(Solved): Consider a linear regression model \( Y_{i}=\beta_{1}+\beta_{2} X_{i}+u_{i} \). Data are given in ...

Consider a linear regression model \( Y_{i}=\beta_{1}+\beta_{2} X_{i}+u_{i} \). Data are given in the table below. Calculate the residual sum of squares (RSS), \( \sum \hat{u}_{i}^{2} \), and the (unbiased) OLS estimate of the true but unknown \( \sigma^{2}, \hat{\sigma}^{2} \). (Hint: For the calculation of \( \sum \hat{u}_{i}^{2} \), use equation (3.3.6) in the textbook. Note \( \sigma^{2} \) is the homoscedastic variance of \( u_{i} \).) \[ \begin{array}{l} 132.75,16.59 \\ 132.75,14.75 \\ 1062,132.75 \\ 1062,118 \\ 0,0 \end{array} \]