Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Linear Regression: Ozone Data Analysis

In course

MATH-131: Probability and statistics

Le cours présente les notions de base de la théorie des probabilités et de l'inférence statistique. L'accent est mis sur les concepts principaux ainsi que les méthodes les plus utilisées. ...

Description

This lecture covers the analysis of ozone data using linear regression models. The instructor explains the process of imputing missing values, adjusting models, and interpreting results. Topics include coefficient of determination, least squares estimators, and model validation.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Ontological neighbourhood

Statistics

Data analysis: Regression analysis

Statistical inference: Mathematical statistics

Related concepts (32)

Statistics

Statistics (from German: Statistik, () "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal".

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.

Linear least squares

Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals. Numerical methods for linear least squares include inverting the matrix of the normal equations and orthogonal decomposition methods. The three main linear least squares formulations are: Ordinary least squares (OLS) is the most common estimator.

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.

Least squares

The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting.

Related lectures (49)

Linear Regression: Estimation and Inference

Explores linear regression estimation, linearity assumptions, and statistical tests in the context of model comparison.

Linear Regression: Estimation and Testing

Explores linear regression estimation, hypothesis testing, and practical applications in statistics.

Probabilistic Linear Regression

Explores probabilistic linear regression, covering joint and conditional probability, ridge regression, and overfitting mitigation.

Probability and Statistics

Covers fundamental concepts in probability and statistics, emphasizing data analysis techniques and statistical modeling.

Probabilities and Statistics

Covers fundamental concepts in probabilities and statistics, including linear regression, exploratory statistics, and the analysis of probabilities.

Related concepts (32)

Statistics

Linear regression

Linear least squares

Simple linear regression

Least squares