Mean Squared Error (MSE) Calculator

Calculate the Mean Squared Error between predicted and observed values. Input your values and visualize the differences between them.

Predicted Values (comma separated):

Observed Values (comma separated):

Mean Squared Error (MSE):

Understanding Mean Squared Error (MSE)

The Mean Squared Error (MSE) measures the average squared difference between predicted values (P_i) and observed values (O_i). It is widely used to assess the performance of regression models.

Formula for Mean Squared Error

$$ \text{MSE} = \frac{1}{n} \sum_{i=1}^{n} (P_{i} - O_{i})^2 $$

Example Calculation

Suppose we have the following predicted and observed values:

Predicted values: [2.3, 3.1, 4.0]
Observed values: [2.5, 3.0, 3.8]

The MSE is calculated as follows:

Step 1: Compute the differences between each pair of predicted and observed values:

Difference 1: $ 2.3 - 2.5 = -0.2 $
Difference 2: $ 3.1 - 3.0 = 0.1 $
Difference 3: $ 4.0 - 3.8 = 0.2 $

Step 2: Square each of the differences:

$(-0.2)^2 = 0.04$
$(0.1)^2 = 0.01$
$(0.2)^2 = 0.04$

Step 3: Sum the squared differences:

$ 0.04 + 0.01 + 0.04 = 0.09 $

Step 4: Divide by the number of data points ($n = 3$):

$ \text{MSE} = \frac{0.09}{3} = 0.03 $

Thus, the Mean Squared Error (MSE) for this example is: 0.03

Implementations

How to Calculate Mean Squared Error (MSE) in R with a Real-Life Example

Attribution

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Suf

Senior Advisor, Data Science | [email protected] | + posts

Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.