CORRELATION , MULTIPLE AND PARTIAL
CORRELATION
• Correlation
The interdependence of two or more variables is called correlation.
Or
The liner relationship b/w two or more variables is called correlation. For example, an increase
in the amount of rainfall will increase the sales of raincoats. Ages and weights of children are
correlated with each other.
• Positive Correlation
The correlation in the same direction is called positive correlation. If one variable increase other
is also increase, and one variable is decrease other is also decrease. For example, an increase
in heights of children is usually accompanied by an increase in their weights. The length of an
iron bar will increase as the temperature increase.
• Negative Correlation
The correlation in opposite (different) direction is called negative correlation. If one variable
increase other is decrease, and one variable is decrease other is increase. For example, the
volume gas will decrease as the pressure increase.
• No Correlation Or Zero Correlation
If there are no relationship b/w two variables then it is called no correlation or zero correlation.
• Coefficient of Correlation
It is a measurement of the degree of interdependence b/w the variable. It is a pure number and
lies b/w -1 to +1 and intermediate value of zero indicates the absence of correlation. it denoted
by r.
• Properties of Correlation Coefficient
1. The correlation coefficient is symmetrical with respect to X and Y i.e. xy
r = yx
r
2. The correlation co-efficient is the geometric mean of the two regression coefficients.
r
b d
=
×
Or
xy
yx
r
b
b
=
×
3. The correlation coefficient is independent of origin and unit of measurement i.e. xy
uv
r
r
=
4. The correlation coefficient lies b/w -1 and +1.i.e. 1
1
r
− ≤ ≤ +
5. It is a pure number.
• Formulas of Correlation Coefficient
For ungrouped Data
(1).
(
) (
)
(
)
(
)
2
2
2
2
xy
yx
X
Y
XY
n
r
r
r
X
Y
X
Y
n
n
−
=
=
=
−
−
∑ ∑
∑
∑
∑
∑
∑
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