8. (20%) Given are following observations collected in a regression study on two variables. Consider the linear regression model $$Y = \beta_0 + \beta_1X + \varepsilon$$

| $$x_t$$ | 2 | 3 | 4 | 5 | 6 |
| --- | --- | --- | --- | --- | --- |
| $$y_t$$ | 3 | 7 | 5 | 11 | 14 |

(a) \((5\%)\) Find the estimated regression equation for these data.