Question
Write the properties of correlation coefficient.
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Answer
The properties of correlation coefficient are as follows:
- The value of correlation coefficient $r$ lies in the interval $-1$ to $1 .$ i.e., $-1 \leq r \leq 1$.
- The correlation coefficient $r$ is free from unit of measurement, i.e., it does not have any unit of measurement.
- The correlation coefficient between variables $X$ and $Y$ is same as that of between $Y$ and $X$, i.e., $r(x, y)=r(y, x)$.
- The value of correlation coefficient $r$ does not change with the change of origin and scale, i.e., $r(x, y)=r(u, v)$ where, $\mathbf{u}=\frac{x-\mathrm{A}}{\mathrm{C}_{\mathrm{x}}} ; \mathbf{v}=\frac{y-\mathrm{B}}{\mathrm{C}_{\mathrm{y}}} \cdot \mathrm{C}_{\mathrm{x}}>0, \mathrm{C}_{\mathrm{y}}>0$
- and $A, B, C_x, C_y$ are constant.
- The correlation coefficient $r$ is an absolute measure.
- If the sign of any one of two variables is changed then the sign of the correlation coefficient also changes, i.e., $r(-x, y)=-r(x, y) ; r(x,-y)=-r(x, y)$
- If the signs of both the variables are changed then the sign of the correlation remain unchanged, i.e., $r(-x,-y)$ $=r(x, y)$.
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