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
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...
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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
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