Linear Regression Models

By Michael N Sakano1, Saaketh Desai1, Alejandro Strachan1

1. Materials Engineering, Purdue University, West Lafayette, IN

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Abstract

This module introduces linear regression in the context of materials science and engineering. We will apply liner regression to predict materials properties and to explore correlations between materials properties via hands-on online simulations. Linear regression is a supervised machine learning technique where a model functional form is provided, and the equation is parameterized using training data. In this module, we will explore linear regression to compute Young’s modulus and yield stress from context of stress and strain, as well as to determine correlations between Young’s modulus and melting temperature for various elements.

This end-to-end module is designed to be self-contained and easy to incorporate in existing courses or used for self-study. The module consists of three components:

This module is part of a series on data science and machine learning for engineering and physical sciences. Users will be able to run interactive code online using nanoHUB, no need to download or install any software.

Learning objectives. After completing this module, you will:

  • Apply regression techniques to create a linear model
  • Construct and train a linear model to explore materials data
    • Extract materials properties (Young’s modulus and yield stress)
    • Find correlations between materials properties
  • Evaluate uncertainties in the fitted parameters
  • Compute errors in the fitting procedure

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Researchers should cite this work as follows:

  • Michael N Sakano, Saaketh Desai, Alejandro Strachan (2020), "Linear Regression Models," https://nanohub.org/resources/34286.

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