# The co-efficient of correlation is independent of:

89 views

closed
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.

by (54.3k points)
selected

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.