How to Calculate Mean Squared Error (MSE) in Python

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