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.
