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 AXRidgeb² as a function of b. (d) Using Ridge = 1, plot the Ridge penalized sum of squared residuals (y₁ − bæ₁)² + XRidgeb². Please put all three lines in one plot. (e) 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 AXRidgeb² as a function of b. (d) Using Ridge = 1, plot the Ridge penalized sum of squared residuals (y₁ − bæ₁)² + XRidgeb². Please put all three lines in one plot. (e) 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
Parts B and E only.
![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 Ridge = 1, plot the Ridge penalty term ARidgeb² as a function of b.
-
(d) Using Ridge = 1, plot the Ridge penalized sum of squared residuals (y₁ – bæ₁)² + XRidgeb².
Please put all three lines in one plot.
(e) Find the value of Ridge](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61ff295b-afd4-43c3-8ed2-2cc17b9c2249%2Fda216f88-c1a1-4cc8-86eb-34b2b6b466e9%2Fy17j1gq_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 – 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 Ridge = 1, plot the Ridge penalty term ARidgeb² as a function of b.
-
(d) Using Ridge = 1, plot the Ridge penalized sum of squared residuals (y₁ – bæ₁)² + XRidgeb².
Please put all three lines in one plot.
(e) Find the value of Ridge
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