Incorrect least-squares regression coefficients in method-comparison analysis.

1979 ◽  
Vol 25 (3) ◽  
pp. 432-438 ◽  
Author(s):  
P J Cornbleet ◽  
N Gochman
Keyword(s):  
Standard Deviation ◽  
Least Squares ◽  
Least Squares Method ◽  
Regression Line ◽  
Method Comparison ◽  
Regression Coefficients ◽  
Least Squares Regression ◽  
Data Set ◽  
Data Points ◽  
Regression Slopes

Abstract The least-squares method is frequently used to calculate the slope and intercept of the best line through a set of data points. However, least-squares regression slopes and intercepts may be incorrect if the underlying assumptions of the least-squares model are not met. Two factors in particular that may result in incorrect least-squares regression coefficients are: (a) imprecision in the measurement of the independent (x-axis) variable and (b) inclusion of outliers in the data analysis. We compared the methods of Deming, Mandel, and Bartlett in estimating the known slope of a regression line when the independent variable is measured with imprecision, and found the method of Deming to be the most useful. Significant error in the least-squares slope estimation occurs when the ratio of the standard deviation of measurement of a single x value to the standard deviation of the x-data set exceeds 0.2. Errors in the least-squares coefficients attributable to outliers can be avoided by eliminating data points whose vertical distance from the regression line exceed four times the standard error the estimate.

Comparison of the Least-Squares Regression Line and a Truncated Discrete Fourier Transform when describing Linearly Correlated data

2020 ◽  
Author(s):  
Chris Anto
Keyword(s):  
Fourier Transform ◽  
Least Squares ◽  
Discrete Fourier Transform ◽  
Least Squares Method ◽  
Regression Line ◽  
Correlated Data ◽  
Least Squares Regression

For long, the least squares regression line has been a primary tool for analyzing linear data. In this paper, the author suggests a method involving a truncated fourier transform that would achieve everything the least squares method achieves and more, including details about the magnitude of deviation.

scholarly journals La distancia más corta. El método de los mínimos cuadrados.

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Manuel Molina
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Regression Line ◽  
Regression Method ◽  
Regression Coefficients ◽  
Least Squares Regression ◽  
Linear Regression Line ◽  
Shortest Distance ◽  
The Way

El método de los mínimos cuadrados se utiliza para calcular la recta de regresión lineal que minimiza los residuos, esto es, las diferencias entre los valores reales y los estimados por la recta. Se revisa su fundamento y la forma de calcular los coeficientes de regresión con este método. ABSTRACT The shortest distance. Least squares regression. Least squares regression method is used to calculate the linear regression line that minimizes residuals, that is, the differences among real values and those estimated by the line. Its basis and the way of calculating the regression coefficients with this method are reviewed.

Quantitative Analysis of Shells from a Site in Goleta, California

1961 ◽  
Vol 26 (3Part1) ◽  
pp. 416-420 ◽  
Author(s):  
Roberta S. Greenwood
Keyword(s):  
Quantitative Analysis ◽  
Least Squares ◽  
Analysis Of Variance ◽  
Least Squares Method ◽  
Applied Mathematics ◽  
Regression Line ◽  
Dry Weight ◽  
Convincing Evidence ◽  
Least Squares Regression ◽  
Significant Difference

AbstractThis shell study was designed to test and perfect methods of quantitative analysis in addition to providing the usual identification of species. Experiments were performed to determine the optimum size of sample, dimension of screen, number of samples, and the practicability of rapid analysis in the field to guide the progress of excavation. Analysis of variance was used to measure up to five variables at once; differences were shown graphically with direction of change indicated by a least-squares regression line. The analysis of 69 excavation units revealed an overwhelming preference for mud-dwelling species which showed no change in horizontal distribu-give guidance to the excavation team. Used with dry-weight analysis, field sorting would also indicate areas of richer occupation debris in time for this information to be useful. The use of applied mathematics in midden analysis adds a precise tool to the archaeological inventory. The data compiled on screen size, sample size, horizontal and vertical distributions, and such, were subjected to the analysis of variance, and where significant difference was indicated, the statistics were fitted to a regression line by the least-squares method. By using standardized systems and quantitative analysis, the archaeologist may obtain convincing evidence to support his conclusions. These procedures would be equally applicable to the study of skeletal, artifactual, or other ecological remains, and would add authority to the theories derived from such analysis.

