HP 9g Instruction Manual page 2

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HP 9g Statistics –Non-Linear Regression
Non-linear regression
In addition to the linear regression (described in the HP 9g learning module Statistics – Linear Regression) the HP 9g
provides five more types of regression of a variable y on a variable x, namely:
♦ Logarithmic model:
♦ Exponential model:
=
♦ Power model: y a
=
♦ Inverse model: y
♦ Quadratic model: y
Bear in mind that this model needs at least three points. An example is the relation between
kinetic energy and speed.
Regression curves can be found by following the same procedure used with linear regressions. That is, press ` 1,
select REG, and press =. The REG menu is now displayed showing all the types of regression available. Select the
desired one then press =. Once the data has been entered, regression results are shown in the STATVAR menu
(~e), which displays the values of a and b (and c) and also the correlation coefficient r (except in the case of
quadratic regression). Also in this menu are the functions
all this with some examples.
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= +
y a b ln x
.
The logarithmic curve-fitting model requires positive x-values. An example of this model is the
psychophysics law of Weber-Fechner.
bx
= ⋅
y a e
.
This model requires positive y-values. Examples of this model are the number of undecayed
nuclei of radioactive materials after a period x of time, the discharging process in Capacitor-
Resistance circuits, etc.
b
⋅
x
.
The power model requires positive x-values and positive y-values, otherwise the DOMAIN error
occurs when attempting to display the STATVAR menu. Newton's law of gravitation is a classic
example.
b
+
a
.
x
Zero cannot be one of the x-values, since it will trigger the DIVIDE BY 0. Examples are Curie-
Weiss' law, the reactance of a capacitor, relation between potential energy and distance, etc.
= + +
a bx cx 2
.
y ˆ x ˆ
and , which are used for predicting values. Let's illustrate
- 2 - HP 9g Statistics – Non-Linear Regression - Version 1.0