Question: Question 4: Consider the model \(y={{\beta }_{0}}+{{\beta }_{1}}x+u\). With 10 data points we have:

\[X'X=\left( \begin{matrix} 10 & 500 \\ 500 & 28400 \\ \end{matrix} \right)\],\[X'y=\left( \begin{matrix} 1100 \\ 61800 \\ \end{matrix} \right)\]

SSTotal = 134660, SSResidual = 60

a. Find \({{\hat{\beta }}_{0}}\) and \({{\hat{\beta }}_{1}}\).

b. Find a 95% confidence interval for the mean response of y at x = 50.