Ridge regression is often the method of choice in ill–conditioned systems. A canonical form identifies regions in the parameter space where Ordinary Least Squares (OLS) is problematic. A curious but unrecognized property of ridge solutions emerges: Under spherical errors with or without moments, the relative concentrations of the canonical estimators reverse as the ridge scalar evolves, the est...

A simple and efficient FeCl(3)-promoted cyclization/chlorination of cyclic tosylamine-tethered 8-aryl-2-en-7-yn-1-ols was observed. The reaction proceeded instantaneously at 23 °C in air to afford (Z)-4-(arylchloromethylene)-substituted azaspirocycles in good to excellent yields. This transformation can also be applied to the synthesis of spirocarbocyclic analogues from cyclic 8-aryl-2-en-7-yn-...

Cross sectional estimation of convergence regressions is known to be hazardous if there is convergence towards heterogeneous steady state values. In this paper, Monte Carlo methods are used to investigate the implications of this parameter heterogeneity problem. The cross sectional and pooled OLS estimators are compared with a panel estimator which is unaffected by heterogeneity. If there is he...

When independent variables have high linear correlation in a multiple linear regression model, we can have wrong analysis. It happens if we do the multiple linear regression analysis based on common Ordinary Least Squares (OLS) method. In this situation, we are suggested to use ridge regression estimator. We conduct some simulation study to compare the performance of ridge regression estimator ...

Since 1782, when Euler addressed the question of existence of a pair of Orthogonal Latin Squares (OLS) by stating his famous conjecture ([8, 9, 13]), these structures have remained an active area of research due to their theoretical properties as well as their applications in a variety of fields. In the current work we consider the polyhedral aspects of OLS. In particular we establish the dimen...

This article reports the findings from a localized spatial modeling approach and visual assessment of crime determinants in Flint, Michigan. Factors pertaining to socioeconomic condition, public health, social capital, environmental stress, and neighborhood context were analyzed spatially and statistically using exploratory data analysis, exploratory spatial data analysis (ESDA), ordinary least...

Most readability formulas calculate a global readability score by combining several indicator values by a linear combination. Typical indicators are Average sentence length, Average number of syllables per word, etc. Usually the parameters of the linear combination are determined by a linear OLS (ordinary least square estimation) minimizing the sum of the squared residuals in comparison with hu...

Ornithine lipids (OLs) are phosphorus-free membrane lipids widespread in bacteria but absent from archaea and eukaryotes. In addition to the unmodified OLs, a variety of OL derivatives hydroxylated in different structural positions has been reported. Recently, methylated derivatives of OLs were described in several planctomycetes isolated from a peat bog in Northern Russia, although the gene/en...