Principal component regression (PCR) is often used in regression with multicollinearity. Although this method avoids the problems which can arise in the least squares (LS) approach, it is not optimized with respect to the ability to predict the response variable. We propose a method which combines the two steps in the PCR procedure, namely finding the principal components (PCs) and regression o...

Background: Hox gene collinearity is a universal phenomenon most emphatically observed during the development of vertebrate embryos. The last decade or so, a series of genetic engineering experiments have been performed including Hox gene deletions, duplications or transpositions. These experiments are illuminating and helpful to understand the mechanisms responsible for Hox gene collinearity. ...

The primary objective is to bring out and discuss the issues raised by the differences between the numerical and the statistical perspective on nearcollinearity in the context of the Linear Regression model. The numerical perspective views the problem as stemming from the ill-conditioning of the (X|X) matrix, which does not necessarily originate in high sample correlations among the regressors....

We study questions in incidence geometry where the precise position of points is ‘blurry’ (e.g. due to noise, inaccuracy or error). Thus lines are replaced by narrow tubes, and more generally affine subspaces are replaced by their small neighborhood. We show that the presence of a sufficiently large number of approximately collinear triples in a set of points in C implies that the points are cl...

This Monte Carlo study explored relationships among standard and unstandardized regression coefficients, structural coefficients, multiple R_ squared, and significance level of predictors for a variety of linear regression scenarios. Ten regression models with three predictors were included, and four conditions were varied that were expected to have influences on the relationship under investig...

Ill-posed inverse problems of the form y = Xp where y is J-dimensional vector of a data, p is m-dimensional probability vector which can not be measured directly and matrix X of observable variables is a known J ×m matrix, J < m, are frequently solved by Shannon’s entropy maximization (MaxEnt, ME). Several axiomatizations were proposed (see for instance [1], [2], [3], [4], [5], [6], [7], [8], a...