Lecture

Linear Regression Essentials

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In course

CS-411: Digital education

This course addresses the relationship between specific technological features and the learners' cognitive processes. It also covers the methods and results of empirical studies: do student actually learn due to technologies? In fall 2025, P. Dillenbourg w ...

Description

This lecture covers the essentials of linear regression, focusing on using multiple quantitative explanatory variables to predict a quantitative outcome. The instructor explains how to build a linear regression model, estimate parameters, interpret coefficients, and check model assumptions. The lecture also demonstrates how to apply linear regression in practice using a dataset about cars, discussing model fit, hypothesis testing, and model comparison. Additionally, it explores the concept of ANOVA and ANCOVA in the context of regression analysis.

Instructors (2)

Patrick Jermann

After studies in Geneva (TECFA) and Pittsburgh (LRDC) I joined EPFL in 2003 to coordinate eLearning projects and conduct research in the field of Computer Supported Collaborative Learning (CSCL). Starting 2013 I am responsible for MOOCs production at the Center for Digital Education (CEDE).Former Associate Editor for the IEEE Transactions on Learning Technologies and former Member of the Editorial Board for the International Journal of Computer Supported Collaborative Learning (iJCSCL). Specialties: Interaction analysis, research methods, statistical methods, prototyping, software development, pedagogical design.

Pierre Dillenbourg

A former teacher in elementary school, Pierre Dillenbourg graduated in educational science (University of Mons, Belgium). He started his research on learning technologies in 1984. In 1986, he has been on of the first in the world to apply machine learning to develop a self-improving teaching system. He obtained a PhD in computer science from the University of Lancaster (UK), in the domain of artificial intelligence applications for education. He has been assistant professor at the University of Geneva. He joined EPFL in 2002. He has been the director of Center for Research and Support on Learning and its Technologies, then academic director of Center for Digital Education, which implements the MOOC strategy of EPFL (over 2 million registrations). He is full professor in learning technologies in the School of Computer & Communication Sciences, where he is the head of the CHILI Lab: "Computer-Human Interaction for Learning & Instruction ». He is the director of the leading house DUAL-T, which develops technologies for dual vocational education systems (carpenters, florists,...). With EPFL colleagues, he launched in 2017 the Swiss EdTech Collider, an incubator with 80 start-ups in learning technologies. He (co-)-founded 4 start-ups, does consulting missions in the corporate world and joined the board of several companies or institutions. In 2018, he co-founded LEARN, the EPFL Center of Learning Sciences that brings together the local initiatives in educational innovation. He is a fellow of the International Society for Learning Sciences. He currently is the Associate Vice-President for Education at EPFL.

Official source

Ontological neighbourhood

Statistics

Data analysis: Regression analysis

Related concepts (32)

Bayesian linear regression

Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables, with the goal of obtaining the posterior probability of the regression coefficients (as well as other parameters describing the distribution of the regressand) and ultimately allowing the out-of-sample prediction of the regressand (often labelled ) conditional on observed values of the regressors (usually ).

General linear model

The general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In that sense it is not a separate statistical linear model. The various multiple linear regression models may be compactly written as where Y is a matrix with series of multivariate measurements (each column being a set of measurements on one of the dependent variables), X is a matrix of observations on independent variables that might be a design matrix (each column being a set of observations on one of the independent variables), B is a matrix containing parameters that are usually to be estimated and U is a matrix containing errors (noise).

Segmented regression

Segmented regression, also known as piecewise regression or broken-stick regression, is a method in regression analysis in which the independent variable is partitioned into intervals and a separate line segment is fit to each interval. Segmented regression analysis can also be performed on multivariate data by partitioning the various independent variables. Segmented regression is useful when the independent variables, clustered into different groups, exhibit different relationships between the variables in these regions.

Regression analysis

In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one or more independent variables (often called 'predictors', 'covariates', 'explanatory variables' or 'features'). The most common form of regression analysis is linear regression, in which one finds the line (or a more complex linear combination) that most closely fits the data according to a specific mathematical criterion.

Simple linear regression

In statistics, simple linear regression is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the x and y coordinates in a Cartesian coordinate system) and finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts the dependent variable values as a function of the independent variable. The adjective simple refers to the fact that the outcome variable is related to a single predictor.

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