5. For ridge regression, we choose parameter estimators b which minimise j-0 where A is a constant penalty parameter. (a) Show that these estimators are given by (b) Calculate the ridge regres...
5. For ridge regression, we choose parameter estimators b which minimise j-0 where A is a constant penalty parameter. (a) Show that these estimators are given by (b) Calculate the ridge regression estimates for the data from Q2 with penalty parameter λ-0.5 In order to avoid penalising some parameters unfairly, we must first scale every predictor variable so that t is standardised (mean 0, variance 1), and centre the response variable (mean 0), in which case an intercept parameter is not used. (Hint: This can be done with the scale function) 2 (c) One way to calculate the optimal value for the penalty parameter is to minimise the AIC. Since the number of parameters p does not change, we use a slightly modified version: SSRes AIC = n In-te s + 2 d. where df is the "effective degrees of freedom" defined by df = tr(H) = tr(X(XTX + λ1)-"XT). For the data froin Q2, construct a plot of λ against AIC. Thereby find the optimal value for
5. For ridge regression, we choose parameter estimators b which minimise j-0 where A is a constant penalty parameter. (a) Show that these estimators are given by (b) Calculate the ridge regression estimates for the data from Q2 with penalty parameter λ-0.5 In order to avoid penalising some parameters unfairly, we must first scale every predictor variable so that t is standardised (mean 0, variance 1), and centre the response variable (mean 0), in which case an intercept parameter is not used. (Hint: This can be done with the scale function) 2 (c) One way to calculate the optimal value for the penalty parameter is to minimise the AIC. Since the number of parameters p does not change, we use a slightly modified version: SSRes AIC = n In-te s + 2 d. where df is the "effective degrees of freedom" defined by df = tr(H) = tr(X(XTX + λ1)-"XT). For the data froin Q2, construct a plot of λ against AIC. Thereby find the optimal value for