Lecture

Multilinear Regression: Standardized Variables and Effects

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Description

This lecture covers the concept of standardizing variables in multilinear regression, including how to standardize variables, standardized half-effects, and the importance of going back to non-standardized variables. It also discusses the computation of effects, variance of coefficients, confidence intervals of half-effects, and the correlation matrix.

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

Statistical inference: Mathematical statistics

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.

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.

Confidence interval

In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used. The confidence level, degree of confidence or confidence coefficient represents the long-run proportion of CIs (at the given confidence level) that theoretically contain the true value of the parameter; this is tantamount to the nominal coverage probability.

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.

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