Transforming the Method of Least Squares to the Dataflow Paradigm

2021 ◽  
pp. 114-121
Author(s):  
Ilir Murturi
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Algebra ◽  
Control Flow ◽  
Mathematical Statistics ◽  
Regression Equations ◽  
Method Of Least Squares ◽  
The Given ◽  
The Relationship ◽  
Best Fit

In mathematical statistics, an interesting and common problem is finding the best linear or non-linear regression equations that express the relationship between variables or data. The method of least squares (MLS) represents one of the oldest procedures among multiple techniques to determine the best fit line to the given data through simple calculus and linear algebra. Notably, numerous approaches have been proposed to compute the least-squares. However, the proposed methods are based on the control flow paradigm. As a result, this chapter presents the MLS transformation from control flow logic to the dataflow paradigm. Moreover, this chapter shows each step of the transformation, and the final kernel code is presented.

Proton NMR Analysis of Octane Number for Motor Gasoline: Part IV

1992 ◽  
Vol 46 (8) ◽  
pp. 1294-1300 ◽  
Author(s):  
M. Ichikawa ◽  
N. Nonaka ◽  
H. Amano ◽  
I. Takada ◽  
S. Ishimori ◽  
...  
Keyword(s):  
Regression Analysis ◽  
Linear Regression ◽  
Aromatic Compounds ◽  
Octane Number ◽  
Proton Magnetic Resonance ◽  
Linear Regression Analysis ◽  
Regression Equations ◽  
Nmr Analysis ◽  
Motor Gasoline ◽  
The Relationship

Software (a program) for predicting the octane number of motor gasoline by proton magnetic resonance (PMR) spectrometry has been formulated. At the same time, a method has been studied to predict the composition of gasoline (in terms of the contents of paraffin, olefin, and aromatic compounds). The formulated program was evaluated by using it to predict the octane numbers of 31 samples of marketed summer gasoline (including 16 regular and 15 premium products), whose octane numbers and compositions were identified according to the ASTM standards. Also, the relationship between the PMR spectrum and gasoline composition was subjected to linear regression analysis by using the 31 samples whose octane numbers were calculated, and the appropriateness of the resultant regression equations was assessed. This report concerns the results of the study in which the octane numbers of the 31 samples were satisfactorily predicted by the formulated program and useful linear regression equations were obtained for the prediction of the composition of gasoline.

A Task Driven Approach to Unified Synthesis of Planar Four-Bar Linkages Using Algebraic Fitting of a Pencil of G-Manifolds

2013 ◽  
Author(s):  
Q. J. Ge ◽  
Ping Zhao ◽  
Anurag Purwar
Keyword(s):  
Least Squares ◽  
Singular Values ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Motion Approximation ◽  
Value Decomposition ◽  
Four Bar Linkage ◽  
The Given ◽  
Best Fit ◽  
Additional Constraints

This paper studies the problem of planar four-bar motion approximation from the viewpoint of extraction of geometric constraints from a given set of planar displacements. Using the Image Space of planar displacements, we obtain a class of quadrics, called Generalized- or G-manifolds, with eight linear and homogeneous coefficients as a unified representation for constraint manifolds of all four types of planar dyads, RR, PR, and PR, and PP. Given a set of image points that represent planar displacements, the problem of synthesizing a planar four-bar linkage is reduced to finding a pencil of G-manifolds that best fit the image points in the least squares sense. This least squares problem is solved using Singular Value Decomposition. The linear coefficients associated with the smallest singular values are used to define a pencil of quadrics. Additional constraints on the linear coefficients are then imposed to obtain a planar four-bar linkage that best guides the coupler through the given displacements. The result is an efficient and linear algorithm that naturally extracts the geometric constraints of a motion and leads directly to the type and dimensions of a mechanism for motion generation.

scholarly journals Regresión lineal de mínimos cuadrados para la carga y descarga de un condensador

2015 ◽  
Vol 6 (1) ◽  
pp. 34
Author(s):  
José Libardo Santiago-Angarita ◽  
Olga Lucy Rincón-Leal
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Current Source ◽  
Mathematical Software ◽  
Method Of Least Squares ◽  
In Series ◽  
Experimental Errors ◽  
Loading And Unloading ◽  
Lineal Regression ◽  
A Current

ResumenEl objetivo es determinar experimentalmente el proceso de carga y descarga de un condensador estando conectado en serie con una resistencia y una fuente de corriente  continua, utilizando para ello los métodos numéricos en el proceso de ajuste de curvas a través de la regresión lineal de mínimos cuadrados, y con ayuda del software matemático Matlab se realizó la construcción de las respectivas curvas. Se estableció una relación entre el voltaje y el tiempo, formándose así una gráfica exponencial; se dedujeron las relaciones existentes y el comportamiento del fenómeno, dadas las ecuaciones y con la ayuda de lasegunda Ley de Kirchhoff; se determinaron las contantes de tiempo utilizando el método de regresión lineal de mínimos cuadrados, encontrándose un error experimental del 5 % con respecto a la constate de tiempo teórica RC.Palabras Claves: Condensador, resistencia y regresión lineal.ABSTRACTThe objective is to determine experimentally S. Process Loading and unloading of un capacitor being connected in series with a resistor and a current source , using para This numerical methods in the process of adjustment curves Through linear regression Least Squares , with the help of mathematical software Matlab building the respective curves was performed.A relationship between the voltage and time, thus forming exponential graph A is established; the relationships and the behavior of the phenomenon were deducted, given the equations and with the help of the Second Law of Kirchhoff; the Time constants were determined using the method of least squares linear regression, experimental errors UN meeting 5% with respect to the I Theoretical RC time constant.Keywords: Condenser, resistance and lineal regression.

