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Correlation
Correlation is a measure of association between two variables.
The variables are not designated as dependent or independent.
The value of a correlation coefficient can vary from minus one
to plus one (-1 to +1), where the calculated value of the
correlation coefficient indicates the strength of the relationship
while the negative or positive signal indicates the direction of the
relationship (direct or negative correlation).
A minus one ( - 1) indicates a perfect negative correlation, while
a plus one (+1) indicates a perfect positive correlation. A
correlation of zero means there is no relationship between the
two variables.
When there is a negative correlation between two variables, as
the value of one variable increases, the value of the other variable
decreases, and vise versa.
In other words, for a negative correlation, the variables work
opposite each other. When there is a positive correlation between
two variables, as the value of one variable increases, the value of
the other variable also increases. The variables move together.
Note : In general,
the relationship can be considered weak if the correlation
coefficient value is less than 0.30.
the relationship can be considered as medium if the
correlation coefficient value ranges from 0.30 to 0.70.
if the correlation coefficient value is more than 0.70 the
strong relationship between the two variables.
Note : we can use scatter diagramed { the value of the first
variable on the x-axis and the value of the second
variable on the y-axis }to give a quick idea of the strength
and direction of the correlation between two variables.
Different types of correlations
There are three ways to classify the correlation:
Type
- Positive correlation : If two related variables are such that when
one increases (decreases), the other also increases (decreases)
- Negative correlation : If two variables are such that when one
increases (decreases), the other decreases increases)
- No correlation : If both the variables are independent.
Type 2
- Linear correlation : When plotted on a graph it tends to be a perfect
line.
- Non-Linear correlation : When plotted on a graph it is not a
straight line.
Different types of correlations
Type 1
1 - Positive correlation
2 - Negative correlation
3 - No correlation
Type 2
1 - Linear correlation
2 - Non - linear correlation
Type 3
1 - Simple correlation
2 - Multiple correlation
3 - Partial correlation
Interpret a Correlation Coefficient
Correlation Coefficient = 0 No linear relationship
Correlation Coefficient = ± (0.01 – 0.49) A weak linear
relationship
Correlation Coefficient = ± (0.50 – 0.69) A moderate
relationship
Correlation Coefficient = ± (0.70 – 0.90) A strong linear
relationship
Correlation Coefficient = Exactly ±1. A perfect linear
relationship
Types of correlation coefficient formulas
Usually, in statistics, we measure four types of correlations:
Pearson correlation
Kendall rank correlation
Spearman correlation
4) Point-Biserial correlation.
1) Pearson Correlation(r)
A Pearson correlation is a statistical formula that measures linear
correlation between two variables X and Y. It has a value between
(+1 and −1), where 1 is total positive linear correlation, 0 is no
linear correlation, and −1 is total negative linear correlation.
Pearson correlation is widely used in the sciences.
Pearson Correlation (r) – Formula
A Pearson correlation between variables X and Y is calculated by
r =
n(
[𝑛
] [𝑛
]
Where,
r = Pearson Coefficient
n= number of the pairs of the stock
∑xy = sum of products of the paired stocks
∑x = sum of the x scores
∑y= sum of the y scores
∑x
2
= sum of the squared x scores
∑y
2
= sum of the squared y scores
Example 1
Find the Pearson Coefficient (r) for the following table:
