Mean Squared Error (MSE) Calculator

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

Mean Squared Error (MSE):

Understanding Mean Squared Error (MSE)

The Mean Squared Error (MSE) measures the average squared difference between predicted values (Pi) and observed values (Oi). 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

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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.