(Requires Some Calculus) Consider the Sample Regression Function $Y _ { i } = \widehat { \beta _ { 0 } } + \widehat { \beta } _ { 1 } X _ { 1 i } + \widehat { \beta } _ { 2 } X _ { 2 i }$

Essay

(Requires some Calculus) Consider the sample regression function $Y _ { i } = \widehat { \beta _ { 0 } } + \widehat { \beta } _ { 1 } X _ { 1 i } + \widehat { \beta } _ { 2 } X _ { 2 i }$ Take the total derivative. Next show that the partial derivative $\frac { \Delta Y _ { i } } { \Delta X _ { 1 i } }$ is obtained by holding $X _ { 2 i }$ constant, or controlling for $X _ { 2 i }$