Python | Mean Squared Error
The Mean Squared Error (MSE) or Mean Squared Deviation (MSD) of an estimator measures the average of error squares i.e. the average squared difference between the estimated values and true value. It is a risk function, corresponding to the expected value of the squared error loss. It is always non – negative and values close to zero are better. The MSE is the second moment of the error (about the origin) and thus incorporates both the variance of the estimator and its bias.
Steps to find the MSE
- Find the equation for the regression line.
(1)
- Insert X values in the equation found in step 1 in order to get the respective Y values i.e.
(2)
- Now subtract the new Y values (i.e.
) from the original Y values. Thus, found values are the error terms. It is also known as the vertical distance of the given point from the regression line.
(3)
- Square the errors found in step 3.
(4)
- Sum up all the squares.
(5)
- Divide the value found in step 5 by the total number of observations.
(6)
Example:
Consider the given data points: (1,1), (2,1), (3,2), (4,2), (5,4)
You can use this online calculator to find the regression equation / line.
Regression line equation: Y = 0.7X – 0.1
X | Y | ![]() |
---|---|---|
1 | 1 | 0.6 |
2 | 1 | 1.29 |
3 | 2 | 1.99 |
4 | 2 | 2.69 |
5 | 4 | 3.4 |
Now, using formula found for MSE in step 6 above, we can get MSE = 0.21606
MSE using scikit – learn:
from sklearn.metrics import mean_squared_error # Given values Y_true = [ 1 , 1 , 2 , 2 , 4 ] # Y_true = Y (original values) # calculated values Y_pred = [ 0.6 , 1.29 , 1.99 , 2.69 , 3.4 ] # Y_pred = Y' # Calculation of Mean Squared Error (MSE) mean_squared_error(Y_true,Y_pred) |
Output: 0.21606
MSE using Numpy module:
import numpy as np # Given values Y_true = [ 1 , 1 , 2 , 2 , 4 ] # Y_true = Y (original values) # Calculated values Y_pred = [ 0.6 , 1.29 , 1.99 , 2.69 , 3.4 ] # Y_pred = Y' # Mean Squared Error MSE = np.square(np.subtract(Y_true,Y_pred)).mean() |
Output: 0.21606
Recommended Posts:
- ML | Log Loss and Mean Squared Error
- ML | Mathematical explanation of RMSE and R-squared error
- NZEC error in Python
- Python | Assertion Error
- Floating point error in Python
- Python | 404 Error handling in Flask
- Python | Prompt for Password at Runtime and Termination with Error Message
- Reading Python File-Like Objects from C | Python
- Python | Index of Non-Zero elements in Python list
- Python | Merge Python key values to list
- Python | Convert list to Python array
- Important differences between Python 2.x and Python 3.x with examples
- Python | Add Logging to Python Libraries
- Python | Add Logging to a Python Script
- Python | Set 4 (Dictionary, Keywords in Python)
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.