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Lecture

Multivariate Polynomial Regression

In course

ENG-209: Data science for engineers with Python

Ce cours propose une immersion progressive et complète dans le domaine de la Data Science à travers le langage Python. Il guide les étudiants depuis la manipulation de données brutes jusqu'à la modélisation et l'extraction de connaissances utiles à partir ...

Description

This lecture covers the application of multivariate polynomial regression to predict the variation of sound velocity in water based on temperature, depth, and salinity measurements. The data used is from oceanographic measurements by NOAA in the Gulf of Mexico.

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Instructors (2)

Olivier Verscheure

Jean-Philippe Pellet

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Related concepts (32)

Polynomial regression

In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E(y |x). Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data.

Gulf of Mexico

The Gulf of Mexico (Golfo de México) is an ocean basin and a marginal sea of the Atlantic Ocean, mostly surrounded by the North American continent. It is bounded on the northeast, north and northwest by the Gulf Coast of the United States; on the southwest and south by the Mexican states of Tamaulipas, Veracruz, Tabasco, Campeche, Yucatán, and Quintana Roo; and on the southeast by Cuba. The Southern U.S.

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.

Atlantic Oceanographic and Meteorological Laboratory

The Atlantic Oceanographic and Meteorological Laboratory (AOML), a federal research laboratory, is part of the National Oceanic and Atmospheric Administration's (NOAA) Office of Oceanic and Atmospheric Research (OAR), located in Miami in the United States. AOML's research spans tropical cyclone and hurricanes, coastal ecosystems, oceans and human health, climate studies, global carbon systems, and ocean observations. It is one of seven NOAA Research Laboratories (RLs).

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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