FUZZY ROBUST REGRESSION ANALYSIS BASED ON THE RANKING OF FUZZY SETS

2008 ◽  
Vol 16 (05) ◽  
pp. 663-681 ◽  
Author(s):  
KAMİLE ŞANLI KULA ◽  
AYŞEN APAYDIN
Keyword(s):  
Regression Analysis ◽  
Least Squares ◽  
Fuzzy Sets ◽  
Robust Regression ◽  
Least Squares Method ◽  
Fuzzy Regression ◽  
Least Squares Regression ◽  
Fuzzy Linear Regression ◽  
Data Set ◽  
Independent Variables

Since fuzzy linear regression was introduced by Tanaka et al., fuzzy regression analysis has been widely studied and applied in various areas. Diamond proposed the fuzzy least squares method to eliminate disadvantages in the Tanaka et al method. In this paper, we propose a modified fuzzy least squares regression analysis. When independent variables are crisp, the dependent variable is a fuzzy number and outliers are present in the data set. In the proposed method, the residuals are ranked as the comparison of fuzzy sets, and the weight matrix is defined by the membership function of the residuals. To illustrate how the proposed method is applied, two examples are discussed and compared in methods from the literature. Results from the numerical examples using the proposed method give good solutions.

EXPRESS: Baseline Correction Based on a Search Algorithm from Artificial Intelligence

2020 ◽  
pp. 000370282097751
Author(s):  
Xin Wang ◽  
Xia Chen
Keyword(s):  
Artificial Intelligence ◽  
Objective Function ◽  
Least Squares ◽  
Least Squares Method ◽  
Search Algorithm ◽  
Absolute Error ◽  
Search Problem ◽  
Baseline Correction ◽  
Current Spectrum ◽  
Data Points

Many spectra have a polynomial-like baseline. Iterative polynomial fitting (IPF) is one of the most popular methods for baseline correction of these spectra. However, the baseline estimated by IPF may have substantially error when the spectrum contains significantly strong peaks or have strong peaks located at the endpoints. First, IPF uses temporary baseline estimated from the current spectrum to identify peak data points. If the current spectrum contains strong peaks, then the temporary baseline substantially deviates from the true baseline. Some good baseline data points of the spectrum might be mistakenly identified as peak data points and are artificially re-assigned with a low value. Second, if a strong peak is located at the endpoint of the spectrum, then the endpoint region of the estimated baseline might have significant error due to overfitting. This study proposes a search algorithm-based baseline correction method (SA) that aims to compress sample the raw spectrum to a dataset with small number of data points and then convert the peak removal process into solving a search problem in artificial intelligence (AI) to minimize an objective function by deleting peak data points. First, the raw spectrum is smoothened out by the moving average method to reduce noise and then divided into dozens of unequally spaced sections on the basis of Chebyshev nodes. Finally, the minimal points of each section are collected to form a dataset for peak removal through search algorithm. SA selects the mean absolute error (MAE) as the objective function because of its sensitivity to overfitting and rapid calculation. The baseline correction performance of SA is compared with those of three baseline correction methods: Lieber and Mahadevan–Jansen method, adaptive iteratively reweighted penalized least squares method, and improved asymmetric least squares method. Simulated and real FTIR and Raman spectra with polynomial-like baselines are employed in the experiments. Results show that for these spectra, the baseline estimated by SA has fewer error than those by the three other methods.

