TI-84 Plus CE and Casio fx-CG 50: Mean Squared Error
Introduction
The mean square error computes the mean distance from observed (y) versus predicted (y’) values. With the n data points, the standard formula for mean squared error (MSE) is calculated as:
MSE = 1 / n * Σ((y_i – y’_i)^2 for i=1 to n)
Where:
n = number of data points
y = observed points
y’ = predicted points. Any regression can be used, but the linear regression is typically used (y = a + b * x).
When MSE is small, (as closed to zero as possible), the better the data fits the regression curve. MSE is sensitive to how much data points stray from the regression line. [see Source]
TI-84 Plus CE Program: MSE
How to retrieve the statistical variables and the apostrophe character:
a: [ vars ], 5, [ → ], [ → ], 2
b: [ vars ], 5, [ → ], [ → ], 3
n: [ vars ], ,5 ,1
‘: [ 2^{nd} ] [ apps ] <angle>, 2
Lists used:
L1 = x data
L2 = y data
L3 = y’ (predicted y) data
Download the program here: https://drive.google.com/file/d/1toVMgznJOGdaK4uhvfrcvvb3t__D9yJD/view?usp=drive_link
Casio fx-CG 50
The Casio fx-CG 50 (and other modern Casio graphing calculators such as the fx-9750GIII/9860GIII) has a MSe variable (Mean Square Error) included in the statistics variables. However, Casio’s calculation of Mse vary depending on the regression model selected. For the linear regression mode, Mse is calculated with the following formula:
Mse = 1 / (n – 2) * Σ((y_i – y’_i)^2 for i=1 to n)
Apparently the are different approaches.
.
Examples (with the Presented Formula)
Linear Regression is assumed (y = a + b * x, a = y-intercept, b = slope). Results are shown using the MSE program (TI-84 Plus CE).
Set 1:
L1 = x |
L2 = y |
1 |
1.035 |
2 |
1.076 |
3 |
1.112 |
4 |
1.400 |
5 |
1.558 |
6 |
1.827 |
a: 0.7652666667
b: 0.1626857143
MSE: 0.0066101841
Set 2:
L1 = x |
L2 = y |
40 |
385 |
41 |
349 |
40 |
376 |
41 |
358 |
39 |
333 |
38 |
326 |
39 |
371 |
40 |
350 |
a: 22.1
b: 8.4
MSE: 306.85
Source
Encord. “Mean Square Error”. Encord Computer Vision Glossary. 2023. Retrieved May 25, 2024. https://encord.com/glossary/mean-square-error-mse/
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Eddie
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