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Solving linear models

Solving linear models. The two-parameter linear model. y. x. Linear / statistically linear. Linear model = fit a straight line Statistically linear = linear in the parameters Ex. Residual term. y. x. modelling methods. minimize least square sum

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Solving 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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