Calculating Mean Absolute Error, Mean Squared Error (MSE), and Root Mean Squared Error (RMSE) using Python

by | Jan 13, 2023 | AI, Machine Learning and Deep Learning, Featured, Machine Learning Using Python, Python Scikit-learn, Statistics For Machine Learning

MAE, MSE, And RMSE Using Python

What is the Mean Absolute Error (MAE)?

Let’s say we created a linear regression model. The expected output of the model is: [ya1, ya2, ya3, … yan] And the model gave the following output: [y1, y2, …, yn] The Mean Absolute Error (MAE) is the average of absolute error that is obtained by subtracting the actual output from the predicted output.

In other words, the Mean Absolute Error (MAE) is calculated using the following formula:

MAE=\frac{ \sum_{i=1}^{n} | y_{i}-y_{ai}|}{n}

Here, n is the total number of observations.

What is the Mean Squared Error (MSE)?

The Mean Squared Error (MSE) is obtained by squaring the absolute error and then, dividing the result with the total number of observations n.

In other words, if a model gives the output [y1, y2, …, yn] and the expected output is [ya1, ya2, ya3, … yan] then, the Mean Squared Error (MSE) is calculated using the following formula:

MSE=\frac{\sum_{i=1}^{n} (y_{i}-y_{ai})^2}{n}

What is the Root Mean Squared Error (RMSE)?

The Root Mean Squared Error (RMSE) is obtained by taking a square root of the Mean Squared Error (MSE). In other words, if a model gives the output [y1, y2, …, yn] and the expected output is [ya1, ya2, …, yan] then, the Mean Squared Error (MSE) is calculated using the following formula:

RMSE=\sqrt{\frac{\sum_{i=1}^{n} (y_{i}-y_{ai})^2}{n}}

How to calculate Mean Absolute Error (MAE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE) using Python?

We can use the following Python code to calculate the Mean Absolute Error (MAE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE)…

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Amrita Mitra

Author

Ms. Amrita Mitra is an author, who has authored the books “Cryptography And Public Key Infrastructure“, “Web Application Vulnerabilities And Prevention“, “A Guide To Cyber Security” and “Phishing: Detection, Analysis And Prevention“. She is also the founder of Asigosec Technologies, the company that owns The Security Buddy.

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