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Least Square Error Calculator

Formula

To calculate the Least Square Error (LSE):

$LSE = \frac{1}{n} \sum (observed - predicted)^2$

Where:

$LSE$ is the Least Square Error
$n$ is the number of data points
$observed$ is the array of observed values
$predicted$ is the array of predicted values

What is Least Square Error?

Least square error is a measure used in statistical models to quantify the difference between the values predicted by a model and the values actually observed from the environment that is being modeled. It is a common measure of the overall 'fit' of a model, with lower values indicating a better fit.

Example Calculation

Let's assume the following values:

Observed Values: [3, 4, 5, 6, 7]
Predicted Values: [2.8, 4.1, 4.9, 6.2, 7.1]

Using the formula:

$LSE = \frac{1}{5} \left( (3-2.8)^2 + (4-4.1)^2 + (5-4.9)^2 + (6-6.2)^2 + (7-7.1)^2 \right)$

$LSE = \frac{1}{5} \left( 0.04 + 0.01 + 0.01 + 0.04 + 0.01 \right) = \frac{1}{5} \times 0.11 = 0.022$

The Least Square Error is 0.022.