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“Correlation Coefficient has certain essential properties”-substantiate.

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Correlation Coefficient has certain essential properties as discussed below. 

1. r has no unit. It is a pure number. It means units of measurement are not part of r. r between height in feet and weight in kilograms, for instance, is 0.7. 

2. A negative value of /-indicates an inverse relation. 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. 

3. If r is positive the two variables move in the same direction. If/”= 0 the two variables are uncorrelated. There is no linear relation between them. However other types of relationships may be there. 

4. If r = 1 or r = -1 the correlation is perfect. The relation between them is exact. 

5. A high value of r indicates strong linear relationship. Its value is said to be high when it is close to+1 or-1. 

6. A low value of r indicates a weak linear relation. Its value is said to be low when it is dose to zero. 

7. The value of the correlation coefficient lies between minus one and plus one, -1 < r < +1. If, in any exercise, the value of r \s outside this range indicates error in calculation.

8. The value of r is unaffected by the change of origin and change of scale. Given two variables X and Y let us dene two new variables.

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