(Solved): Consider a classical normal linear regression model (CNLRM): \( Y_{i}=\beta_{1}+\beta_{2} X_{i}+u_ ...

Consider a classical normal linear regression model (CNLRM): \( Y_{i}=\beta_{1}+\beta_{2} X_{i}+u_{i} \), where \( u_{i} \sim \mathrm{NID}\left(0, \sigma^{2}\right. \) ). Data are given in the table below. Calculate the \( 90 \% \) confidence interval for \( \beta_{1} \). So, this data can be summarized as follows: \[ \begin{array}{l} \sum X_{i}=28 \\ \sum Y_{i}=24.9 \\ \sum X_{i}^{2}=140 \\ \sum Y_{i}^{2}=94.15 \\ \sum X_{i} Y_{i}=111.6 \end{array} \] Also, you may need the following relationships. \[ \begin{array}{l} \sum\left(X_{i}-\bar{X}\right)^{2}=\sum X_{i}^{2}-n \bar{X}^{2} \\ \sum\left(Y_{i}-\bar{Y}\right)^{2}=\sum Y_{i}^{2}-n \bar{Y}^{2} \\ \sum\left(X_{i}-\bar{X}\right)\left(Y_{i}-\bar{Y}\right)=\sum X_{i} Y_{i}-n \bar{X} \bar{Y} \\ (1.34,2.34) \\ (1.84,2.84) \\ (0.94,1.94) \\ (1.45,2.15) \end{array} \] Cannot calculate it. (need more assumption)