following quantities: XTX = 56/15 = 3.7333; XTY = 42/15 = 2.8 and YTY = 54/15 = 3.6. Ridge regression R Q1 For λ = 1.31, compute and write in the provided space the ridge estimate ẞ (1.31). Use decimal numbers, not fractions. R Q2 Using the ridge estimate B (1.31) you just computed, determine the percentage of shrinkage achieved with respect to the L1 (Manhattan) norm. That is, compute the shrinkage R using || (1.31)||||||₁ with  the OLS estimate. In the provided space, write the shrinkage as percentage between 0 and 100 with decimal values. Lasso Q3 The following are several expressions for the lasso estimate: L L ² (a) = 0.75 * (1 − 0.34881); (a) = 0.75 * (1 – 0.3571λ); L B (2) = 0.7679 * (1 − 0.3571λ); and ˜¯ (λ) = 0.7679 * (1 − 0.34882). Only one of the expressions given is correct for the given data. Determine which is the correct version and write it in the provided space. Hint: Follow the development shown in lectures. Q4 Determine the numerical value of the lasso parameter λ such that the lasso path vanishes, L i.e. such that B (2) = 0. Write the value of 1 as a decimal number, no fractions.
following quantities: XTX = 56/15 = 3.7333; XTY = 42/15 = 2.8 and YTY = 54/15 = 3.6. Ridge regression R Q1 For λ = 1.31, compute and write in the provided space the ridge estimate ẞ (1.31). Use decimal numbers, not fractions. R Q2 Using the ridge estimate B (1.31) you just computed, determine the percentage of shrinkage achieved with respect to the L1 (Manhattan) norm. That is, compute the shrinkage R using || (1.31)||||||₁ with  the OLS estimate. In the provided space, write the shrinkage as percentage between 0 and 100 with decimal values. Lasso Q3 The following are several expressions for the lasso estimate: L L ² (a) = 0.75 * (1 − 0.34881); (a) = 0.75 * (1 – 0.3571λ); L B (2) = 0.7679 * (1 − 0.3571λ); and ˜¯ (λ) = 0.7679 * (1 − 0.34882). Only one of the expressions given is correct for the given data. Determine which is the correct version and write it in the provided space. Hint: Follow the development shown in lectures. Q4 Determine the numerical value of the lasso parameter λ such that the lasso path vanishes, L i.e. such that B (2) = 0. Write the value of 1 as a decimal number, no fractions.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
Related questions
Question
Transcribed Image Text:following quantities: XTX = 56/15 = 3.7333; XTY = 42/15 = 2.8 and
YTY = 54/15 = 3.6.
Ridge regression
R
Q1 For λ = 1.31, compute and write in the provided space the ridge estimate ẞ (1.31). Use
decimal numbers, not fractions.
R
Q2 Using the ridge estimate B (1.31) you just computed, determine the percentage of
shrinkage achieved with respect to the L1 (Manhattan) norm. That is, compute the shrinkage
R
using || (1.31)||||||₁ with  the OLS estimate. In the provided space, write the shrinkage
as percentage between 0 and 100 with decimal values.
Lasso
Q3 The following are several expressions for the lasso estimate:
L
L
² (a) = 0.75 * (1 − 0.34881);
(a) = 0.75 * (1 – 0.3571λ);
L
B (2) = 0.7679 * (1 − 0.3571λ); and ˜¯ (λ) = 0.7679 * (1 − 0.34882). Only one of the
expressions given is correct for the given data. Determine which is the correct version and write
it in the provided space.
Hint: Follow the development shown in lectures.
Q4 Determine the numerical value of the lasso parameter λ such that the lasso path vanishes,
L
i.e. such that B (2) = 0. Write the value of 1 as a decimal number, no fractions.
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