The following table contains output from a lasso fit to a linear model with d = 5 variables and n columns are A, and ẞ1,..., ẞ5, i.e. each row has A and the transposed column vector B(A). 0.00000 0.75584 0.41796 -0.24405 0.11323 1.70520 0.72641 0.33129 -0.19092 0.04822 2.78550 0.70492 0.28198 -0.15505 0.00000 8.05886 0.56802 0.12830 12.55110 0.43967 0.00000 27.50000 0.00000 0.00000 == 50 observations. Starting from the left, the -0.04956 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 For each of the required computations below, briefly report your procedure and the required quantity. a) For each row in the table, compute s, the proportion of shrinkage defined as s = · 8(A) = ||B(A)||1/max ||B(A)||1. b) Consider X = 10.30498. Note that X' is the intermediate value between λ = 8.05886 and Using this value of A', compute and report the shrunk estimator ẞ(A'). Note that ẞ(A') is a vector. c) Give the proportion of shrinkage s(A') for the shrunk estimator ẞ(X'). = = 12.5511 of the 4th and 5th rows above. (0,0.78431, -1.01961, 1.03922, 0.07843). Using your shrunk estimator B(X) (as column vector) d) Consider the vector of predictors compute the predicted value y = x² B(X').

The following table contains output from a lasso fit to a linear model with d = 5 variables and n columns are A, and ẞ1,..., ẞ5, i.e. each row has A and the transposed column vector B(A). 0.00000 0.75584 0.41796 -0.24405 0.11323 1.70520 0.72641 0.33129 -0.19092 0.04822 2.78550 0.70492 0.28198 -0.15505 0.00000 8.05886 0.56802 0.12830 12.55110 0.43967 0.00000 27.50000 0.00000 0.00000 == 50 observations. Starting from the left, the -0.04956 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 For each of the required computations below, briefly report your procedure and the required quantity. a) For each row in the table, compute s, the proportion of shrinkage defined as s = · 8(A) = ||B(A)||1/max ||B(A)||1. b) Consider X = 10.30498. Note that X' is the intermediate value between λ = 8.05886 and Using this value of A', compute and report the shrunk estimator ẞ(A'). Note that ẞ(A') is a vector. c) Give the proportion of shrinkage s(A') for the shrunk estimator ẞ(X'). = = 12.5511 of the 4th and 5th rows above. (0,0.78431, -1.01961, 1.03922, 0.07843). Using your shrunk estimator B(X) (as column vector) d) Consider the vector of predictors compute the predicted value y = x² B(X').