Solving linear models. x y The two-parameter linear model.

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Presentation transcript:

Solving linear models

x y The two-parameter linear model

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

Residual term x y

modelling methods minimize least square sum sum of residuals minmax

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)

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

1.Ruskeepää, H.: Mallintamisen perusteet 2.Lawson, C. L., Hanson, R.J.: Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, New Jersey, 1974