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Types of Correlation
There are four types of correlations which are:
r=+1 r=–1
Positive Negative
Correlation Correlation
a. b.
No Correlation Correlation is not linear
r=0
c. d.
• Positive Correlation: Positive correlation is the relationship between two variables, in which both variables have a
linear relationship. As one variable increases/decreases, the second variable too increases/decreases. For example,
when fuel prices increase, prices of airline tickets also increase.
• Negative Correlation: Negative correlation is the relationship between two variables, where one variable increases
as the second variable decreases, and vice versa. For example, more exercising leads to a decrease in body weight.
• No Correlation: No correlation means that there is no relationship between two variables. If the value of a variable is
changed, another variable is not affected. For example, shirt size and monthly expense, body weight and intelligence, etc.
• Non-linear Correlation: A non-linear correlation is a correlation in which all the points of a scatter plot are tend to
lie near a smooth curve.
Pearson's r—Correlation Coefficient
The degree of association is measured by a correlation coefficient, represented by r. It is also called Pearson's correlation
coefficient and measures linear association between two variables. If a curved line is needed to state the relationship,
more complicated measures of correlation should be used.
The correlation coefficient is measured on a scale that varies from + 1 to – 1.
• 1 is a perfect positive correlation.
• 0 is no correlation (the values don't seem linked at all).
• –1 is a perfect negative correlation.
Pearson’s Coefficient, r, is denoted by:
NΣxy–(Σx)(Σy)
r =
2
2
2
2
[NΣx – (Σx) ][NΣy (Σy) ]
Where N represents the number of samples. Following are the guidelines given for interpreting the Pearson’s
Coefficient ‘r’:
Regression 283

