Casio fx-CG50 and TI-84 Plus CE: Multiple Linear Regression
We have arrived at the last month of 2024. What a crazy year. I hope for smoother and peaceful times ahead.
Introduction
The program MLREG fits bi-variate data to the linear regression equation:
y = b0 + b1 * t + b2 * x
where t and x are the independent variables, and y is the dependent variable. The program uses a numerical method known as normal equations, to solve the system:
n * b0 + Σ(t) * b1 + Σ(x) * b2 = Σ(y)
Σ(t) * b0 + Σ(t^2) * b1 + Σ(t*x) * b2 = Σ(t*y)
Σ(x) * b0 + Σ(t*x) * b1 + Σ(x^2) * b2 = Σ(x*y)
or in matrix form:
[ [ n ,Σ(t), Σ(x) ] [ Σ(t), Σ(t^2), Σ(t*x) ] [ Σ(x), Σ(t*x), Σ(x^2) ] ] * [ [ b0 ] [ b1 ] [ b2 ] ]
= [ [ Σ(y) ] [ Σ(t*y) ] [ Σ(x*y) ] ]
where:
n is the number of data points,
Σ(t) is the sum of all t data,
Σ(x) is the sum of all x data,
Σ(y) is the sum of all y data,
x * t, t * y, x * y, t^2, x^2 are all represent of the variable element-by-element multiplication of each set
The calculator programs assign the following variables:
n * b0 + Σ(t) * b1 + Σ(x) * b2 = Σ(y)
Σ(t) * b0 + Σ(t^2) * b1 + Σ(t*x) * b2 = Σ(t*y)
Σ(x) * b0 + Σ(t*x) * b1 + Σ(x^2) * b2 = Σ(x*y)
A = n
B = Σ(t)
C = Σ(x)
D = Σ(t^2)
E = Σ(t*x)
F = Σ(x^2)
X = Σ(y)
Y = Σ(t*y)
Z = Σ(x*y)
Casio fx-CG 50 Program: MLREG
This is programmed in Casio Basic.
“Y=B0+B1×T+B2×X”
“T LIST”? → List 4
“X LIST”? → List 5
“Z LIST”? → List 6
If Dim List 4 ≠ Dim List 5 Or Dim List 5 ≠ Dim List 6 Or Dim List 4 ≠ Dim List 6
Then
“LISTS NOT SAME LENGTH” ◢
Stop
IfEnd
Dim List 4 → A
Sum List 4 → B
Sum List 5 → C
Sum (List 4²) → D
Sum (List 4 × List 5) → E
Sum (List 5²) → F
Sum List 6 → X
Sum (List 6 × List 4) → Y
Sum (List 6 × List 5) → Z
“B0,B1,B2=” ◢
[ [A, B, C ][B, D, E][C, E, F] ] ⁻¹ × [ [ X ][ Y ][ Z ] ] → Mat Z
TI-84 Plus CE Program: MLREG
ClrHome
Disp “Y=B0+B1*T+B2*X”
Input “T LIST: “, L₄
Input “X LIST: “, L₅
Input “Y LIST: “, L₆
If dim(L₄) ≠ dim(L₅) or dim(L₅) ≠ dim(L₆) or dim(L₄) ≠ dim(L₆)
Then
Disp “LISTS NOT EQUAL SIZE”
Stop
End
dim(L₄) → A
sum(L₄) → B
sum(L₅) → C
sum(L₄ ²) → D
sum(L₄ * L₅) → E
sum(L₅ ²) → F
sum(L₆) → X
sum(L₆ * L₄) → Y
sum(L₆ * L₅) → Z
[ [ A, B, C ] [ B, D, E ] [ C, E, F ] ] ⁻¹ * [ [ X ] [ Y ] [ Z ] ] → [ J ]
Disp “B0,B1,B2= “, [ J ]
Note: [ J ] is matrix J is called form the Matrix menu.
An Online Multiple Linear Regression Calculator
A multiple linear regression calculator which determine coefficients, quadrants, and other statistics can be found on the stats.blue web page: https://stats.blue/Stats_Suite/multiple_linear_regression_calculator.html
Examples
Example 1
t |
x |
y |
1.12 |
22.3 |
100 |
1.16 |
22.1 |
104 |
1.19 |
21.8 |
107 |
1.23 |
21.4 |
110 |
1.28 |
21.1 |
114 |
Result:
B0 = -48.8333333
B1 = 99.99999999 (TI-84 Plus CE rounds this to 100)
B2 = 1.666666666
Equation:
y = -48.8333333 + 99.99999999 * t + 1.666666666 * x
Example 2
t |
x |
y |
10.2 |
1.95 |
1000 |
10.5 |
3.00 |
1002 |
10.8 |
4.00 |
1005 |
11.1 |
4.95 |
1007 |
11.6 |
5.80 |
1009 |
11.8 |
6.75 |
1012 |
12.1 |
7.80 |
1015 |
Result:
B0 = 1008.157502
B1 = -1.429759754
B2 = 3.052897088
y = 1008.157502 – 1.429759754 * t + 3.052897088 * x
Until next time, when a new series will be introduced. Stay tuned,
Eddie
All original content copyright, © 2011-2024. 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.
