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The **mean squared error (MSE) **is a common way to measure the prediction accuracy of a model. It is calculated as:

**MSE **= (1/n) * Σ(actual – prediction)^{2}

where:

**Σ**– a fancy symbol that means “sum”**n**– sample size**actual**– the actual data value**forecast**– the predicted data value

The lower the value for MSE, the better a model is able to predict values accurately.

**How to Calculate MSE in Python**

We can create a simple function to calculate MSE in Python:

import numpy as np def mse(actual, pred): actual, pred = np.array(actual), np.array(pred) return np.square(np.subtract(actual,pred)).mean()

We can then use this function to calculate the MSE for two arrays: one that contains the actual data values and one that contains the predicted data values.

actual = [12, 13, 14, 15, 15, 22, 27] pred = [11, 13, 14, 14, 15, 16, 18] mse(actual, pred) 17.0

The mean squared error (MSE) for this model turns out to be **17.0**.

In practice, the **root mean squared error (RMSE) **is more commonly used to assess model accuracy. As the name implies, it’s simply the square root of the mean squared error.

We can define a similar function to calculate RMSE:

import numpy as np def rmse(actual, pred): actual, pred = np.array(actual), np.array(pred) return np.sqrt(np.square(np.subtract(actual,pred)).mean())

We can then use this function to calculate the RMSE for two arrays: one that contains the actual data values and one that contains the predicted data values.

actual = [12, 13, 14, 15, 15, 22, 27] pred = [11, 13, 14, 14, 15, 16, 18] rmse(actual, pred) 4.1231

The root mean squared error (RMSE) for this model turns out to be **4.1231**.

**Additional Resources**

Mean Squared Error (MSE) Calculator

How to Calculate Mean Squared Error (MSE) in Excel