Problem 2. [SW 14.9] You have a sample of size n = 1 with data y₁ = 2 and x₁ = 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. You can choose your own range for b, one reasonable choice is b € [-2,5]. (Use any software you prefer. Excel is one option.) (b) Show that the least squares estimate of 3 is BOLS = 2. (c) Using ARidge = 1, plot the Ridge penalty term ARidgeb² as a function of b. (d) Using XRidge = 1, plot the Ridge penalized sum of squared residuals (y₁ − bæ₁)² + ARidgeb². Please put all three lines in one plot. Ridge (e) Find the value of 3 (f) Using ARidge = 0.5, repeat (c) and (d) (put both lines in one plot). Find the value of Ridge (g) Using ARidge = 3, repeat (c) and (d) (put both lines in one plot). Find the value of Ridge
Problem 2. [SW 14.9] You have a sample of size n = 1 with data y₁ = 2 and x₁ = 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. You can choose your own range for b, one reasonable choice is b € [-2,5]. (Use any software you prefer. Excel is one option.) (b) Show that the least squares estimate of 3 is BOLS = 2. (c) Using ARidge = 1, plot the Ridge penalty term ARidgeb² as a function of b. (d) Using XRidge = 1, plot the Ridge penalized sum of squared residuals (y₁ − bæ₁)² + ARidgeb². Please put all three lines in one plot. Ridge (e) Find the value of 3 (f) Using ARidge = 0.5, repeat (c) and (d) (put both lines in one plot). Find the value of Ridge (g) Using ARidge = 3, repeat (c) and (d) (put both lines in one plot). Find the value of Ridge
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
Part G. It should be one figure with two lines on it in excel.
![Problem 2. [SW 14.9]
You have a sample of size n = 1 with data y₁ = 2 and x₁ = 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 – bæ₁)² as function of b. You can choose your own range
for b, one reasonable choice is b = [-2,5]. (Use any software you prefer. Excel is one option.)
OLS
(b) Show that the least squares estimate of ß is 3
= 2.
(c) Using Ridge = 1, plot the Ridge penalty term XRidgeb² as a function of b.
(d) Using Ridge = 1, plot the Ridge penalized sum of squared residuals (y₁ - bx₁)² + XRidgeb².
Please put all three lines in one plot.
(e) Find the value of Ridge
3
Ridge
(f) Using Ridge = 0.5, repeat (c) and (d) (put both lines in one plot). Find the value of 3
(g) Using Ridge = 3, repeat (c) and (d) (put both lines in one plot). Find the value of 3*
Ridge](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61ff295b-afd4-43c3-8ed2-2cc17b9c2249%2F07fe405a-7647-43aa-ad97-e10fda4c11ef%2Fwtfqpl_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2. [SW 14.9]
You have a sample of size n = 1 with data y₁ = 2 and x₁ = 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 – bæ₁)² as function of b. You can choose your own range
for b, one reasonable choice is b = [-2,5]. (Use any software you prefer. Excel is one option.)
OLS
(b) Show that the least squares estimate of ß is 3
= 2.
(c) Using Ridge = 1, plot the Ridge penalty term XRidgeb² as a function of b.
(d) Using Ridge = 1, plot the Ridge penalized sum of squared residuals (y₁ - bx₁)² + XRidgeb².
Please put all three lines in one plot.
(e) Find the value of Ridge
3
Ridge
(f) Using Ridge = 0.5, repeat (c) and (d) (put both lines in one plot). Find the value of 3
(g) Using Ridge = 3, repeat (c) and (d) (put both lines in one plot). Find the value of 3*
Ridge
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman