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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 ≤ r ≤ 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, u = \(\frac{x−A}{C_x}\); v = \(\frac{ y−B}{C_y}\). Cx > 0, Cy > 0 and A, B, Cx, Cy 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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