Which of the following is NOT a property of Correlation Coefficient?

The magnitude of r is affected by the change of origin and change of scale.

The correct answer is Option 3: The magnitude of r is affected by the change of origin and change of scale.

Properties of Correlation Coefficient

• r has no unit. It is a pure number (Option 1 is correct). It means units of measurement are not part of r. r between height in feet and weight in kilograms, for instance, could be say 0.7.

• A negative value of r indicates an inverse relation (Option 2 is correct). A change in one variable is associated with change in the other variable in the opposite direction. When price of a commodity rises, its demand falls. When the rate of interest rises the demand for funds also falls. It is because now funds have become costlier.

• If r is positive the two variables move in the same direction. When the price of coffee, a substitute of tea, rises the demand for tea also rises. Improvement in irrigation facilities is associated with higher yield. When temperature rises the sale of ice-creams becomes brisk.

The value of the correlation coefficient lies between minus one and plus one, –1 ≤ r ≤1. If, in any exercise, the value of r is outside this range it indicates error in calculation.

• The magnitude of r is unaffected by the change of origin and change of scale. (Option 3 is incorrect)

If r = 0 the two variables are uncorrelated (Option 4 is correct). There is no linear relation between them.