Determine whether the given property istrue, and explain your answer.

Because the same sample values areused, the correlation coefficient remains unchanged if we rearrange the order of thex-values that are paired with they-values.

Choose the correct answer below.

A.

The property is false. Swapping thex-values of two distinct data points would invariably change the magnitude of the correlationcoefficient, despite leaving the sign unchanged.

B.

The property is false. Reversing the order of thex-values would flip the sign of the correlationcoefficient; however, every rearrangement would leave the magnitude of the correlation coefficient unchanged.

C.

The property is false. Reversing the order of thex-values would flip the sign of the correlationcoefficient, and other rearrangements would also change the magnitude of the correlation coefficient.

D.

The property is true. Since the calculation of the correlation only relies on the sums of thex- andy-values, and not on any paired productterm, the order in which the coordinates are arranged does not matter.