Property	Value
Hex Value	`$F7`
Categories	Catalog > P Statistics > Operations
Localizations	FR: `RegPuiss`

`PwrReg`

Overview

Fits a power regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

Availability: Token available everywhere.

Syntax

PwrReg [Xlistname,Ylistname,freqlist,regequ]

Arguments

Name	Type	Optional
Xlistname	list	Yes
Ylistname	list	Yes
freqlist	list	Yes
regequ		Yes

Location

stat, CALC, A:PwrReg

Description

PwrReg tries to fit a power curve (y=a*x^b) through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points.

The calculator does this regression by taking the natural log ln( of the x- and of the y-coordinates (this isn't stored anywhere) and then doing a linear regression. The result, ln(y)=bln(x)+ln(a), is transformed into y=e^ln(a)x^b, which is a power curve. This algorithm shows that if any coordinates are negative or 0, the calculator will instantly quit with ERR:DOMAIN.

In its simplest form, PwrReg takes no arguments, and fits a power curve through the points in L₁ and L₂:

:{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:LnReg

On the home screen, or as the last line of a program, this will display the equation of the curve: you'll be shown the format, y=a*x^b, and the values of a and b. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, r, and r² will be set as well. These latter two variables will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

:{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:PwrReg ʟFAT,ʟCALS

You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

Finally, you can enter an equation variable (such as Y₁) after the command, so that the curve's equation is stored to this variable automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the equation will be in terms of X anyway, this doesn't make much sense.

An example of PwrReg with all the optional arguments:

:{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:PwrReg ʟFAT,ʟCALS,ʟFREQ,Y1

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

History

Calculator	OS Version	Description
TI-82	1.0	Added

Authors: Adrien Bertrand

PwrReg