Deriving the Least Squares Regression Equation

1983 ◽  
Vol 37 (3) ◽  
pp. 232
Author(s):  
A. S. C. Ehrenberg
Keyword(s):  
Least Squares ◽  
Regression Equation ◽  
Least Squares Regression

The Isothermal Compressibility of Organic Liquids by Ultracentrifugation. Correlation with Surface Tension

1971 ◽  
Vol 49 (24) ◽  
pp. 3956-3959 ◽  
Author(s):  
Alfred J. Richard ◽  
Kenneth S. Rogers
Keyword(s):  
Surface Tension ◽  
Least Squares ◽  
Isothermal Compressibility ◽  
Regression Equation ◽  
Organic Liquids ◽  
Least Squares Regression ◽  
Analytical Ultracentrifuge ◽  
Surface Tensions ◽  
Temperature Range ◽  
Good Agreement

Isothermal compressibilities of seven organic liquids have been determined by analytical ultracentrifuge techniques, in good agreement with literature values obtained by other methods.A least squares regression equation was derived that correlated the logarithmic values of isothermal compressibilities of 7 organic liquids, determined experimentally, with the liquids' surface tensions. This equation was shown to be valid for 11 other organic liquids (values obtained from literature) over a temperature range of 0° through 50°, and a surface tension range of 13 to 44 dyn per cm.

Deriving the Least Squares Regression Equation

1983 ◽  
Vol 37 (3) ◽  
pp. 232-232
Author(s):  
A. S.C. Ehrenberg
Keyword(s):  
Least Squares ◽  
Regression Equation ◽  
Least Squares Regression

Use of reflectance spectroscopy to estimate the organic carbon and CaCO3 contents of soils

2012 ◽  
Vol 61 (2) ◽  
pp. 277-290 ◽  
Author(s):  
Ádám Csorba ◽  
Vince Láng ◽  
László Fenyvesi ◽  
Erika Michéli
Keyword(s):  
Organic Carbon ◽  
Least Squares ◽  
Partial Least Squares ◽  
Partial Least Squares Regression ◽  
Mean Squared Error ◽  
Reflectance Spectroscopy ◽  
Least Squares Regression ◽  
Root Mean Squared Error ◽  
Squared Error

Napjainkban egyre nagyobb igény mutatkozik olyan technológiák és módszerek kidolgozására és alkalmazására, melyek lehetővé teszik a gyors, költséghatékony és környezetbarát talajadat-felvételezést és kiértékelést. Ezeknek az igényeknek felel meg a reflektancia spektroszkópia, mely az elektromágneses spektrum látható (VIS) és közeli infravörös (NIR) tartományában (350–2500 nm) végzett reflektancia-mérésekre épül. Figyelembe véve, hogy a talajokról felvett reflektancia spektrum információban nagyon gazdag, és a vizsgált tartományban számos talajalkotó rendelkezik karakterisztikus spektrális „ujjlenyomattal”, egyetlen görbéből lehetővé válik nagyszámú, kulcsfontosságú talajparaméter egyidejű meghatározása. Dolgozatunkban, a reflektancia spektroszkópia alapjaira helyezett, a talajok ösz-szetételének meghatározását célzó módszertani fejlesztés első lépéseit mutatjuk be. Munkánk során talajok szervesszén- és CaCO3-tartalmának megbecslését lehetővé tévő többváltozós matematikai-statisztikai módszerekre (részleges legkisebb négyzetek módszere, partial least squares regression – PLSR) épülő prediktív modellek létrehozását és tesztelését végeztük el. A létrehozott modellek tesztelése során megállapítottuk, hogy az eljárás mindkét talajparaméter esetében magas R2értéket [R2(szerves szén) = 0,815; R2(CaCO3) = 0,907] adott. A becslés pontosságát jelző közepes négyzetes eltérés (root mean squared error – RMSE) érték mindkét paraméter esetében közepesnek mondható [RMSE (szerves szén) = 0,467; RMSE (CaCO3) = 3,508], mely a reflektancia mérési előírások standardizálásával jelentősen javítható. Vizsgálataink alapján arra a következtetésre jutottunk, hogy a reflektancia spektroszkópia és a többváltozós kemometriai eljárások együttes alkalmazásával, gyors és költséghatékony adatfelvételezési és -értékelési módszerhez juthatunk.

Speech Emotion Recognition Based on Sparse Representation

2013 ◽  
Vol 38 (4) ◽  
pp. 465-470 ◽  
Author(s):  
Jingjie Yan ◽  
Xiaolan Wang ◽  
Weiyi Gu ◽  
LiLi Ma
Keyword(s):  
Dimensionality Reduction ◽  
Emotion Recognition ◽  
Least Squares ◽  
Partial Least Squares ◽  
Partial Least Squares Regression ◽  
Speech Emotion Recognition ◽  
Least Squares Regression ◽  
Computer Science Pedagogy ◽  
Reduction Methods ◽  
Analysis Computer

Abstract Speech emotion recognition is deemed to be a meaningful and intractable issue among a number of do- mains comprising sentiment analysis, computer science, pedagogy, and so on. In this study, we investigate speech emotion recognition based on sparse partial least squares regression (SPLSR) approach in depth. We make use of the sparse partial least squares regression method to implement the feature selection and dimensionality reduction on the whole acquired speech emotion features. By the means of exploiting the SPLSR method, the component parts of those redundant and meaningless speech emotion features are lessened to zero while those serviceable and informative speech emotion features are maintained and selected to the following classification step. A number of tests on Berlin database reveal that the recogni- tion rate of the SPLSR method can reach up to 79.23% and is superior to other compared dimensionality reduction methods.

An Approach of the Madeira Wine Chemistry

Beverages ◽  
2020 ◽  
Vol 6 (1) ◽  
pp. 12 ◽  
Author(s):  
Rosa Perestrelo ◽  
Catarina Silva ◽  
Carolina Gonçalves ◽  
Mariangie Castillo ◽  
José S. Câmara
Keyword(s):  
Mass Spectrometry ◽  
Gas Chromatography ◽  
Least Squares ◽  
Partial Least Squares ◽  
Chemical Reactions ◽  
Ageing Process ◽  
Gas Chromatography Mass Spectrometry ◽  
Wine Aroma ◽  
Least Squares Regression ◽  
Volatile Composition

Madeira wine is a fortified Portuguese wine, which has a crucial impact on the Madeira Island economy. The particular properties of Madeira wine result from the unique and specific winemaking and ageing processes that promote the occurrence of chemical reactions among acids, sugars, alcohols, and polyphenols, which are important to the extraordinary quality of the wine. These chemical reactions contribute to the appearance of novel compounds and/or the transformation of others, consequently promoting changes in qualitative and quantitative volatile and non-volatile composition. The current review comprises an overview of Madeira wines related to volatile (e.g., terpenes, norisoprenoids, alcohols, esters, fatty acids) and non-volatile composition (e.g., polyphenols, organic acids, amino acids, biogenic amines, and metals). Moreover, types of aroma compounds, the contribution of volatile organic compounds (VOCs) to the overall Madeira wine aroma, the change of their content during the ageing process, as well as the establishment of the potential ageing markers will also be reviewed. The viability of several analytical methods (e.g., gas chromatography-mass spectrometry (GC-MS), two-dimensional gas chromatography and time-of-flight mass spectrometry (GC×GC-ToFMS)) combined with chemometrics tools (e.g., partial least squares regression (PLS-R), partial least squares discriminant analysis (PLS-DA) was investigated to establish potential ageing markers to guarantee the Madeira wine authenticity. Acetals, furanic compounds, and lactones are the chemical families most commonly related with the ageing process.

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