Intergenerational Earnings Mobility in Italy

2007 ◽  
Vol 7 (2) ◽  
Author(s):  
Sauro Mocetti
Keyword(s):  
Labor Market ◽  
Least Squares ◽  
Household Income ◽  
Intergenerational Mobility ◽  
Least Squares Method ◽  
Developed Countries ◽  
Data Set ◽  
Labor Market Success ◽  
Term Labor

Abstract This paper contributes to the growing number of studies on intergenerational mobility by providing a measure of earnings elasticity for Italy. The absence of an appropriate data set is overcome by adopting the two-sample two-stage least squares method. The analysis, based on the Survey of Household Income and Wealth, shows that intergenerational mobility is lower in Italy than it is in other developed countries. We also examine the reasons why the long-term labor market success of children is related to that of their fathers.

scholarly journals Tolerance Intervals in a Heteroscedastic Linear Regression Context with Applications to Aerospace Equipment Surveillance

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Janet Myhre ◽  
Daniel R. Jeske ◽  
Michael Rennie ◽  
Yingtao Bi
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Performance Metrics ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Automated System ◽  
Least Squares Regression ◽  
Data Set ◽  
Tolerance Intervals ◽  
Power Of The Test

A heteroscedastic linear regression model is developed from plausible assumptions that describe the time evolution of performance metrics for equipment. The inherited motivation for the related weighted least squares analysis of the model is an essential and attractive selling point to engineers with interest in equipment surveillance methodologies. A simple test for the significance of the heteroscedasticity suggested by a data set is derived and a simulation study is used to evaluate the power of the test and compare it with several other applicable tests that were designed under different contexts. Tolerance intervals within the context of the model are derived, thus generalizing well-known tolerance intervals for ordinary least squares regression. Use of the model and its associated analyses is illustrated with an aerospace application where hundreds of electronic components are continuously monitored by an automated system that flags components that are suspected of unusual degradation patterns.

The Effect of Knowledge Management Strategies and Enablers on Knowledge Creation Process and Organizational Performance by Using Partial Least Squares Regression Method

2012 ◽  
Vol 3 (4) ◽  
pp. 38-52 ◽  
Author(s):  
Cheng-Ping Shih ◽  
Hsin-Fu Chou
Keyword(s):  
Knowledge Management ◽  
Organizational Performance ◽  
Least Squares ◽  
Partial Least Squares ◽  
Knowledge Creation ◽  
Least Squares Method ◽  
Management Strategies ◽  
Integrative Model ◽  
Least Squares Regression ◽  
Creation Process

Under Knowledge-based economy, knowledge has been recognized as a form of capital for organizations and provides sustainable competitive advantages. knowledge is not only one of the few recyclable assets that continuously lends itself to new intellectual capital but also be integrated in many different ways in order to maximize its value. This paper has three research objectives. Firstly, measure the effect of Knowledge Management (KM) Strategies on KM Enablers; secondly, measure the effect of KM Enablers on the Knowledge Creation Process (KCP); thirdly, to measure the effect of KCP on the three aspects of Organizational Performance. A knowledge integrative model was built by using Partial Least Squares method, and the findings indicate that KM Strategies do have a significant effect on KM enablers, which in turn does have a significant effect on the KCP. KCP also has a significant effect on innovation, customer’s satisfaction and financial performance for Taiwan multinational company in Thailand.

A Comparison of Accuracy Based on Data Imputation between Unconstrained Structural Equation Modeling and Weighted Least Squares Regression

2011 ◽  
Vol 130-134 ◽  
pp. 730-733
Author(s):  
Narong Phothi ◽  
Somchai Prakancharoen
Keyword(s):  
Structural Equation Modeling ◽  
Least Squares ◽  
Structural Equation ◽  
Weighted Least Squares ◽  
Equation Modeling ◽  
Data Imputation ◽  
Least Squares Regression ◽  
Waveform Generator ◽  
Data Set ◽  
Testing Group

This research proposed a comparison of accuracy based on data imputation between unconstrained structural equation modeling (Uncon-SEM) and weighted least squares (WLS) regression. This model is developed by University of California, Irvine (UCI) and measured using the mean magnitude of relative error (MMRE). Experimental data set is created using the waveform generator that contained 21 indicators (1,200 samples) and divided into two groups (1,000 for training and 200 for testing groups). In fact, training group was analyzed by three main factors (F1, F2, and F3) for creating the models. The result of the experiment show MMRE of Uncon-SEM method based on the testing group is 34.29% (accuracy is 65.71%). In contrast, WLS method produces MMRE for testing group is 55.54% (accuracy is 44.46%). So, Uncon-SEM is high accuracy and MMRE than WLS method that is 21.25%.

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