570 Appendix B: Reference Information
8992APPBDOC TI
-
89/TI
-
92Plus:8992a
pp
bdoc (English) SusanGullord Revised:02/23/01 1:54 PM Printed:02/23/01 2:24 PM Page570 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 xi and yi
xi is the independent variable list
yi 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(bxi+c)+d
ì
yi
For SinReg, therefore, the least-squares algorithm finds the
constants a, b, c, and d that minimize the function:
[]
Jabxcdy
ii
i
N
=++−
=
∑sin() 2
1
Regression Description
CubicReg Uses the least-squares algorithm to fit the third-order
polynomial:
y=ax3+bx2+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=abx
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