MSR stands for Mean Squared Residuals. MSR can be used to compare the the difference between estimated Y and observed Y in model.

It is ratio between Sum Squared Residuals and the number of observations, i.e., n. The following is the formula of MSR. **MSR has the exact same formula as the biased MSE. **

\[ MSR=\frac{\sum_{i=1}^{n} (\hat{y_i}-y_i)^2 }{n}\]

## How to calculate MSR in Python

**Method 1: Use Python Numpy to Calculate MSR**

np.square(np.subtract(Y_Observed,Y_Estimated)).mean()

**Method 2:** **Use** `sklearn.metrics`

**to Calculate MSR**

MSR is the same as biased MSE. Thus, we can use the MSE function to calculate MSR.

mean_squared_error(Y_Observed,Y_Estimated)

## Example 1: Use Numpy to calculate MSR

The following use Numpy to calculate MSR. In the code, it has the Y observed and Y estimated. Then, it uses `np.square(np.subtract(Y_Observed,Y_Estimated)).mean()`

to calculate MSR.

```
import numpy as np
# Obseved values
Y_Observed = [5,4,3,5,1,4,5]
# Estimated values
Y_Estimated = [4.4,5.2,2.5,4.5,2,4,4.5]
# Use Numpy to calculate MSR
np.square(np.subtract(Y_Observed,Y_Estimated)).mean()
```

Output:

0.5071428571428571

Thus, the MSR is 0.51.

## Example 2: **Use** `sklearn.metrics`

**to Calculate MSR**

`sklearn.metrics`

The following use ** sklearn.metrics** to calculate MSR. We can use

`mean_squared_error()`

to calculate MSR, because MSR has the same formula as biased MSE (see my another tutorial).```
from sklearn.metrics import mean_squared_error
import numpy as np
# Obseved values
Y_Observed = [5,4,3,5,1,4,5]
# Estimated values
Y_Estimated = [4.4,5.2,2.5,4.5,2,4,4.5]
#Use sklearn.metrics mean_squared_error to MSR
mean_squared_error(Y_Observed,Y_Estimated)
```

Output:

0.5071428571428571

Thus, the MSR is 0.51.