When the value of a variable is influenced by another variable, the relationship between them is a simple correlation.

**MULTIPLE CORRELATION**

When the value of a variable is
influenced by another variable, the relationship between them is a simple correlation.
In a real life situation, a variable may be influenced by many other variables.
For example, the sales achieved for a product may depend on the income of the
consumers, the price, the quality of the product, sales promotion techniques,
the channels of distribution, etc. In this case, we have to consider the joint
influence of several independent variables on the dependent
variable. Multiple correlations arise in this context.

Suppose Y is a dependent
variable, which is influenced by n other variables X_{1}, X_{2}, …,X_{n}. The multiple correlation is a
measure of the relationship between Y and X_{1}, X_{2},…, X_{n} considered together.

The multiple correlation
coefficients are denoted by the letter R. The dependent variable is denoted by
X_{1}. The independent variables are denoted by X_{2}, X_{3}, X_{4},…, etc.

**Meaning of notations:**

R_{1.23} denotes the multiple correlation
of the dependent variable X_{1} with two independent variables X _{2} and X_{3} . It is a measure of the relationship that X_{1} has with X_{2} and X_{3} .

R_{2.13} is the multiple correlation of
the dependent variable X_{2} with two independent variables X_{1} and X_{3}.

R_{3.12} is the multiple correlation of
the dependent variable X_{3} with two independent variables X_{1} and X_{2}.

R_{1.234} is the multiple correlation of
the dependent variable X_{1} with three independent variables X_{2} , X_{3} and X_{4}.

**Coefficient Of Multiple Linear Correlations**

The
coefficient of multiple linear correlation is given in terms of the partial
correlation coefficients as follows:

**Properties Of The Coefficient Of Multiple Linear
Correlations:**

1. The
coefficient of multiple linear correlations R is a non-negative quantity. It
varies between 0 and 1.

Tags : Research Methodology - Partial And Multiple Correlation

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