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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
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|| = 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
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