Appendix B: Technical Reference
936
Regression Formulas
This section describes how the statistical regressions are calculated.
Least-Squares Algorithm
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:
where:residualExpression is in terms of xi and yi
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
“
y
i
For
SinReg
, therefore, the least-squares algorithm finds the constants
a
,
b
,
c
, and
d
that
minimize the function:
Regressions
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.
[
]
J
residualExpression
i
N
=
=
∑
1
2
[
]
J
a
bx
c
d y
i
i
i
N
=
+
+ −
=
∑
sin
(
)
2
1
Summary of Contents for Voyage 200
Page 36: ...Getting Started 36 D B D B Press Result ...
Page 45: ...Getting Started 45 3 0 D B D D B D Press Result ...
Page 46: ...Getting Started 46 D 2 0 0 2 D B Scroll down to October and press Press Result ...
Page 60: ...Getting Started 60 B D Press Result ...
Page 139: ...Previews 139 8 Complete the operation Press 2 d Steps and keystrokes Display 5 f 2 ...
Page 453: ...Differential Equation Graphing 453 ...
Page 468: ...Tables 468 ...
Page 777: ...Activities 777 ...
