By using the method of least squares, find the best line through the points: (−2,−1), (2,1), (0,—3). Step 1. The general equation of a line is c + ₁ = y. Plugging the data points into this formula gives a matrix equation Ac = y. Step 2. The matrix equation Ac = y has no solution, so instead we use the normal equation AªAê=A¹y ATA = ATy Step 3. Solving the normal equation gives the answer Ĉ= which corresponds to the formula y = [a]

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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By using the method of least squares, find the best line through the points:
(−2,−1), (2,1), (0,–3).
Step 1. The general equation of a line is c + ₁ = y. Plugging the data points into this formula gives a matrix equation Ac = y.
Step 2. The matrix equation Ac = y has no solution, so instead we use the normal equation ATA ĉ = A¹y
ATA=
ATy =
Step 3. Solving the normal equation gives the answer
Ĉ=
which corresponds to the formula
y =
Analysis. Compute the predicted y values: y
ŷ =
Compute the error vector: e=y-ŷ.
= Aĉ.
Compute the total error: SSE = e² + e² + ez.
SSE =
Transcribed Image Text:By using the method of least squares, find the best line through the points: (−2,−1), (2,1), (0,–3). Step 1. The general equation of a line is c + ₁ = y. Plugging the data points into this formula gives a matrix equation Ac = y. Step 2. The matrix equation Ac = y has no solution, so instead we use the normal equation ATA ĉ = A¹y ATA= ATy = Step 3. Solving the normal equation gives the answer Ĉ= which corresponds to the formula y = Analysis. Compute the predicted y values: y ŷ = Compute the error vector: e=y-ŷ. = Aĉ. Compute the total error: SSE = e² + e² + ez. SSE =
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