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Solving Linear Models: Understanding Two-Parameter Linear Models

Learn about the two-parameter linear model y = mx + b, a statistically linear approach to fitting a straight line. Explore modeling methods that minimize residuals, including least square sum and the optimizing solution by methods like QR decomposition or Singular Value Decomposition (SVD). Understand the Nonnegative Least Square Algorithm (NNLS) for solving least square problems efficiently.

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Solving Linear Models: Understanding Two-Parameter Linear Models

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  1. Solving linear models

  2. The two-parameter linear model y x

  3. Linear / statistically linear • Linear model = fit a straight line • Statistically linear = linear in the parameters Ex.

  4. Residual term y x

  5. modelling methods minimize • least square sum • sum of residuals • minmax

  6. Solving least square problems Ex. • Derivation of the object function • QR decomposition of E • Singular value decomposition (SVD) of E • Nonnegative least square algorithm (NNLS)

  7. Singular value decomposition • E=USV, U and V are orthogonal and S is a diagonal matrix • We get x=Vp • Approximately as fast as e. g. NNLS

  8. Ruskeepää, H.: Mallintamisen perusteet • Lawson, C. L., Hanson, R.J.: Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, New Jersey, 1974

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