween
the independent (explanatory)
variablesandtheonedependent
(prediction)variable.
Rvalue Interpretation*
1
Perfect linear
relationship
0 No linear relationship
Rvalue Interpretation
0.9 Strong association
0.5 Moderate association
0.25 Weak association
Multiple Correlation Coefficient

4. The R
2
is the percentage of variance
in DV explained by the linear
combination of IVs

5. R = 0
R = 0.2
R = 0.4
R
2
= 0
R
2
= 0.04
R
2
= 0.16
Variance = 0 %
Variance = 4 %
Variance = 16 %
X Y
X Y
X Y

6. R = 0.8
R = 1
R
2
= 36
R
2
= 0.64
R
2
= 1
Variance = 36 %
Variance = 64 %
Variance = 100 %
X Y R = 0.6
X
X Y
Y

7. Anxiety
X
Academic
Achievement
Y
Intelligence
Z
R
AcademicAchievement (Y) .Anxiety (X) Intelligence (Z)
Correlation can be represented as

8. Academic
Achievement
IntelligenceAnxiety

9. Eg:
Ifwetakethecaseofone’sacademicachievement,itmaybe
foundassociatedwithordependentonvariableslikeintelligence,
socio-economicstatus,educationoftheparents,themethodsof
teaching,thequalityofteachers,aptitude,interest,environmental
setup,numberofhoursspentonstudiesandsoon.
Inmanystudiesrelatedtoeducationandpsychology,we
findthatthevariableisdependentonanumberofother
variablescalledindependentvariables.

10. Interpretation ofR
StrengthoftheAssociation:
Thestrengthoftheassociationis
measured bytheMultipleCorrelation
Coefficient,R.Rcanbeanyvaluefrom0to
+1.
•ThecloserRistoone,thestrongerthe
linearassociationis.
•IfRequalszero,thenthereisnolinear
associationbetween thedependent
variableandtheindependentvariables.
Unlikethesimplecorrelationcoefficient,r,
whichtellsboththestrengthanddirectionof
theassociation,Rtellsonlythestrengthof
theassociation.Risneveranegative
value.Thiscanbeseenfromtheformula
below,sincethesquarerootofthisvalue
indicatesthepositiveroot.

11. Given variablesx, y andz, we define
themultiple correlation coefficient

14. Example:
Inastudy,aresearcherwantedto
know theimpactofaperson’s
intelligenceandhissocio-economic
statsonhisacademicsuccess.For
computingthecoefficientofmultiple
correlation,hecollectedtherequired
dataandcomputedthefollowing
intercorrelations:
r
12=0.60; r
13=0.40; r
23=0.50
Where1,2,3representthevariables
‘AcademicSuccess’,‘Intelligence’and
‘socio-economicstatus’respectively.In
thiscase,findouttherequired
multiplecorrelationcoefficient.

15. r
12=0.60; r
13=0.40; r
23=0.50
Where1,2,3representthevariables‘Academic
Success’,‘Intelligence’and‘socio-economicstatus’
respectively.Inthiscase,findouttherequired
multiplecorrelationcoefficient.

16. Thank
You
K.THIYAGU,Assistant
Professor,Department of Education,
Central University of Kerala,Kasaragod