DSE 2012 Question 33: Linear regression and OLS

Consider the regressions $Y_{i}^{*}=\hat{\beta}_{1}^{*}+\hat{\beta}_{2}^{*}X_{i}^{*}+\hat{u}_{i}^{*}$, and $Y_{i}=\hat{\beta}_{1}+\hat{\beta}_{2}X_{i}+\hat{u}_{i}$, where $Y_{i}^{*}=w_{1}Y_{i}$ and $X_{i}^{*}=w_{2}X_{i}$; $w_{1},w_{2}$ are constants. Is it true that