**Mean squared error** (**MSE**) of an estimator measures the average of the squared errors, it means averages squared difference between the actual and estimated value.

**MSE **is almost positive because MSE of an estimator does not account for information that could produce more accurate estimate.

In statistical modelling, `MSE `

is defined as the difference between actual values and predicted values by the model and used to determine prediction accuracy of a model.

In this tutorial, we will discuss about how to calculate **mean squared error** (MSE) in python.

## Mean Squared Error Formula

The mean squared error (**MSE**) formula is defined as follows:

Where,

n = sample data points

y – actual size

y^ – predictive values

**MSE** is the means of squares of the errors ( yi – yi^)^{2}.

We will be using `numpy `

library to generate actual and predication values.

As there is no in built function available in python to calculate mean squared error (*MSE*), we will write simple function for calculation as per **mean squared error formula**.

## pip install numpy

If you don’t have `numpy `

package installed on your system, use below command in command prompt

pip install numpy

## How to Calculate MSE in Python

Lets understand with examples about how to **calculate mean squared error (MSE) **in python with given below python code

import numpy as np def mse(actual,prediction): return np.square(np.subtract(actual,prediction)).mean() #define Actual and Prediction data array actual = np.array([10,11,12,12,14,18,20]) pred = np.array([9,10,13,14,17,16,18]) #Calculate MSE result = mse(actual,pred) #print the result print("Mean squared error (MSE) :", result)

In the above example, we have created actual and prediction array with the help of `numpy `

package `array `

function.

We have written simple function `mse() `

as per **mean squared error formula** which takes two parameters actual and prediction data array. It calculates mean of the squares of (actual – prediction) using `numpy `

packages `square `

and `mean `

function.

Above code returns mean squared error (**MSE**) value for given actual and prediction model is 3.42857

Lets check out **Mean squared Error** (MSE) calculation with few other examples

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## Example 1 – Mean Squared Error Calculation

Lets assume we have actual and forecast dataset as below

actual = [4,7,3,9,12,8,14,10,12,12]

prediction = [5,7,3,8,10,8,12,11,11,13]

Calculate MSE for given model.

Here, again we will be using `numpy `

package to create actual and prediction array and simple` mse() `

function for *mean squared error *calculation in python code as below

import numpy as np def mse(actual,pred): return np.square(np.subtract(actual,pred)).mean() #define Actual and Prediction data array actual = np.array([4,7,3,9,12,8,14,10,12,12]) pred = np.array([5,7,3,8,10,8,12,11,11,13]) #Calculate MSE result = mse(actual,pred) #print the result print("Mean squared error (MSE) :", result)

Above code returns mean squared error (**MSE**) for given actual and prediction dataset is `1.3`

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## Example 2 – Mean Squared Error Calculation

Lets take another example with below actual and prediction data values

actual = [-2,-1,1,4]

prediction = [-3,-1,2,3]

Calcualte MSE for above model.

Using below python code, lets calculate **MSE**

import numpy as np def mse(actual,pred): return np.square(np.subtract(actual,pred)).mean() #define Actual and Prediction data array actual = np.array([-2,-1,1,4]) pred = np.array([-3,-1,2,3]) #Calculate MSE result = mse(actual,pred) #print the result print("Mean squared error (MSE) :", result)

Above code returns mean squared error (**MSE**) for given actual and prediction dataset is `0.75`

. It means it has less squared error and hence this model predicts more accuracy.

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## Conclusion

I hope, you may find **how to calculate MSE in python** tutorial with step by step illustration of examples educational and helpful.

Mean squared error (**MSE**) measures the prediction accuracy of model. Minimizing MSE is key criterion in selecting estimators.