You have a sample of size n = 1 with data y₁ = 2 and ₁= 1. You are interested in the value of 3 in the regression Y = XB+ u. (Note there is no intercept.) (a) Plot the sum of squared residuals (y₁ - bx₁)² as function of b. Use the range x₁ € [−2,5] for your plot, and combine all plots of this exercise in one figure. (Use any software you prefer. Excel is one option.) BOLS = 2. (b) Show that the least squares estimate of 3 is 3 (c) Using ALasso = 1, plot the Lasso penalty term XLasso [b] as a function of b.
You have a sample of size n = 1 with data y₁ = 2 and ₁= 1. You are interested in the value of 3 in the regression Y = XB+ u. (Note there is no intercept.) (a) Plot the sum of squared residuals (y₁ - bx₁)² as function of b. Use the range x₁ € [−2,5] for your plot, and combine all plots of this exercise in one figure. (Use any software you prefer. Excel is one option.) BOLS = 2. (b) Show that the least squares estimate of 3 is 3 (c) Using ALasso = 1, plot the Lasso penalty term XLasso [b] as a function of b.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section: Chapter Questions
Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...
Related questions
Question
100%
![Problem 3. [SW 14.10]
You have a sample of size n = 1 with data y₁ = 2 and ₁= 1. You are interested in the value
of 3 in the regression Y = XB+ u. (Note there is no intercept.)
(a) Plot the sum of squared residuals (y₁ – br₁)² as function of b. Use the range x₁ € [−2,5] for
your plot, and combine all plots of this exercise in one figure. (Use any software you prefer.
Excel is one option.)
(b) Show that the least squares estimate of ß is BOLS = 2.
(c) Using ›Lasso = 1, plot the Lasso penalty term XLasso b as a function of b.
(d) Using Lasso = 1, plot the Lasso penalized sum of squared residuals (y₁ - bx₁)² + XLasso |b|.
(e) Find the value of
Lasso
Las
Lasso
(f) Using Lasso = 0.5, repeat (c) and (d). Find the value of B
(g) Using Lasso = 5, repeat (c) and (d). Find the value of Lasso
(h) Use the graphs that you produced in (a)-(d) for the various values of ALasso to explain why a
larger value of Lasso results in more shrinkage of the OLS estimate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61ff295b-afd4-43c3-8ed2-2cc17b9c2249%2Faaeb61a5-9765-4214-bf8e-d2cb5c7141d9%2F8hfe2uj_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 3. [SW 14.10]
You have a sample of size n = 1 with data y₁ = 2 and ₁= 1. You are interested in the value
of 3 in the regression Y = XB+ u. (Note there is no intercept.)
(a) Plot the sum of squared residuals (y₁ – br₁)² as function of b. Use the range x₁ € [−2,5] for
your plot, and combine all plots of this exercise in one figure. (Use any software you prefer.
Excel is one option.)
(b) Show that the least squares estimate of ß is BOLS = 2.
(c) Using ›Lasso = 1, plot the Lasso penalty term XLasso b as a function of b.
(d) Using Lasso = 1, plot the Lasso penalized sum of squared residuals (y₁ - bx₁)² + XLasso |b|.
(e) Find the value of
Lasso
Las
Lasso
(f) Using Lasso = 0.5, repeat (c) and (d). Find the value of B
(g) Using Lasso = 5, repeat (c) and (d). Find the value of Lasso
(h) Use the graphs that you produced in (a)-(d) for the various values of ALasso to explain why a
larger value of Lasso results in more shrinkage of the OLS estimate.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 2 images
Recommended textbooks for you
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill