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.