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The co-efficient of correlation is independent of:
1. change of scale only.
2. change of origin only.
3. both change of scale and change of origin.
4. neither change of scale nor change of origin.

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Correct Answer - Option 3 : both change of scale and change of origin.

Concept:

Co-efficient of Correlation (r):
In simple linear regression analysis, the co-efficient of correlation is a statistic which indicates an association between the independent variable and the dependent variable. The co-efficient of correlation is represented by "r" and its value lies between -1.00 and +1.00.

  • When the co-efficient of correlation is positive, such as +0.80, it means the dependent variable is increasing/decreasing when the independent variable is increasing/decreasing. A negative value indicates an inverse association; the dependent variable is increasing/decreasing when the independent variable is decreasing/increasing.
  • A co-efficient of correlation of +0.8 or -0.8 indicates a strong correlation between the independent variable and the dependent variable. An r of +0.20 or -0.20 indicates a weak correlation between the variables. When the co-efficient of correlation is 0.00, there is no correlation.
  • r = \(\rm \frac{\sum\left(x_i-\bar x\right)\left(y_i-\bar y\right)}{\sqrt{\sum\left(x_i-\bar x\right)^2\sum\left(y_i-\bar y\right)^2}}\).

 

Calculation:

From the properties/nature of the co-efficient of correlation, we know that the correlation coefficient is independent of the choice of origin and scale.

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