The following table contains output from a lasso fit to a linear model with d = 5 variables and n = 50 observations. Starting from the left, the columns are A, and B1,..., Bs, i.e. each row has A and the transposed column vector B(A). 0.00000 1.20706 -0.66487 0.46392 0.19746 -0.38526 6.18304 1.05715 -0.50740 0.27952 0.00000 -0.17280 12.48795 0.91734 -0.36985 0.11063 0.00000 0.00000 16.89171 0.82829 -0.28890 0.00000 0.00000 0.00000 33.19002 0.53551 0.00000 0.00000 0.00000 59.28000 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 8 = = 8(A) = ||B(A)||1/maxx ||B(A)||1- b) Consider X' estimator B(X'). = 25.040865. Note that X' is the intermediate value between A = 16.89171 and X = 33.19002 of the 4th and 5th rows above. Using this value of A', compute and report the shrunk c) Give the proportion of shrinkage s(A) for the shrunk estimator B(X').

The following table contains output from a lasso fit to a linear model with d = 5 variables and n = 50 observations. Starting from the left, the columns are A, and B1,..., Bs, i.e. each row has A and the transposed column vector B(A). 0.00000 1.20706 -0.66487 0.46392 0.19746 -0.38526 6.18304 1.05715 -0.50740 0.27952 0.00000 -0.17280 12.48795 0.91734 -0.36985 0.11063 0.00000 0.00000 16.89171 0.82829 -0.28890 0.00000 0.00000 0.00000 33.19002 0.53551 0.00000 0.00000 0.00000 59.28000 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 8 = = 8(A) = ||B(A)||1/maxx ||B(A)||1- b) Consider X' estimator B(X'). = 25.040865. Note that X' is the intermediate value between A = 16.89171 and X = 33.19002 of the 4th and 5th rows above. Using this value of A', compute and report the shrunk c) Give the proportion of shrinkage s(A) for the shrunk estimator B(X').

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.4: Linear Regression

Problem 12SBE: Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4

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The following table contains output from a lasso fit to a linear model with d = 6 variables and n = 70 observations. Starting from the left, the columns are λ, and B1, ..., B6, i.e. each row has and the transposed column vector ẞ(λ). 0.00000 0.14473 -0.01238 -0.16257 -0.02082 -0.19404 0.08851 0.58488 0.13477 0.00000 -0.14698 -0.00910 1.12126 0.12656 0.00000 -0.13565 0.00000 7.27740 0.03425 0.00000 -0.02504 0.00000 8.69332 0.01007 0.00000 0.00000 0.00000 -0.02773 0.00000 9.29266 0.00000 0.00000 0.00000 0.00000 -0.01778 0.00000 10.52807 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -0.18503 0.08213 -0.17573 0.07534 -0.05573 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 ass = s(λ) = ||B(a)||₁/max ||B(1)||1. b) Consider λ = 8.99299. Note that λ' is the intermediate value between λ = 8.69332 and λ = 9.29266 of the 5th and 6th rows above. Using this…
The following table contains output from a lasso fit to a linear model with d = 5 variables and n = 100 observations. Starting from the left, the columns are λ, and B1, ..., B5, i.e. each row has λ and the transposed column vector ẞ(λ). 0.00000 0.05470 0.13093 -0.04217 0.09980 -0.01947 1.39802 0.03968 0.11610 -0.01917 0.08656 0.00000 3.00093 0.02288 0.09856 5.70455 0.00000 0.06926 9.18968 0.00000 0.02941 12.13018 0.00000 0.00000 0.00000 0.06971 0.00000 0.00000 0.04054 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
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