Rapid Analysis of Chrome Ores, Chrome-Magnesia, and Magnesia-Chrome Materials by X-Ray Fluorescence

1978 ◽  
Vol 32 (6) ◽  
pp. 576-579 ◽  
Author(s):  
Subrata Banerjee ◽  
B. G. Olsen
Keyword(s):  
Linear Regression ◽  
Lanthanum Oxide ◽  
Rapid Analysis ◽  
Sodium Hexametaphosphate ◽  
Regression Equations ◽  
British Standard ◽  
X Ray ◽  
Low Concentration ◽  
Relative Standard ◽  
Best Fit

A rapid x-ray fluorescence method has been developed for analysis of chrome ores, chrome-magnesia, and magnesia-chrome materials by fusion of the powdered samples with sodium hexametaphosphate and lanthanum oxide. Three NBS standards, one British standard and a few in-house wet chemically analyzed samples were run for SiO2, Fe2O3, Al2O3, CaO, MgO, and Cr2O3 for standardizing the method. Linear regression equations were applied for determining the best fit line. Relative standard deviations were 3% or less except for CaO (5.4%) because of its usually very low concentration.

scholarly journals A method to compensate for incomplete 24-hour urine collections in nutritional epidemiology studies

1999 ◽  
Vol 2 (4) ◽  
pp. 587-591 ◽  
Author(s):  
Gunnar Johansson ◽  
Sheila Bingham ◽  
Marie Vahter
Keyword(s):  
Linear Regression ◽  
Epidemiological Studies ◽  
Drop Out ◽  
Nutritional Epidemiology ◽  
Regression Equations ◽  
Men And Women ◽  
Epidemiology Studies ◽  
The Relationship ◽  
The Town ◽  
Sodium And Potassium

AbstractObjective:To develop a method to make use of incomplete 24-hour urinary samples in nutritional epidemiology, especially when validating the dietary intake of nitrogen (protein), sodium and potassium.Design:Urinary data for men and women collected in three different studies were evaluated. The concentration of para-aminobenzoic acid (PABA) in one 24-hour urine sample per person was compared with the concentrations of nitrogen, sodium, potassium and creatinine.Setting:Men and women living in Cambridge, UK and women living in the town of Varberg, Sweden.Subjects:In total, this study consists of data from 73 Swedish women (20–50 years of age), 165 UK women (50–65 years) and 75 UK men (55–88 years).Results:On average four out of 10 people in this study had a PABA recovery below 85%. The linear regression equations for urinary excretion of nitrogen, sodium and potassium in relation to PABA recovery were y = 2.3 + 0.088 * x (r = 0.99), y = 45 + 0.82 * x (r = 0.87) and y = 19 + 0.60 * x (r = 0.93), respectively.Conclusions:The linear regression equations can be used for adjusting urinary nitrogen, sodium and potassium in urinary collections in cases where the PABA recovery is below 85%. Since it is common to obtain 24-hour urine collections with a PABA recovery below 85%, this method should increase the usefulness of biological markers of food intake in nutritional epidemiological studies and also increase the possibilities to study people that previously have been part of the drop-out group or the group with low motivation and cooperation. It is important to stress that we have not studied the relationship between PABA recovery and various urinary variables below the PABA recovery of 50%. Thus, in a case of PABA recovery below 50%, we do not recommend the use of this method to compensate for incomplete collections.

scholarly journals A Task-Driven Approach to Unified Synthesis of Planar Four-Bar Linkages Using Algebraic Fitting of a Pencil of G-Manifolds

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Q. J. Ge ◽  
Anurag Purwar ◽  
Ping Zhao ◽  
Shrinath Deshpande
Keyword(s):  
Least Squares ◽  
Singular Values ◽  
Singular Value ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Value Decomposition ◽  
Four Bar Linkage ◽  
The Given ◽  
Best Fit ◽  
Additional Constraints

This paper studies the problem of planar four-bar motion generation from the viewpoint of extraction of geometric constraints from a given set of planar displacements. Using the image space of planar displacements, we obtain a class of quadrics, called generalized- or G-manifolds, with eight linear and homogeneous coefficients as a unified representation for constraint manifolds of all four types of planar dyads, RR, PR, and PR, and PP. Given a set of image points that represent planar displacements, the problem of synthesizing a planar four-bar linkage is reduced to finding a pencil of G-manifolds that best fit the image points in the least squares sense. This least squares problem is solved using singular value decomposition (SVD). The linear coefficients associated with the smallest singular values are used to define a pencil of quadrics. Additional constraints on the linear coefficients are then imposed to obtain a planar four-bar linkage that best guides the coupler through the given displacements. The result is an efficient and linear algorithm that naturally extracts the geometric constraints of a motion and leads directly to the type and dimensions of a mechanism for motion generation.

scholarly journals Isotonic Optimization in Tariff Construction

1975 ◽  
Vol 8 (2) ◽  
pp. 175-203 ◽  
Author(s):  
W.S. Jewell
Keyword(s):  
Network Flow ◽  
Optimal Solutions ◽  
Order Restrictions ◽  
General Inequality ◽  
Optimal Insurance ◽  
Order Relations ◽  
Insurance Rate ◽  
The Given ◽  
The Relationship ◽  
Best Fit

AbstractThe problem of the best fit to set ideal values under general inequality order restrictions is examined for asymmetric, quadratic, absolute, and Chebyshev norms. Special solution procedures are given in terms of network flow algorithms over a network associated with the given isotonic order relations, and the nature of the optimal solutions is characterized for the different norms.The model is formulated in terms of finding an optimal insurance rate structure over given risk classes for which a desired pattern of tariffs can be specified. The suitability of different norms is considered in the context of corporate profitability, and the relationship to a simple rate relativities model is described.

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