Let r denote the correlation coefficient between two variables. r≥ is interpreted using the following properties:
Properties Of Correlation Coefficient
Let r denote the correlation coefficient between two variables. r≥ is
interpreted using the following properties:
1. The value
of r ranges from – 1.0 to 0.0 or from 0.0 to 1.0
2. A value of r = 1.0 indicates that
there exists perfect positive correlation between the two variables.
3. A value of r = - 1.0 indicates
that there exists perfect negative correlation between the two variables.
4. A value r = 0.0 indicates zero
correlation i.e., it shows that there is no correlation at all between the two
variables.
5. A positive value of r shows a
positive correlation between the two variables.
6. A negative value of r shows a
negative correlation between the two variables.
7. A value of r = 0.9 and above
indicates a very high degree of positive correlation between the two variables.
8. A value of - 0.9 ≥ r > - 1.0
shows a very high degree of negative correlation between the two variables.
9. For a reasonably high degree of
positive correlation, we require r to be from 0.75 to 1.0.
10. A value of r from 0.6 to 0.75 may
be taken as a moderate degree of positive correlation.
Problem 1
The
following are data on Advertising Expenditure (in Rupees Thousand) and Sales
(Rupees in lakhs) in a company.
![](/media/extra1/fP4MzFn.jpg)
Determine the correlation coefficient between them and
interpret the result.
![](/media/extra1/VA2RZW0.jpg)
Interpretation
The value of r is 0.92. It
shows that there is a high, positive correlation between the two variables ‘Advertising
Expenditure’ and ‘Sales’. This provides a basis to consider some functional
relationship between them.
Problem 2Consider
the following data on two variables X and Y.![](/media/extra1/BRTn5iD.jpg)
Determine the correlation coefficient between the two
variables and interpret the result.
Interpretation
The value of r is 0.21.
Even though it is positive, the value of r is very less. Hence we conclude that
there is no correlation between the two variables X and Y. Consequently we
cannot construct any functional relational relationship between them.
Problem 3 Consider
the following data on supply and price. Determine the correlation Coefficient
between the two variables and interpret the result.![](/media/extra1/VXuRNQ7.jpg)
Determine the correlation coefficient between the two
variables and interpret the result.
InterpretationThe value of r is - 0.92. The negative sign in r shows that the two
variables move in opposite directions. The absolute value of r is 0.92 which is
very high. Therefore we conclude that there is high negative correlation
between the two variables ‘Supply’ and ‘Price’. Problem 4 Consider
the following data on income and savings in Rs. Thousand.![](/media/extra1/iepYDEZ.jpg)
Determine the correlation coefficient between the two
variables and interpret the result.
InterpretationThe value of r is 0.93. The positive sign in r shows that the two
variables move in the same direction. The value of r is very high. Therefore we
conclude that there is high positive correlation between the two variables ‘Income’
and ‘Savings’. As a result, we can construct a functional relationship between
them.
Tags : Research Methodology - Correlation And Regression Analysis
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