12. (Strang 4.3.1, 5) Consider the four points (t;, b;): (0,0), (1,8), (3, 8), and (4, 20). (a) Set up and solve the system of equations A" Aî = line, b = c+ dt. What are the errors for each point relative to the best fit line? (b) Find the best fit horizontal line, b= c; again, set up and solve a system of equations AT AÎ = ATb, but think carefully about what A is. What are the errors for each ATb in order to find the best fit %3D %3D %3D

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
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12. (Strang 4.3.1, 5) Consider the four points (t;, b;): (0,0), (1,8), (3, 8), and (4, 20).
(a) Set up and solve the system of equations AT Aî = A"b in order to find the best fit
line, b = c+ dt. What are the errors for each point relative to the best fit line?
(b) Find the best fit horizontal line, b = c; again, set up and solve a system of equations
AT Aâ = ATb, but think carefully about what A is. What are the errors for each
point relative to this best fit line.
Transcribed Image Text:12. (Strang 4.3.1, 5) Consider the four points (t;, b;): (0,0), (1,8), (3, 8), and (4, 20). (a) Set up and solve the system of equations AT Aî = A"b in order to find the best fit line, b = c+ dt. What are the errors for each point relative to the best fit line? (b) Find the best fit horizontal line, b = c; again, set up and solve a system of equations AT Aâ = ATb, but think carefully about what A is. What are the errors for each point relative to this best fit line.
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