Lecture

Multilinear Regression: Least Square Fit

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

ENG-606: EU EIT Urban Mobility 3-day seminar

The 3-Day Seminar provides an insight into Urban mobility aspects including fuels (electricity, batteries, fuel cells, hydrogen, biomethane), charging infrastructure, country overviews (CH, FIN, ISR, IT, N, UK), market-active companies, and notions of ente ...

Description

This lecture covers the concepts related to multilinear regression, including variance of coefficients, confidence intervals, correlation matrix, variance inflation factors, model coordinate, standardized response variance, and information function. It also discusses design optimization and orthogonality, project teamwork, abstract submission, design optimization criteria, industrial process optimization, and the optimization procedure. The algebraic form of ANOVA is also explained, along with the method candexch in Matlab for candidate exchange selection.

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)

Pearson correlation coefficient

In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations.

Analysis of variance

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation.

Correlation

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.

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.

Cross-correlation

In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions.

Related lectures (64)

Describing Data: Statistics and Hypothesis Testing

Covers descriptive statistics, hypothesis testing, and correlation analysis with various probability distributions and robust statistics.

Multilinear Regression: Standardized Variables and Effects

Explores standardizing variables and effects in multilinear regression analysis.

Describing Data: Statistics & Uncertainty

Introduces descriptive statistics, uncertainty quantification, and variable relationships, emphasizing the importance of statistical interpretation and critical analysis.

Linear Regression: Estimation and Inference

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

Dependence and Correlation