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Least squares method

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Full-Text Articles in Physical Sciences and Mathematics

Estimating The Parameters Of A Simple Linear Regression Model Without Using Differential Calculus, Mamunur Rashid, Jyotirmoy Sarkar Aug 2022

Estimating The Parameters Of A Simple Linear Regression Model Without Using Differential Calculus, Mamunur Rashid, Jyotirmoy Sarkar

Mathematics Faculty Publications

To estimate the parameters of a simple linear regression model, students who already know calculus can minimize the total squared deviations by setting its first-order partial derivatives to zero and solving simultaneously. For students who do not know calculus, most teachers/textbooks simply state the formulas without justifying them. Students accept the formulas on faith; and for given data, they evaluate the estimates using a calculator or a statistical software. In this paper, we justify the formulas without invoking calculus. We hope the users of statistics will benefit from our proposed justifications.

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On The Extension Of Exponentiated Pareto Distribution, Amal S. Hassan, Saeed Elsayed Hemeda, Said G. Nassr Oct 2021

On The Extension Of Exponentiated Pareto Distribution, Amal S. Hassan, Saeed Elsayed Hemeda, Said G. Nassr

Journal of Modern Applied Statistical Methods

In this study, an extended exponentiated Pareto distribution is proposed. Some statistical properties are derived. We consider maximum likelihood, least squares, weighted least squares and Bayesian estimators. A simulation study is implemented for investigating the accuracy of different estimators. An application of the proposed distribution to a real data is presented.

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Inverse Problem For A Parabolic System, Reza Pourgholi, Amin Esfahani, Hassan D. Mazraeh Jun 2017

Inverse Problem For A Parabolic System, Reza Pourgholi, Amin Esfahani, Hassan D. Mazraeh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper a numerical approach combining the least squares method and a genetic algorithm is proposed for the determination of the source term in an inverse parabolic system (IPS). A numerical experiment confirm the utility of this algorithm as the results are in good agreement with the exact data. Results show that a reasonable estimation can be obtained by the genetic algorithm within a CPU with clock speed 2.7 GHz.

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Space-Time Cfosls Methods With Amge Upscaling, Martin Neumüller, Panayot Vassilevski, Umberto E. Villa Mar 2017

Space-Time Cfosls Methods With Amge Upscaling, Martin Neumüller, Panayot Vassilevski, Umberto E. Villa

Mathematics and Statistics Faculty Publications and Presentations

This work considers the combined space-time discretization of time-dependent partial differential equations by using first order least square methods. We also impose an explicit constraint representing space-time mass conservation. To alleviate the restrictive memory demand of the method, we use dimension reduction via accurate element agglomeration AMG coarsening, referred to as AMGe upscaling. Numerical experiments demonstrating the accuracy of the studied AMGe upscaling method are provided.

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Solution To The Multicollinearity Problem By Adding Some Constant To The Diagonal, Hanan Duzan, Nurul Sima Binti Mohamaed Shariff May 2016

Solution To The Multicollinearity Problem By Adding Some Constant To The Diagonal, Hanan Duzan, Nurul Sima Binti Mohamaed Shariff

Journal of Modern Applied Statistical Methods

Ridge regression is an alternative to ordinary least-squares (OLS) regression. It is believed to be superior to least-squares regression in the presence of multicollinearity. The robustness of this method is investigated and comparison is made with the least squares method through simulation studies. Our results show that the system stabilizes in a region of k, where k is a positive quantity less than one and whose values depend on the degree of correlation between the independent variables. The results also illustrate that k is a linear function of the correlation between the independent variables.

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Observation Of Sulfate Aerosols And So₂ From The Sarychev Volcanic Eruption Using Data From The Atmospheric Chemistry Experiment (Ace), D. Doeringer, A. Eldering, C. D. Boone, G. González Abad, P. F. Bernath Jan 2012

Observation Of Sulfate Aerosols And So₂ From The Sarychev Volcanic Eruption Using Data From The Atmospheric Chemistry Experiment (Ace), D. Doeringer, A. Eldering, C. D. Boone, G. González Abad, P. F. Bernath

Chemistry & Biochemistry Faculty Publications

[1] Infrared spectra measured by the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) on the SCISAT satellite were used to analyze the Sarychev volcanic aerosol after the eruption in June 2009. Evidence of the Sarychev eruptions was first detected in July 2009 from enhanced SO2 concentrations and atmospheric extinction. By February 2010, the atmosphere had returned to pre-Sarychev conditions. In July 2009, the volcanic plume was found between 8.5 km and 17.5 km in altitude at mid- and high latitudes (55°N–70°N). The first SO2 and sulfate aerosol retrievals carried out using the infrared solar occultation spectra recorded with …

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Linear Reconstruction Of Non-Stationary Image Ensembles Incorporating Blur And Noise Models, Stephen D. Ford Mar 1998

Linear Reconstruction Of Non-Stationary Image Ensembles Incorporating Blur And Noise Models, Stephen D. Ford

Theses and Dissertations

Two new linear reconstruction techniques are developed to improve the resolution of images collected by ground-based telescopes imaging through atmospheric turbulence. The classical approach involves the application of constrained least squares (CLS) to the deconvolution from wavefront sensing (DWFS) technique. The new algorithm incorporates blur and noise models to select the appropriate regularization constant automatically. In all cases examined, the Newton-Raphson minimization converged to a solution in less than 10 iterations. The non-iterative Bayesian approach involves the development of a new vector Wiener filter which is optimal with respect to mean square error (MSE) for a non-stationary object class degraded …

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A Photometric And Spectroscopic Study Of The Cataclysmic Variable Sx Leonis Minoris In Quiescence And Superoutburst, R. Mark Wagner, John R. Thorstensen, R. K. Honeycutt, S. B. Howell Feb 1998

A Photometric And Spectroscopic Study Of The Cataclysmic Variable Sx Leonis Minoris In Quiescence And Superoutburst, R. Mark Wagner, John R. Thorstensen, R. K. Honeycutt, S. B. Howell

Dartmouth Scholarship

We present CCD imaging, CCD photometry on long and short timescales, and time-resolved spectroscopy of SX LMi, a new SU Ursae Majoris type dwarf nova. The quiescent optical spectrum shows broad double-peaked Balmer, He I, and He II emission lines, similar to other quiescent dwarf novae. Absorption lines from a late-type secondary are not detected. Time-resolved spectra obtained in quiescence reveal radial velocity variations of the Balmer emission lines on a period of 0.06717 ± 0.00011 days, or 96.72 ± 0.16 minutes, with only a slight possibility of a daily cycle-count error. Optical photometry obtained between 1987 and 1991 shows …

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A Comparison Of Variable Selection Criteria For Multiple Linear Regression: A Second Simulation Study, David P. Woollard Mar 1993

A Comparison Of Variable Selection Criteria For Multiple Linear Regression: A Second Simulation Study, David P. Woollard

Theses and Dissertations

This thesis implements a variable selection method proposed by Alan J. Miller, and makes an extension of Ross J. Hansen's 1988 thesis research by comparing the methods he examined: Minimum MSE, Minimum Sp, and Minimum Cp with Miller's method. Response Surface methodology is employed with two performance measures: the percentage of correct variables in a model and the Theoretical Mean Squared Error of Prediction (TMSEP). Each technique is applied on generated data with known multicollinearities, variances, random predictors, and sample sizes. Both performance measures are computed for models selected under each technique. A full factorial design using each performance measure …

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