by Qiang Gao, updated at Mar 21, 2017
...
Does a change in the unit of measurement for the dependent variable change $$ R^2 $$? A change in the unit of measurement for the regressors? Hint: Check whether the change affects the denominator and the numerator in the definition for $$ R^2 $$.
By definition,
$$ R^2 = \frac{ \sum_{i=1}^n (\hat{y}i - \bar{y})^2 } { \sum{i=1}^n (y_i - \bar{y})^2 }. $$
(1) If we change the unit of measurement of the dependent variable $$ y
(2) If we change the unit of measurement of the regressors, then $$ y_i
Copyright ©2017 by Qiang Gao