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
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