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Find the least-squares line given the matrix products ATA 608.4 5942.2 A¹b- = y = Ex: 1.2 +Ex: 1.2 € - 4 31 31 415 and

Find the least-squares line given the matrix products ATA 608.4 5942.2 A¹b- = y = Ex: 1.2 +Ex: 1.2 € - 4 31 31 415 and

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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Find the least-squares line given the matrix products AA A¹b 608.4 5942.2 y= Ex12 + Ex: 1.2 3 || 4 31 31 415 and
Transcribed Image Text:Find the least-squares line given the matrix products AA A¹b 608.4 5942.2 y= Ex12 + Ex: 1.2 3 || 4 31 31 415 and
Expert Solution
Step 1: Derivation of the normal equation

Let us to find a least square line for the set of values {(xi,yi):i=1,2,⋯,n}


Let the equation of line be y=a+bx

Then satisfies the data set points

a+bx1=y1a+bx2=y2a+bx3=y3⋮      ⋮        ⋮a+bxn=yn

Then it can be written as

[1x11x21x3⋮⋮1xn][ab]=[y1y2y3⋮yn]

In Matrix form

Ax=b

Then the normal equation

ATAx=ATb


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