Appendix B: Technical Reference 917
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)+d
ì
y
i
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
=
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
To Next Page
Loading...
Need help?
General
