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||            Electronic Proceedings of the Eighth Annual             ||
||  International Conference on Technology in Collegiate Mathematics  ||
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CONTRIBUTED PAPER: 8-C91

Modelling with the TI-85

Neil Eklund
Centre College
600 W. Walnut
Danville, KY 40422-1394
Phone: (606) 238-5405;  Fax: (606) 236-9610
E-mail: eklund@centre.edu


ABSTRACT

If the overdetermined system of equations is written in the
form Xa = y where a is the vector of unknown coefficients,
the normal equations for a are (XTX)a = XTy.  Under
appropriate conditions XTX is invertible as well as
symmetric and, hence, a = (XTX)-1XTy.  The least squares
error is shown to be E = yT{I - X(XTX)-1XT}y.  This
modelling technique will be applied to non-linear data.

Mathematical Notation:
     X is a matrix
     a is a vector
     y is a vector
     (XTX) is the product of X transpose with X
     XTy is the product of X transpose with the vector y
     (XTX)-1XTy is the product of the inverse of (XTX) times X
     transpose times the vector y
     yT{I - X(XTX)-1XT}y is the product of y transpose with { }
     times the vector y
     {I - X(XTX)-1XT} is the identity minus X times the
     inverse of (XTX) times X transpose