# Properties of Correlation co-efficient

The following are the main properties of correlation.

**Coefficient of Correlation lies between -1 and +1:**

The coefficient of correlation cannot take value less than -1 or more than one +1. Symbolically,

-1<=r<= + 1 or | r | <1.

**Coefficients of Correlation are independent of Change of Origin:**

This property reveals that if we subtract any constant from all the values of X and Y, it will not affect the coefficient of correlation.

**Coefficients of Correlation possess the property of symmetry:**

The degree of relationship between two variables is symmetric as shown below:

**Coefficient of Correlation is independent of Change of Scale:**

This property reveals that if we divide or multiply all the values of X and Y, it will not affect the coefficient of correlation.

- Co-efficient of correlation measures only linear correlation between X and Y.
- If two variables X and Y are independent, coefficient of correlation between them will be zero.

**Karl Pearson’s Coefficient of Correlation** is widely used mathematical method wherein the numerical expression is used to calculate the degree and direction of the relationship between linear related variables.

Pearson’s method, popularly known as a **Pearsonian Coefficient of Correlation, **is the most extensively used quantitative methods in practice. The coefficient of correlation is denoted by **“r”.**

If the relationship between two variables X and Y is to be ascertained, then the following formula is used:

Properties of Coefficient of Correlation

- The value of the coefficient of correlation (r) always
**lies between±1**. Such as:

r=+1, perfect positive correlation

r=-1, perfect negative correlation

r=0, no correlation - The coefficient of correlation is independent of the
**origin and scale.**By origin, it means subtracting any non-zero constant from the given value of X and Y the vale of “r” remains unchanged. By scale it means, there is no effect on the value of “r” if the value of X and Y is divided or multiplied by any constant. - The coefficient of correlation is a
**geometric mean of two regression coefficient.**Symbolically it is represented as:

- The coefficient of correlation is
**“zero”**when the variables X and Y are independent. But, however, the converse is not true.

Assumptions of Karl Pearson’s Coefficient of Correlation

- The relationship between the variables is
**“Linear”,**which means when the two variables are plotted, a straight line is formed by the points plotted. - There are a large number of independent causes that affect the variables under study so as to form a
**Normal Distribution**. Such as, variables like price, demand, supply, etc. are affected by such factors that the normal distribution is formed. - The variables are independent of each other.

**Note:** The coefficient of correlation measures not only the magnitude of correlation but also tells the direction. Such as, r = -0.67, which shows correlation is negative because the sign is **“-“**and the magnitude is **0.67**.

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