CORRELATION
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CORRELATION
Correlation is a statistical tool that helps to measure
and analyze the degree of relationship between two
variables.
Correlation analysis deals with the association
between two or more variables.
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CORRELATION
The degree of relationship between the variables
under consideration is measure through the
correlation analysis.
The measure of correlation called the correlation
coefficient .
The degree of relationship is expressed by
coefficient which range from correlation
( -1 ≤ r ≥ +1)
The direction of change is indicated by a sign.
The correlation analysis enable us to have an
idea about the degree & direction of the
relationship between the two variables under
study.
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TYPES OF CORRELATION – TYPE I
Correlation
Positive Correlation Negative Correlation
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TYPES OF CORRELATION TYPE I
Positive Correlation: The correlation is said to be
positive correlation if the values of two variables
changing with same direction.
Ex. Pub. Exp. & Sales, Height & Weight.
Negative Correlation: The correlation is said to be
negative correlation when the values of variables change
with opposite direction.
Ex. Price & Quantity demanded.
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DIRECTION OF THE CORRELATION
Positive relationship – Variables change in the
same direction.
As X is increasing, Y is increasing
As X is decreasing, Y is decreasing
Indicated by
E.g., As height increases, so does weight.
sign; (+) or (-).
Negative relationship – Variables change in
opposite directions.
As X is increasing, Y is decreasing
As X is decreasing, Y is increasing
E.g., As TV time increases, grades decrease
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EXAMPLES
Positive Correlation Negative Correlation
Water consumption Alcohol consumption
and temperature. and driving ability.
Study time and Price & quantity
grades. demanded
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TYPES OF CORRELATION TYPE II
Correlation
Simple Multiple
Partial Total
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TYPES OF CORRELATION TYPE II
Simple correlation: Under simple correlation
problem there are only two variables are studied.
Multiple Correlation: Under Multiple
Correlation three or more than three variables
are studied. Ex. Qd = f ( P,PC, PS, t, y )
Partial correlation: analysis recognizes more
than two variables but considers only two
variables keeping the other constant.
Total correlation: is based on all the relevant
variables, which is normally not feasible.
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Types of Correlation
Type III
Correlation
LINEAR NON LINEAR
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TYPES OF CORRELATION TYPE
III
Linear correlation: Correlation is said to be
linear when the amount of change in one
variable tends to bear a constant ratio to the
amount of change in the other. The graph of the
variables having a linear relationship will form
a straight line.
Ex X = 1, 2, 3, 4, 5, 6, 7, 8,
Y = 5, 7, 9, 11, 13, 15, 17, 19,
Y = 3 + 2x
Non Linear correlation: The correlation
would be non linear if the amount of change in
one variable does not bear a constant ratio to
the amount of change in the other variable.
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CORRELATION & CAUSATION
Causation means cause & effect relation.
Correlation denotes the interdependency among the
variables for correlating two phenomenon, it is
essential that the two phenomenon should have
cause-effect relationship,& if such relationship does
not exist then the two phenomenon can not be
correlated.
If two variables vary in such a way that movement
in one are accompanied by movement in other, these
variables are called cause and effect relationship.
Causation always implies correlation but correlation
does not necessarily implies causation.
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DEGREE OF CORRELATION
Perfect Correlation
High Degree of Correlation
Moderate Degree of Correlation
Low Degree of Correlation
No Correlation
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METHODS OF STUDYING CORRELATION
Birinder Singh, Assistant Professor, PCTE
Methods
Graphic Algebraic
Methods Methods
Karl
Scatter Correlation Rank Concurrent
Pearson’s
Diagram Graph Correlation Deviation
Coefficient
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SCATTER DIAGRAM METHOD
Scatter Diagram is a graph of
observed plotted points where each
points represents the values of X & Y
as a coordinate.
It portrays the relationship between
these two variables graphically.
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A PERFECT POSITIVE
CORRELATION
Weight
Weight
of B
Weight A linear
of A
relationship
Height
Height Height
of A of B
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HIGH DEGREE OF POSITIVE
CORRELATION
Positive relationship
r = +.80
Weight
Height
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DEGREE OF CORRELATION
Moderate Positive Correlation
r = + 0.4
Shoe
Size
Weight
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DEGREE OF CORRELATION
Perfect Negative Correlation
r = -1.0
TV
watching
per
week
Exam score
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DEGREE OF CORRELATION
Moderate Negative Correlation
r = -.80
TV
watching
per
week
Exam score
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DEGREE OF CORRELATION
Weak negative Correlation
Shoe
Size r = – 0.2
Weight
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DEGREE OF CORRELATION
No Correlation (horizontal line)
r = 0.0
IQ
Height
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DEGREE OF CORRELATION (R)
r = +.80 r = +.60
r = +.40 r = +.20
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DIRECTION OF THE RELATIONSHIP
Positive relationship – Variables change in the same
direction.
As X is increasing, Y is increasing
Indicated by
As X is decreasing, Y is decreasing
E.g., As height increases, so does weight. sign; (+) or (-).
Negative relationship – Variables change in opposite
directions.
As X is increasing, Y is decreasing
As X is decreasing, Y is increasing
E.g., As TV time increases, grades decrease
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ADVANTAGES OF SCATTER DIAGRAM
Simple & Non Mathematical method
Notinfluenced by the size of extreme
item
step in investing the relationship
First
between two variables
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DISADVANTAGE OF SCATTER DIAGRAM
Can not adopt the an exact
degree of correlation
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CORRELATION GRAPH
300
250
200
150 Consumption
Production
100
50
0
2012 2013 2014 2015 2016 2017
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KARL PEARSON’S COEFFICIENT OF
CORRELATION
It is quantitative method of measuring
correlation
This method has been given by Karl Pearson
It’s the best method
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PROPERTIES OF COEFFICIENT OF
CORRELATION
Karl Pearson’s coefficient of correlation lies between –
1 & 1, i.e. – 1 ≤ r ≤ +1
If the scale of a series is changed or the origin is
Birinder Singh, Assistant Professor, PCTE
shifted, there is no effect on the value of ‘r’.
‘r’ is the geometric mean of the regression coefficients
byx & bxy, i.e. r = 𝑏𝑥𝑦 . 𝑏𝑦𝑥
If X & Y are independent variables, then coefficient of
correlation is zero but the converse is not necessarily
true.
‘r’ is a pure number and is independent of the units of measurement.
The coefficient of correlation between the two
variables x & y is symmetric. i.e. ryx = rxy