Casio fx-CG 50: Parametric Regression

Casio fx-CG 50:  Parametric Regression

Introduction

The program PARFIT2 attempts to pair data (x,y) using a pair of parametric equations [ x(t), y(t) ].   Each list of data will have its own curve.   

x(t), 1 ≤ t ≤ n

y(t), 1 ≤ t ≤ n

n = number of data points

Each point is assigned at t-value, which the program does automatically:

t = 1 refers to (x1, y1) → (t1, x1), (t1, y1)

t = 2 refers to (x2, y2) → (t2, x2), (t2, y2)

t = 3 refers to (x3, y3) → (t3, x3), (t3, y3)

and so on.

The program offers four regression types:

1.  Linear:  a + b*t

2.  Logarithm:  a + b*ln t

3.  Exponential:  a * b^t

4.  Power:  a * t^b

Variables used:

A = intercept for x(t)

B = slope for x(t)

R = correlation for x(t)

C = intercept for y(t)

D = slope for y(t)

S = correlation for y(t)

This allows for greater curve fitting control, which can accounts for different growth of the x data and y data, separately.

The program ends with a graph of the calculated parametric equation.  

Casio fx-CG 50 Program: PARTFIT

ClrText

Locate 1,1,"PARAMETRIC"

Locate 1,2,"FIT - 2022"

Locate 1,3,"EWS"

For 1→I To 750: Next

ParamType

ClrText

"X DATA"?→List 1

"Y DATA"?→List 2

Seq(x,x,1,Dim List 1, 1)→List 3

Menu "X=","A+BT",1,"A+Bln T",2,"A×B^T",3,"A×T^B",4

Lbl 1

LinearReg(a+bx) List 3, List 1

a→A: b→B: r→R

"A+BT"→Xt1

Goto 5

Lbl 2

LogReg List 3, List 1

a→A: b→B: r→R

"A+B×ln T"→Xt1

Goto 5

Lbl 3

ExpReg(a∙b^x) List 3, List 1

a→A: b→B: r→R

"A+B^T"→Xt1

Goto 5

Lbl 4

PowerReg List 3, List 1

a→A: b→B: r→R

"A+T^B"→Xt1

Goto 5

Lbl 5

"A, B, CORR=" ◢

[ [ A ] [ B ] [ R ] ] ◢

Menu "Y=","C+DT",A,"C+Dln T",B,"C×D^T",C,"C×T^D",D

Lbl A

LinearReg(a+bx) List 2, List 1

a→C: b→D: r→S

"C+DT"→Yt1

Goto E

Lbl B

LogReg List 2, List 1

a→C: b→D: r→S

"C+D×ln T"→Yt1

Goto E

Lbl C

ExpReg(a∙b^x) List 3, List 1

a→C: b→D: r→S

"C+D^T"→Yt1

Goto E

Lbl D

PowerReg List 3, List 1

a→C: b→D: r→S

"C+T^D"→Yt1

Goto E

Lbl E

"C, D, CORR=" ◢

[ [ C ] [ D ] [ S ] ] ◢

DrawGraph

ZoomAuto

Download the program here:  https://drive.google.com/file/d/1UVEHNZ7WILv3rSAgXy0_5kQ1lBPGEvKc/view?usp=sharing

Examples

Example 1:

(x,y):

(100.0, 10.0)

(101.3, 20.0)

(103.0, 31.7)

(104.3, 42.9)

(105.6, 54.2)

(107.0, 65.6)

(110.0, 77.0)

Fit x to linear and y to exponential.

Results:  

x(t) = 98.17142857 + 1.571428571*t,  corr = 0.9904886791

y(t) = 9.829695698 * 1.308085656^t, corr = 0.9639002639

Example 2:

(x,y):

(5.0, 0.41)

(2.9, 0.30)

(1.7, 0.20)

(0.9, 0.18)

(0.1, 0.12)

Fit x to logarithmic, y to power.

Results:  

x(t) = 5.002357022 - 3.010299732 * ln t, corr = -0.9997066364

y(t) = 0.4487684406* t^-0.7312889362,  corr = -0.9684707132

Eddie

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

HP Prime: Linear Exponential Combination Fit

 HP Prime:  Linear Exponential Combination Fit

The program LINEXPREG attempts to fit bivariate data to the curve:

y = a + b * x + c * e^x

The LSQ (least square) function is used.  The output is a list of three matrices:

*  A matrix of coefficients:  [ [ a ] [ b ] [ c ] ] 

*  A matrix of y values entered

*  A matrix of predicted y values

HP Prime Program LINEXPREG

EXPORT LINEXPREG(lx,ly)

BEGIN

// 2020-11-17 EWS

// x list, y list

LOCAL n,lx2,lx3,mx,my,k,mr,mq;

n:=SIZE(lx);

lx2:=e^(lx);

lx3:={};

FOR k FROM 1 TO n DO

lx3:=CONCAT(lx3,{1,lx(k),lx2(k)});

END;

mx:=list2mat(lx3,3);

my:=list2mat(ly,1);

mq:=LSQ(mx,my);

mr:=mq(1,1)+mq(2,1)*lx+

mq(3,1)*e^(lx);

mr:=list2mat(mr,1);

RETURN {mq,my,mr};

END;

Example

x list:  {0, 1, 2, 3, 4, 5}

y list:  {2, 7, 13, 18, 26, 34}

LINEXPREG({0, 1, 2, 3, 4, 5},{2, 7, 13, 18, 26, 34})

Results:  {coefficients, y values, predicted y values}

coefficients:

[ [ 1.74935499143 ]

[ 5.39455446221 ]

[ 3.66584105034E-2 ] ] 

y values:

[ [ 2 ]

[ 7 ]

[ 13 ]

[ 18 ]

[ 26 ]

[ 34 ] ]

predicted y values:

[ [  1.78601340193 ]

[ 7.24355734477 ]

[ 12.8093349675 ]

[ 18.6693222357 ]

[ 25.3290542368 ]

[ 34.1627178129 ] ] 

Equation:

y = 1.74935499143 + 5.39455446221 * x + 3.66584105034E-2 * e^x

On to the last month of 2020...

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.