(Requires Appendix Material)Consider the Following Population Regression Function Model with Two

Essay

(Requires Appendix material)Consider the following population regression function model with two explanatory variables: $Y _ { i } = \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } X _ { 1 i } + \hat { \beta } _ { 2 } X _ { 2 i }$ It is easy but tedious to show that SE( $\hat { \beta } _ { 2 }$ )is given by the following formula: $\sigma_{\hat{\beta_{1}}}^{2}=\frac{1}{n}\left[\frac{1}{1-\rho_{x_{1}, x_{2}}^{2}}\right] \frac{\sigma_{u}^{2}}{\sigma^{2} \mathrm{X}_{1}}$
Sketch how SE( $\hat { \beta } _ { 2 }$ )increases with the correlation between $X _ { 1 i }$ and $X _ { 2 i }$