Question

Following two statements are related to regression coefficient

(I) Independent of the change of origin

(II) Independent of the change of scale

1. Both (I) and (II) are correct
2. Only (I) is correct
3. Only (II) is correct
4. Neither (I) nor (II) is correct

Answer 1

Correct Answer - Option 2 : Only (I) is correct

Explanation:

Variance is independent of change of origin as the change in origin is uniformly added to all the values and hence the mean also and hence, when (x − \(\rm \overline{x}\))² is calculated, it remains unaffected. But, change of scale alters all values unevenly and hence, variation changes. 

The coefficient of variance is standard deviation by mean which doesn't depend on the unit of observation.

So, Statement 1 is correct Statement 2 is incorrect.