Least absolute deviations

Least absolute deviations (LAD) refers to a statistical method of regression analysis that minimizes the sum of the absolute differences between the target value and the estimated values. It is also known as L1 regression or L1-norm error, and is a more robust estimator that performs well in the presence of heavy tail error.From: Linear Models with Python [2021], A study on the carbonation of binary and ternary blended cement mortar and concrete [2022], Linear and Integer Optimization [2019], Decision Sciences [2019]

Simple and Multiple Linear Regression

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Published in Alan R. Jones, Best Fit Lines and Curves, and Some Mathe-Magical Transformations, 2018

Alan R. Jones

In terms of defining what we mean by ‘Best Fit’, the most commonly used criteria is that based on ‘Least Squares’. There are others, such as ‘Least Absolute Deviations’, which we could find using our favourite internet search engine, but we are only going to consider the Least Squares technique here (except for a brief mention in Section 4.1.1 to highlight the difference in relation to Least Squares).

A study on the carbonation of binary and ternary blended cement mortar and concrete

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Published in Journal of Structural Integrity and Maintenance, 2022

Shaik Hussain, Dipendu Bhunia, S. B. Singh, Jitendra Singh Yadav

The values of intercept and slope for the Equation (2) has been obtained for every design mix proportion. To obtain the closest value of “n” for all nine mix proportions, linear program for L1-norm error has been adopted. L1-norm error, also known as least absolute deviations (LAD), least absolute errors (LAE) is basically minimizing the sum of the absolute differences (M) between the target value (Yi) and the estimated values (f(xi)).

Least absolute deviations

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Simple and Multiple Linear Regression

A study on the carbonation of binary and ternary blended cement mortar and concrete