題組內容

4. [30%] Based on the following 10 pairs of data: | X | 6 | -3 | 4 | 3 | -2 | -4 | 0 | -1 | -5 | 2 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Y | 10 | 1 | 8 | 7 | 1 | 2 | 5 | 3 | 2 | 6 | and assuming the following linear regression model, Y = α + βX + ε, where ε has zero mean and variance equal to σ². Please answer the following questions:

(a) Compute the least-squares point estimator of \( \alpha \) and \( \beta \).