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Research Methodology - Partial And Multiple Correlation

PARTIAL CORRELATION - Partial And Multiple Correlation

   Posted On :  27.05.2018 12:18 am

Simple correlation is a measure of the relationship between a dependent variable and another independent variable.

PARTIAL CORRELATION
 
 
Simple correlation is a measure of the relationship between a dependent variable and another independent variable. For example, if the performance of a sales person depends only on the training that he has received, then the relationship between the training and the sales performance is measured by the simple correlation coefficient r. However, a dependent variable may depend on several variables. For example, the yarn produced in a factory may depend on the efficiency of the machine, the quality of cotton, the efficiency of workers, etc. It becomes necessary to have a measure of relationship in such complex situations. Partial correlation is used for this purpose. The technique of partial correlation proves useful when one has to develop a model with 3 to 5 variables.
 
Suppose Y is a dependent variable, depending on n other variables X1, X2, …, Xn.. Partial correlation is a measure of the relationship between and any one of the variables X1, X2,…,Xn, as if the other variables have been eliminated from the situation.

The partial correlation coefficient is defined in terms of simple correlation coefficients as follows:
 
Let r12. 3 denote the correlation of X1 and X2 by eliminating the effect of X3.
 
Let r12 be the simple correlation coefficient between X1 and X2.

Let r13 be the simple correlation coefficient between X1 and X3.
 
Let r23 be the simple correlation coefficient between X2 and X3.
 
Then we have



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