Orthogonal linear regression

Orthogonal least square, parameterize unit vector using trigs (green)

Orthogonal least square, unit vector constraint using Lagrange multiplier (green)

k = a/b-b/a, solve quadratic equation

Uttryck 48: "m" Subscript, "l" , Baseline equals "N" left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "X" left bracket, "i" , right bracket "Y" left bracket, "i" , right bracket , right parenthesis minus left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "X" left bracket, "i" , right bracket , right parenthesis left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "Y" left bracket, "i" , right bracket , right parenthesis

Uttryck 49: "k" Subscript, "l" , Baseline equals StartFraction, 1 Over "m" Subscript, "l" , Baseline , EndFraction left parenthesis, "N" left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "X" left bracket, "i" , right bracket squared , right parenthesis minus "N" left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "Y" left bracket, "i" , right bracket squared , right parenthesis plus left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "Y" left bracket, "i" , right bracket , right parenthesis squared minus left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "X" left bracket, "i" , right bracket , right parenthesis squared , right parenthesis

Uttryck 50: "a" Subscript, "l" , Baseline equals "k" Subscript, "l" , Baseline minus signum left parenthesis, "m" Subscript, "l" , Baseline , right parenthesis times StartRoot, "k" squared plus 4 , EndRoot

Uttryck 51: "b" Subscript, "l" , Baseline equals 2 times 10 to the 0 power

Uttryck 52: "c" Subscript, "l" , Baseline equals negative StartFraction, 1 Over "N" , EndFraction left parenthesis, "a" Subscript, "l" , Baseline left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "X" left bracket, "i" , right bracket , right parenthesis plus "b" Subscript, "l" , Baseline left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "Y" left bracket, "i" , right bracket , right parenthesis , right parenthesis

Uttryck 53: "a" Subscript, "l" , Baseline "x" plus "b" Subscript, "l" , Baseline "y" plus "c" Subscript, "l" , Baseline equals 0

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