
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Question
thumb_up100%
Part f only. It should be one figure with two lines.
![## Problem 3. [SW 14.10]
You have a sample of size \( n = 1 \) with data \( y_1 = 2 \) and \( x_1 = 1 \). You are interested in the value of \( \beta \) in the regression \( Y = X \beta + u \). (Note there is no intercept.)
(a) Plot the sum of squared residuals \( (y_1 - b x_1)^2 \) as a function of \( b \). You can choose your own range for \( b \), one reasonable choice is \( b \in [-2, 5] \). *(Use any software you prefer. Excel is one option.)*
(b) Show that the least squares estimate of \( \beta \) is \( \hat{\beta}^{OLS} = 2 \).
(c) Using \( \lambda_{Lasso} = 1 \), plot the Lasso penalty term \( \lambda_{Lasso} |b| \) as a function of \( b \).
(d) Using \( \lambda_{Lasso} = 1 \), plot the Lasso penalized sum of squared residuals \( (y_1 - b x_1)^2 + \lambda_{Lasso} |b| \). Please put all three lines in one plot.
(e) Find the value of \( \hat{\beta}^{Lasso} \).
(f) Using \( \lambda_{Lasso} = 0.5 \), repeat (c) and (d) (put both lines in one plot). Find the value of \( \hat{\beta}^{Lasso} \).](https://content.bartleby.com/qna-images/question/61ff295b-afd4-43c3-8ed2-2cc17b9c2249/f2e2ece6-7450-482d-98c5-3e6254b5429c/kyjtkx_thumbnail.png)
Transcribed Image Text:## Problem 3. [SW 14.10]
You have a sample of size \( n = 1 \) with data \( y_1 = 2 \) and \( x_1 = 1 \). You are interested in the value of \( \beta \) in the regression \( Y = X \beta + u \). (Note there is no intercept.)
(a) Plot the sum of squared residuals \( (y_1 - b x_1)^2 \) as a function of \( b \). You can choose your own range for \( b \), one reasonable choice is \( b \in [-2, 5] \). *(Use any software you prefer. Excel is one option.)*
(b) Show that the least squares estimate of \( \beta \) is \( \hat{\beta}^{OLS} = 2 \).
(c) Using \( \lambda_{Lasso} = 1 \), plot the Lasso penalty term \( \lambda_{Lasso} |b| \) as a function of \( b \).
(d) Using \( \lambda_{Lasso} = 1 \), plot the Lasso penalized sum of squared residuals \( (y_1 - b x_1)^2 + \lambda_{Lasso} |b| \). Please put all three lines in one plot.
(e) Find the value of \( \hat{\beta}^{Lasso} \).
(f) Using \( \lambda_{Lasso} = 0.5 \), repeat (c) and (d) (put both lines in one plot). Find the value of \( \hat{\beta}^{Lasso} \).
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 5 steps with 3 images

Knowledge Booster
Similar questions
- Write an equation of a line parallel 3x-y=4 I need help showing workarrow_forwardFind the equation of the line PERPENDICULAR to x+3y+2=0 that goes through the point (2,-1). Write your answer in y=mx+b form. Could you please detail the steps in the resolution? Also provide a graph for visual?arrow_forwardB. Match each equation with its graph. Write the correct letter on the line. а. 1. y = -X 2 -2 2 2. y = -3 b. 2 -2 3. x = -3 с. -2 2 34 Chapter 6 Writing Linear Equationsarrow_forward
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman

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