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.

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.

scholarly journals An open-access CMIP5 pattern library for temperature and precipitation: description and methodology

2017 ◽  
Vol 9 (1) ◽  
pp. 281-292 ◽  
Author(s):  
Cary Lynch ◽  
Corinne Hartin ◽  
Ben Bond-Lamberty ◽  
Ben Kravitz
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Regression Method ◽  
Pattern Generation ◽  
Cmip5 Models ◽  
Climate Projections ◽  
Linear Regression Method ◽  
High Latitudes ◽  
Least Squares Regression ◽  
Temperature And Precipitation

Abstract. Pattern scaling is used to efficiently emulate general circulation models and explore uncertainty in climate projections under multiple forcing scenarios. Pattern scaling methods assume that local climate changes scale with a global mean temperature increase, allowing for spatial patterns to be generated for multiple models for any future emission scenario. For uncertainty quantification and probabilistic statistical analysis, a library of patterns with descriptive statistics for each file would be beneficial, but such a library does not presently exist. Of the possible techniques used to generate patterns, the two most prominent are the delta and least squares regression methods. We explore the differences and statistical significance between patterns generated by each method and assess performance of the generated patterns across methods and scenarios. Differences in patterns across seasons between methods and epochs were largest in high latitudes (60–90° N/S). Bias and mean errors between modeled and pattern-predicted output from the linear regression method were smaller than patterns generated by the delta method. Across scenarios, differences in the linear regression method patterns were more statistically significant, especially at high latitudes. We found that pattern generation methodologies were able to approximate the forced signal of change to within  ≤  0.5 °C, but the choice of pattern generation methodology for pattern scaling purposes should be informed by user goals and criteria. This paper describes our library of least squares regression patterns from all CMIP5 models for temperature and precipitation on an annual and sub-annual basis, along with the code used to generate these patterns. The dataset and netCDF data generation code are available at doi:10.5281/zenodo.495632.

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.

scholarly journals How cann soccer improve statistical learning?

2014 ◽  
Vol 2 (7) ◽  
pp. 83-87
Author(s):  
Enivaldo C. Rocha ◽  
Dalson Britto Figueiredo Filho ◽  
Ranulfo Paranhos ◽  
José Alexandre Silva Jr. ◽  
Denisson Silva
Keyword(s):  
Linear Regression ◽  
Statistical Learning ◽  
Undergraduate Students ◽  
Ordinary Least Squares ◽  
Regression Coefficients ◽  
Least Squares Regression ◽  
Practical Application ◽  
Implementation Cost ◽  
Home Team ◽  
Classical Hypothesis

This paper presents an active classroom exercise focusing on the interpretation of ordinary least squares regression coefficients. Methodologically, undergraduate students analyze Brazilian soccer data, formulate and test classical hypothesis regarding home team advantage. Technically, our framework is simply adapted for others sports and has no implementation cost. In addition, the exercise is easily conducted by the instructor and highly enjoyable for the students. The intuitive approach also facilitates the understanding of linear regression practical application.

Dosimetric evaluation of tandem-based cervical high-dose-rate brachytherapy treatment planning using American Brachytherapy Society 2011 recommendations

2016 ◽  
Vol 15 (3) ◽  
pp. 283-289 ◽  
Author(s):  
Manish K. Goyal ◽  
T. S. Kehwar ◽  
Jayanand Manjhi ◽  
Jerry L. Barker ◽  
Bret H. Heintz ◽  
...  
Keyword(s):  
Linear Regression ◽  
Dose Rate ◽  
Regression Line ◽  
High Dose Rate ◽  
Least Square ◽  
High Dose ◽  
Hdr Brachytherapy ◽  
Linear Regression Line ◽  
Significant Difference ◽  
Best Fit

AbstractPurposeThis study evaluated dosimetric parameters for cervical high-dose-rate (HDR) brachytherapy treatment using varying dose prescription methods.MethodsThis study includes 125 tandem-based cervical HDR brachytherapy treatment plans of 25 patients who received HDR brachytherapy. Delineation of high-risk clinical target volumes (HR-CTVs) and organ at risk were done on original computed tomographic images. The dose prescription point was defined as per International Commission in Radiation Units and Measurements Report Number 38 (ICRU-38), also redefined using American Brachytherapy Society (ABS) 2011 criteria. The coverage index (V100) for each HR-CTV was calculated using dose volume histogram parameters. A plot between HR-CTV and V100was plotted using the best-fit linear regression line (least-square fit analysis).ResultsMean prescribed dose to ICRU-38 Point A was 590·47±28·65 cGy, and to ABS Point A was 593·35±30·42 cGy. There was no statistically significant difference between planned ICRU-38 and calculated ABS Point A doses (p=0·23). The plot between HR-CTV and V100is well defined by the best-fit linear regression line with a correlation coefficient of 0·9519.ConclusionFor cervical HDR brachytherapy, dose prescription to an arbitrarily defined point (e.g., Point A) does not provide consistent coverage of HR-CTV. The difference in coverage between two dose prescription approaches increases with increasing CTV. Our ongoing work evaluates the dosimetric consequences of volumetric dose prescription approaches for these patients.

scholarly journals Foot Length as a Predictor of Weight in Children up to Five Years

2019 ◽  
Vol 31 (2) ◽  
pp. 39-44
Author(s):  
Md Shameem ◽  
Nazneen Akhter Banu ◽  
ANM Nurul Haque Bhuiyan ◽  
Ariful Islam
Keyword(s):  
Body Weight ◽  
Linear Regression ◽  
Regression Line ◽  
The Body ◽  
Critically Ill Children ◽  
Linear Regression Line ◽  
Foot Length ◽  
Measured Weight ◽  
Variable Weight

Weight measurement is essential for the management of pediatric patients to calculate the dose of the drugs. But it is not possible to move the child to a weighing scale for determination of body weight when the child is in a critical condition. The purpose of this study was to check if foot length correlates with child’s body weight in our situation and to devise a formula for prediction of weight based on foot– length observed. This Cross-sectional study was carried out in the Department of Pediatrics, Sir Salimullah Medical College, Mitford hospital, Dhaka over a period of 12 months between January 2008 and December 2008. A total of 300 children, between 0 day to five years, meeting the predefined eligibility criteria were included in the study. Using the available data, simple linear regression analysis was performed between the dependent variable weight and independent variable foot length. The estimated linear regression line was: Predicted weight (kg) = a+ [b× foot length]. Data were analyzed using correlation coefficient (r) between foot length and children’s weight. In this study correlation between foot length and weight (r) was 0.92(P<0.001) indicating a perfect linear relationship between them. In the present study determination of correlation (r2) was 0.85 meaning that 85% of the variability in weight might be explained by variation in foot length. The estimated linear regression line was: Predicted weight (kg) = - 4.64 + [1.12 X foot length], where- 4.64 was the intercept and 1.12 was the slope of the regression line. Comparison between measured weight and predicted weight revealed that94% of variation between measured weight and predicted weight was within ±2kg. More than half of the cases (58.3%) the above-mentioned variations were within ±1kg.  This study concluded, there was a strong correlation between foot length and weight in children up to five years. The body weight in children from 0 days up to the age of 5 years can be predicted from foot length. Prediction of weight simply by foot-length measurement could be a great help to the health care provider including doctors and health workers for drug dose calculation in critically ill children. TAJ 2018; 31(2): 39-44

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