Correlation Types of Correlation Correlation Coefficient Limitations of Correlation Examples

1. CORRELATION
Dr. Balamurugan M
Associate Professor
Acharya Institute of Graduate Studies
Bangalore

2. Correlation
• Correlation is a statistical technique used for analyzing
the behavior of two or more variables. Correlation is also
described as co-variation in two or more variables.
• Correlation does not necessarily indicate a cause and
effect relationship, it only provides a quantitative
measure.

3. Degree & Nature of Relationship
 Correlation is a measure of degree of relationship
between X & Y.
With the help of correlation analysis we can measure the
degree of relationship existing between the variables.
For example, there is the relationship between price and
supply.

4.  Correlation does not help in making predictions.
 Correlation coefficients are symmetrical.
Types of Correlations
Positive Correlation
Negative Correlation
No Correlation

5. Positive Correlation
A positive correlation means that this linear relationship is
positive, and the two variables increase or decrease in the
same direction.
Negative Correlation (Inverse Correlation)
A negative correlation is just the opposite. The relationship
line has a negative slope, and the variables change in
opposite directions.
No Correlation
The variables behave very differently and thus, have no
linear relationship.

6. Types of Correlations

7. Correlation Coefficient
• Correlation coefficients give you the measure of the
strength of the linear relationship between two variables.
• The letter r denotes the value, and it ranges between -1
and +1
• If r < 0, it implies negative correlation
• If r > 0, it implies positive correlation
• If r = 0, it implies no correlation

8. Types of Correlationcoefficient
There are mainly two types of correlation coefficients.
1. Karl Pearson Correlation Coefficient
• Formula
• r = Coefficient of correlation
• x bar = Mean of x-variable
• y bar = Mean of y-variable.
• xi & yi = Samples of variable x, y

9. 2. Spearman’s Rank Correlation Coefficient
• Formula
• ρ= Spearman rank correlation
• di= Difference between the ranks of corresponding
variables
• n= Number of Observations

10. Limitationsof Correlation
• Correlation does not indicate causality and cannot
be used to do so.
• We cannot infer that one variable is the cause of
another even though there is a very high relationship
between them.

11. • We are limited by correlation to the information that is
provided. For instance, suppose research revealed a link
between the amount of time students spend on their
homework (from half an hour to three hours) and the
number of G.C.S.E. passes (1 to 6). It would be incorrect to
conclude from this that putting in 6 hours of homework
would probably result in 12 G.C.S.E. passes.

12. Examples
• Let’s see some real-life examples and see what does
negative correlation mean and what does positive
correlation mean.
Body Fat and Running Time
• An individual's body fat tends to be lower the more time
they spend jogging. In other words, there is a negative
correlation between the variable body fat and the variable
running time. Body fat decreases as running time
increases.

13. Examples
Exam Results and TV Viewing Time
• Exam results typically suffer when a student watches
more television. In other words, there is a negative
correlation between the variable amount of time spent
watching TV and the variable exam grade. Exam results
decline as TV viewing time increases.