Modeling with the TI-85

Neil Eklund

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

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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 modeling 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

Keyword(s): modeling, TI-85, linear algebra