Lecture

Likelihood Estimation and Least Squares

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In course

MATH-341: Linear models

Regression modelling is a fundamental tool of statistics, because it describes how the law of a random variable of interest may depend on other variables. This course aims to familiarize students with linear models and some of their extensions, which lie a ...

Description

This lecture covers the concepts of simple normal linear regression, multiple normal linear regression, and maximum likelihood estimation. It explains the jargon, linearity in parameters, data structure, and the process of finding the least squares estimator. Examples include a professor's van fuel consumption and cement heat evolution.

Instructors (2)

Victor Panaretos

Curriculum vitae Background & EducationPublications & PreprintsHonours & AwardsEditorial ActivitiesInvited Talks & Seminars Teaching & PhD PhD Students Ulysse Naepels, Nikitas Georgakis, Ho Yun Past EPFL PhD Students Andrea Kraus, Shahin Tavakoli, Mikael Kuusela, Yoav Zemel, Marie-Hélène Descary, Valentina Masarotto, Tomas Rubin, Tomas Masák, Laya Ghodrati, Kartik Waghmare, Leonardo Santoro Past EPFL PhD Students as codirector Matthieu Simeoni, Ophelia Miralles, Sonia Alouini, Timmy Rong Tian Tse, Krali M

Tomas Masák

Official source

Ontological neighbourhood

Statistics

Data analysis: Regression analysis

Statistical inference: Mathematical statistics

Related concepts (32)

Nonlinear regression

In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations. In nonlinear regression, a statistical model of the form, relates a vector of independent variables, , and its associated observed dependent variables, . The function is nonlinear in the components of the vector of parameters , but otherwise arbitrary.

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

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.

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.

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).

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