[math] \def \bbeta {\bf \beta} [/math]

Consider the simple linear regression model [math]Y_i = \beta_0 + X_{i} \bbeta + \varepsilon_i[/math] for [math]i=1, \ldots, n[/math] and with [math]\varepsilon_i \sim_{i.i.d.} \mathcal{N}(0, \sigma^2)[/math]. The model comprises a single covariate and an intercept. Response and covariate data are: [math]\{(y_i, x_{i})\}_{i=1}^4 = \{ (1.4, 0.0), (1.4, -2.0), (0.8, 0.0), (0.4, 2.0) \}[/math]. Find the value of [math]\lambda[/math] that yields the ridge regression estimate (with an unregularized/unpenalized intercept as is done in part c) of Question) equal to [math](1, -\tfrac{1}{8})^{\top}[/math].