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Relationship Analysis

In business or business related situations multiple variables with respect to customers or

companies exist it becomes critical to understand, establish the relationship between the

variables for example a relationship between amounts spent on advertisement and sales could be

critical.

The relationship between income, age of the customers and bill amount per visit could be critical

to a chain of retail.

Relationship analysis when the data is qualitative:

When the data is qualitative cross tabs, Chi-Square Tests are used primarily to understand the

relationships.

For example to understand the relationship between occupation and defaulting nature of

customers one can use Cross Tabs and Chi-Square Tests.

When the data is quantitative or numeric:

When the data is quantitative relationship analysis is performed by:

1. Scatter Diagram2. Karl Pearsons Coefficient of Correlation or Product moment correlation.3. Spearmans Rank Correlation or Rank Correlation4. Regression

Represent the following data as a Scattered diagram and comment on the Correlation.

X Y

10 60

15 6419 71

21 78

25 82

30 85

32 90

35 91

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From the scatter Diagram One can observe that there is +ve correlation in the data.

Which indicates that behavior of X & Y is same i.e. either both increasing or both decreasing.

Identifying correlation by scatter Diagram:

Scatter Diagram for a data is obtained by taking values of X on X-Axis and of Y on Y-Axis, the

correlation is identified as follows:

1. Perfect positive correlation: Two Variable X & Y said to have perfect +ve correlation ifboth increasing or both decreasing in proportion. The behavior of both the variables is

same.

If variables have Perfect positive correlation then their scatter diagram is as follows:

0

10

20

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90

100

0 10 20 30 40

Y

Y

Linear (Y)

0

1

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0 2 4 6 8 10

y

y

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2. Positive Correlation: Two variable X & Y are said to have +ve correlation if oneincrease then the other also increases, if one decreases other also decreases. If two

variables have Positive correlation then their scatter diagram is as follows:

3. Perfect Negative Correlation: Two variable X & Y are said to have -ve correlation ifone increase the other decreases if one decreases the other increase in propotion. If two

variables have Perfect Negative correlation then their scatter diagram is as follows:

0

10

2030

40

50

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90

100

0 10 20 30 40

Y

Y

Linear (Y)

0

1

2

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y

y

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4. Negative Correlation: Two variable X & Y are said to have -ve correlation if oneincrease the other decreases if one decreases the other increase. If two variables have

Perfect Negative correlation then their scatter diagram is as follows:

If the scatter diagram is none of the above then data said to have no correlationthe

scatter diagram mabe as follows:

0

1

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0 2 4 6 8 10

y

y