Lecture

Multilinear Regression: Basics and Applications

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Description

This lecture covers the basics of multilinear regression, including the least square fit algorithm and its application in analyzing the Young modulus of steel based on temperature, carbon, and sulfur concentrations. It also discusses empirical models, measurement points, and the difference between mechanistic and empirical models.

Instructor

Jan Van Herle

Born in Antwerp, Belgium. In Switzerland since 1983. Became Swiss citizen in 2004 out of conviction of principles of democracy and bottom-up participation. No double nationality. Village Council Member for 2 five-year mandates in 2006-2016. 1987 : Chemist from Basel University (CH). 1988 : Post-graduate IT diploma from Basel Engineering School. 1989 : Industry internship ABB Baden (CH). 1990-1993 : PhD Thesis EPFL, on Solid Oxide Fuel Cell cathode reaction mechanisms. 1994-1995 : Japanese Postdoctoral Fellowship in Tsukuba, Japan, on ceramic powders. 1995-2000 : Researcher at EPFL, Dpt. Chemistry : project responsible in PPM2 (materials), FP4-BriteEuram, NEDO (Japan), Swiss Gas Union (CH, oxygen membranes). 1998-2000 : Masters in Energy Technology, EPFL. 2000 : Cofounder of HTceramix SA (EPFL spin-off), now based in Yverdon (14 employees). Taken over by SOLIDpower in 2007, now 250 employees with 70 MCHF raised. 2000 : 1st Assistant and lecturer at LENI (STI-IGM) : fuel cell group responsible, projects on biogas (Federal Energy Office), woodgas (CCEM), fuel cell stacking (CTI, FP6, FNS), ceramic separation membranes (COST, FNS), microtubes (STI Seed), stability/lifetime/reliability in fuel cells (Electricité de France, swisselectric research). Currently 4 Ph D theses ongoing, 14 theses concluded, of which 5 colateral with SB and IMX. M.E.R. since Nov 2008. Total funding raised so far >18 MCHF (50% as main applicant; 30% outside CH; 20% industry). Scientific output : >135 peer-reviewed publications, >120 conference papers, 40 invited presentations (8 keynotes), >70 granted proposals. Fluent in 5 languages (Dutch, French, German ( Swiss-german), English, Spanish).

Official source

Ontological neighbourhood

Statistics

Data analysis: Regression analysis

Related concepts (32)

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.

Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .

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.

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

Non-linear least squares

Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations. There are many similarities to linear least squares, but also some significant differences.

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