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.
Determine the correlation coefficient between them and
interpret the result.
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. 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. 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.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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