Question

what is meant by correlation what are the properties of coefficient of correlation

Answer 1

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❏Properties of the Coefficient of Correlation. The correlation coefficient is the geometric mean of the two regression coefficients r=√bYX×bXY or r=√b×d.

The correlation coefficient is independent of origin and unit of measurement, i.e. rXY=rUV. The correlation coefficient lies between −1 and +1.

Answer 2

Meaning:-

Correlation is a statistical measure that indicates the extent to which two or more variables fluctuate in tandem.

following are the properties of correlation and coefficient:-

1. 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.

2. 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.

3. Coefficients of Correlation possess the property of symmetry:The degree of relationship between two variables is symmetric

4. 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.

5. Co-efficient of correlation measures only linear correlation between X and Y.

6. If two variables X and Y are independent, coefficient of correlation between them will be zero.