Lecture

Multilinear Regression: Least Square Fit

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Description

This lecture covers the concept of multilinear regression using the least square fit method, focusing on empirical and mechanistic models, model matrices, and the computation of effects. It also discusses the importance of standardizing variables in order to obtain generic solutions.

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 (18)

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.

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.

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.

Ordinary least squares

In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable.

Total least squares

In applied statistics, total least squares is a type of errors-in-variables regression, a least squares data modeling technique in which observational errors on both dependent and independent variables are taken into account. It is a generalization of Deming regression and also of orthogonal regression, and can be applied to both linear and non-linear models. The total least squares approximation of the data is generically equivalent to the best, in the Frobenius norm, low-rank approximation of the data matrix.

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Linear Regression: Basics and Principle of Least Squares

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Box-Jenkins Methodology: Building Time Series Models

Covers the Box-Jenkins methodology for building time series models, including model identification, variance calculations, and model diagnostics.

Multilinear Regression: Standardized Variables and Effects

Explores standardizing variables and effects in multilinear regression analysis.