Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
By using the method of least squares, find the best line through the points: (−2,−1), (0,−2), (−1,3). Step 1. The general equation of a line is co + c₁x = y. Plugging the data points into this formula gives a matrix equation Ac = y. 1 0 0 0 1 [co] 0 0 0 0 Step 2. The matrix equation Ac = y has no solution, so instead we use the normal equation ATAC = ATy 5 -1 ATA= -1 14 0 ATy= 0 Step 3. Solving the normal equation gives the answer 0 E 0 which corresponds to the formula y = || = =

By using the method of least squares, find the best line through the points: (−2,−1), (0,−2), (−1,3). Step 1. The general equation of a line is co + c₁x = y. Plugging the data points into this formula gives a matrix equation Ac = y. 1 0 0 0 1 [co] 0 0 0 0 Step 2. The matrix equation Ac = y has no solution, so instead we use the normal equation ATAC = ATy 5 -1 ATA= -1 14 0 ATy= 0 Step 3. Solving the normal equation gives the answer 0 E 0 which corresponds to the formula y = || = =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
|| = which corresponds to the formula y = Analysis. Compute the predicted y values: y = Ac. ŷ Compute the error vector: e = y - y. e = Compute the total error: SSE = e² + e² + e²3. SSE = ||
Transcribed Image Text:|| = which corresponds to the formula y = Analysis. Compute the predicted y values: y = Ac. ŷ Compute the error vector: e = y - y. e = Compute the total error: SSE = e² + e² + e²3. SSE = ||
By using the method of least squares, find the best line through the points: (−2,−1), (0,−2), (−1,3). Step 1. The general equation of a line is co + C₁x = y. Plugging the data points into this formula gives a matrix equation Ac = y. 1 0 0 0 1 0 = 0 0 0 Step 2. The matrix equation Ac = y has no solution, so instead we use the normal equation ATAC = A¹y 5 -1 ATA = 14 0 ATy 0 Step 3. Solving the normal equation gives the answer 0 18 which corresponds to the formula y = = = -1
Transcribed Image Text:By using the method of least squares, find the best line through the points: (−2,−1), (0,−2), (−1,3). Step 1. The general equation of a line is co + C₁x = y. Plugging the data points into this formula gives a matrix equation Ac = y. 1 0 0 0 1 0 = 0 0 0 Step 2. The matrix equation Ac = y has no solution, so instead we use the normal equation ATAC = A¹y 5 -1 ATA = 14 0 ATy 0 Step 3. Solving the normal equation gives the answer 0 18 which corresponds to the formula y = = = -1
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS