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 (P_{i}) and observed values (O_{i}). It is widely used to assess the performance of regression models.

### Formula for Mean Squared Error

### 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**

### Further Reading

## Implementations

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.