Texas Instruments PLUS TI-89 - Manual (Page 587)

570 Appendix B: Reference Information
8992APPB DOC TI-89/TI-92 Plus:8992appb doc (English) Susan Gullord Revised: 02/23/01 1:54 PM Printed: 02/23/01 2:24 PM Page 570 of 34
Most of the regressions use non-linear recursive least-squares
techniques to optimize the following cost function, which is the sum
of the squares of the residual errors:
[ ]
J residualExpression
i
N
=
=
∑
1
2
where: residualExpression is in terms of x
i
and y
i
x
i
is the independent variable list
y
i
is the dependent variable list
N is the dimension of the lists
This technique attempts to recursively estimate the constants in the
model expression to make J as small as possible.
For example, y=a sin(bx+c)+d is the model equation for SinReg . So
its residual expression is:
a sin(bx
i
+c)+dì y
i
For SinReg , therefore, the least-squares algorithm finds the
constants a, b, c, and d that minimize the function:
[ ]
J a bx c d y
i i
i
N
= + + −
=
∑
sin ( )
2
1
Regression Description
CubicReg Uses the least-squares algorithm to fit the third-order
polynomial:
y =ax 3 +bx 2 +cx+d
For four data points, the equation is a polynomial fit;
for five or more, it is a polynomial regression. At
least four data points are required.
ExpReg Uses the least-squares algorithm and transformed
values x and ln(y) to fit the model equation:
y =ab x
LinReg Uses the least-squares algorithm to fit the model
equation:
y =ax+b
where a is the slope and b is the y-intercept.
Regression Formulas
This section describes how the statistical regressions are
calculated.
Least-Squares
Algorithm
Regressions