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Tutorial 4: Multiple linear regression and polynomial regression

Difficulty level

This is Tutorial 4 of a series on fitting models to data. We start with simple linear regression, using least squares optimization (Tutorial 1) and Maximum Likelihood Estimation (Tutorial 2). We will use bootstrapping to build confidence intervals around the inferred linear model parameters (Tutorial 3). We'll finish our exploration of regression models by generalizing to multiple linear regression and polynomial regression (Tutorial 4). We end by learning how to choose between these various models. We discuss the bias-variance trade-off (Tutorial 5) and Cross Validation for model selection (Tutorial 6).

In this tutorial, we will generalize the regression model to incorporate multiple features.

Topics covered in this lesson
  • Learn how to structure inputs for regression using the 'Design Matrix'
  • Generalize the MSE for multiple features using the ordinary least squares estimator
  • Visualize data and model fit in multiple dimensions
  • Fit polynomial regression models of different complexity
  • Plot and evaluate the polynomial regression fits

Experience with Python Programming Language

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