## Saturday, July 13, 2024

### TI-84 Plus CE and Casio fx-CG 50: Mean Squared Error

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

‘: [ 2nd ] [ apps ] <angle>, 2

Lists used:

L1 = x data

L2 = y data

L3 = y’ (predicted y) data

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/

Next post: Saturday, July 20, 2024

Eddie

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