The general linear model

Fit $y = \beta_0 + \beta_1x$ to the data $x = 1, 2, 3, 4, 5$ and $y = 1, 3, 2, 5, 4$. (a) Compute $\hat\beta_0, \hat\beta_1$. (b) Compute the residuals, $\mathrm{RSS}$ and $s^2$. (c) Compute the $t$ statistic for $\beta_1$ and the F statistic, and check $F = t^2$. (d) Is the slope significant at $5\%$ ($t_{3, 0.025} = 3.182$)?