Changing the Units of Measurement Obviously Will Have an Effect

Essay

Changing the units of measurement obviously will have an effect on the slope of your regression function. For example, let Y^*= aY and X^* = bX. Then it is easy but tedious to show that $$\hat { \beta } _ { 1 } ^ {* } = \frac { \sum _ { i = 1 } ^ { n } x _ { i } ^ { * } y _ { i } ^ { * } } { \sum _ { i = 1 } ^ { n } x _ { i } ^ { * 2 } } = \frac { a } { b } \hat { \beta } _ { 1 }$$ Given this result, how do you think the standard errors and the regression R² will change?