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
RA. BCD…K
Which denotes that A is correlated
with B,C,D up to K variables

3. 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.
R value Interpretation*
1
Perfect linear
relationship
0 No linear relationship
R value Interpretation
0.9 Strong association
0.5 Moderate association
0.25 Weak association
Multiple Correlation Coefficient

4. The R2 is the percentage of variance
in DV explained by the linear
combination of IVs

5. R = 0
R =  0.2
R =  0.4
R2 = 0
R2 = 0.04
R2 = 0.16
Variance = 0 %
Variance = 4 %
Variance = 16 %
X Y
X Y
X Y

6. R =  0.8
R =  1
R2 = 36
R2 = 0.64
R2 = 1
Variance = 36 %
Variance = 64 %
Variance = 100 %
X Y R =  0.6
X
X Y
Y

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

8. Academic
Achievement
IntelligenceAnxiety

9. Eg:
If we take the case of one’s academic achievement, it may be
found associated with or dependent on variables like intelligence,
socio-economic status, education of the parents, the methods of
teaching, the quality of teachers, aptitude, interest, environmental
setup, number of hours spent on studies and so on.
In many studies related to education and psychology, we
find that the variable is dependent on a number of other
variables called independent variables.

10. Interpretation of R
Strength of the Association:
The strength of the association is
measured by the Multiple Correlation
Coefficient, R. R can be any value from 0 to
+1.
• The closer R is to one, the stronger the
linear association is.
• If R equals zero, then there is no linear
association between the dependent
variable and the independent variables.
Unlike the simple correlation coefficient, r,
which tells both the strength and direction of
the association, R tells only the strength of
the association. R is never a negative
value. This can be seen from the formula
below, since the square root of this value
indicates the positive root.

11. Given variables x, y and z, we define
the multiple correlation coefficient

14. Example:
In a study, a researcher wanted to
know the impact of a person’s
intelligence and his socio-economic
stats on his academic success. For
computing the coefficient of multiple
correlation, he collected the required
data and computed the following
intercorrelations:
r12=0.60; r13=0.40; r23=0.50
Where 1,2,3 represent the variables
‘Academic Success’, ‘Intelligence’ and
‘socio-economic status’ respectively. In
this case, find out the required
multiple correlation coefficient.

15. r12=0.60; r13=0.40; r23=0.50
Where 1,2,3 represent the variables ‘Academic
Success’, ‘Intelligence’ and ‘socio-economic status’
respectively. In this case, find out the required
multiple correlation coefficient.

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