Question

Question -
Properties of correlation coefficient
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Answer 1

Properties of the Coefficient of Correlation.

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 as shown below:

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.

Answer 2

• Correlation coefficient (r) has no unit. It is a pure number. Unit measurement are not part of r.

• Negative role of r - Inverse relation - change happens in opposite direction.

• The linear correlation coefficient is a real number between -1 and 1.If the linear correlation coefficient takes a value closer to -1, the correlation is strong and negative and will become stronger the closer approches -1.

• The linear correlation coefficient takes value close to 1, the correlation is strong and positive, and thus will become stronger the closer it approaches to 1.

• If a correlation coefficient takes value closer to 0, the correlation is weak.

• If r= 1 or r= -1, there is a perfect correlation, and the line on the scatter plot is increasing or decreasing. If r= 0 then there is no correlation.