Electronic Proceedings of the Eighth Annual International Conference on Technology in Collegiate MathematicsHouston, Texas, November 1619, 1995Paper C091
Modeling with the TI85 
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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 nonlinear 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, TI85, linear algebra