Ordinary Least-squares Method Research Articles

Progression or Aging? A Deep Learning Approach for Distinguishing Glaucoma Progression from Age-Related Changes in OCT scans

To develop deep learning (DL) algorithm to detect glaucoma progression using optical coherence tomography (OCT) images, in the absence of a reference standard. Retrospective cohort study. Glaucomatous and healthy eyes with ≥5 reliable peripapillary OCT (Spectralis, Heidelberg Engineering) circle scans were included. A weakly supervised time-series learning model, called Noise Positive-Unlabeled (Noise-PU) DL was developed to classify whether sequences of OCT B-scans showed glaucoma progression. The model used two learning schemes, one to identify age-related changes by differentiating test sequences from glaucoma vs. healthy eyes, and the other to identify test-retest variability based on scrambled OCTs of glaucoma eyes. Both models' bases were convolutional neural networks (CNN) and long short-term memory (LSTM) networks which were combined to form a CNN-LSTM model. Model features were combined and jointly trained to identify glaucoma progression, accounting for age-related loss. The DL model's outcomes were compared with ordinary least squares (OLS) regression of retinal nerve fiber layer (RNFL) thickness over time, matched for specificity. The hit ratio was used as a proxy for sensitivity. 8,785 follow-up sequences of 5 consecutive OCT tests from 3253 eyes (1859 subjects) were included in the study. Mean follow-up time was 3.5±1.6 years. In the test sample, the hit ratios of the DL and OLS methods were 0.498 (95%CI:0.470-0.526) and 0.284 (95%CI:0.258-0.309) respectively (P<0.001) when the specificities were equalized to 95%. A DL model was able to identify longitudinal glaucomatous structural changes in OCT B-scans using a surrogate reference standard for progression.

A Remedial Measure of Multicollinearity in Multiple Linear Regression in the Presence of High Leverage Points

The ordinary least squares (OLS) is the widely used method in multiple linear regression model due to tradition and its optimal properties. Nonetheless, in the presence of multicollinearity, the OLS method is inefficient because the standard errors of its estimates become inflated. Many methods have been proposed to remedy this problem that include the Jackknife Ridge Regression (JAK). However, the performance of JAK is poor when multicollinearity and high leverage points (HLPs) which are outlying observations in the X- direction are present in the data. As a solution to this problem, Robust Jackknife Ridge MM (RJMM) and Robust Jackknife Ridge GM2 (RJGM2) estimators are put forward. Nevertheless, they are still not very efficient because they suffer from long computational running time, some elements of biased and do not have bounded influence property. This paper proposes a robust Jackknife ridge regression that integrates a generalized M estimator and fast improvised Gt (GM-FIMGT) estimator, in its establishment. We name this method the robust Jackknife ridge regression based on GM-FIMGT, denoted as RJFIMGT. The numerical results show that the proposed RJFIMGT method was found to be the best method as it has the least values of RMSE and bias compared to other methods in this study.

Life Function Analysis of a Two-Parameter Exponential Distribution Using Robust Rank Regression

In this research, a proposed method is presented to estimate the life function of the two-parameter exponential distribution by using the robust rank regression on the dependent variable, which depends on the robust variance-covariance matrix (the FMCD and OGK method) and the robust mean vector through which the rank regression coefficients are estimated using the method of ordinary least squares and employing it in estimating the scale and location parameters of the exponential distribution and thus analyzing the life function on its basis. A comparison was also made between the proposed method and the classical method of rank regression on the dependent variable of life data at different sample sizes (from 10 to 25) to show the efficiency of the proposed method based on the mean square error of the estimated parameters, through a program prepared by the researcher in MATLAB language dedicated to this purpose. The practical application results concluded that the proposed robust method of rank regression on the dependent variable in estimating the parameters of the exponential distribution was more efficient than the classical method. Paper type: Research paper.

Long-Term and Decadal Sea-Level Trends of the Baltic Sea Using Along-Track Satellite Altimetry

One of the main effects of climate change is rising sea levels, which presents challenges due to its geographically heterogenous nature. Often, contradictory results arise from examining different sources of measurement and time spans. This study addresses these issues by analysing both long-term (1995–2022) and decadal (2000–2009 and 2010–2019) sea-level trends in the Baltic Sea. Two independent sources of data, which consist of 13 tide gauge (TG) stations and multi-mission along-track satellite altimetry (SA), are utilized to calculate sea-level trends using the ordinary least-squares method. Given that the Baltic Sea is influenced by geographically varying vertical land motion (VLM), both relative sea level (RSL) and absolute sea level (ASL) trends were examined for the long-term assessment. The results for the long-term ASL show estimates for TG and SA to be 3.3 mm/yr and 3.9 mm/yr, respectively, indicating agreement between sources. Additionally, the comparison of long-term RSL ranges from −2 to 4.5 mm/yr, while ASL varies between 2 and 5.4 mm/yr, as expected due to the VLM. Spatial variation in long-term ASL trends is observed, with higher rates in the northern and eastern regions. Decadal sea-level trends show higher rates, particularly the decade 2000–2009. Comparison with other available sea-level datasets (gridded models) yields comparable results. Therefore, this study evaluates the ability of SA as a reliable source for determining reginal sea-level trends in comparison with TG data.

Union membership and the wage gap between the public and private sectors: evidence from China

As trade unions are active in corporations worldwide, their effects on the labor market have attracted global attention. However, there is scarce empirical evidence regarding how trade unions’ effects on the wage gap differ between the public and private sectors, especially in the Chinese context. Using national longitudinal survey data from the China Family Panel Studies for the years 2010, 2012, 2014, 2016, and 2018 and the Blinder-Oaxaca decomposition method, this study estimates unions’ effect on the wage gap between the public and private sectors in China. The results from the Ordinary Least Squares (OLS) method indicate the existence of a significant positive union wage premium nationwide. Additionally, the premium in the public sector is greater than that in the private sector. However, this effect becomes insignificant after accounting for individual heterogeneity using the fixed effects model. The decomposition results based on the OLS method indicate that the union coverage difference (the endowment effect) widens the wage gap between the public and private sectors; conversely, the union wage premium difference (the price effect) narrows the wage gap. These results indicate that a policy expanding union coverage in the private sector may effectively narrow the wage gap between both sectors.

Evaluating the Impact of Green Gentrification -A Case Study of London

In this research, we utilize the Ordinary Least Squares (OLS) regression method to explore the relationship between green gentrification and key socioeconomic factors within London's urban landscape. Our aim is to delve into the impact of introducing or expanding green spaces on residents' lives, particularly in relation to income, life expectancy, well-being, housing costs, and unemployment rates. Through the use of OLS regression and an extensive dataset sourced from empirical evidence, we quantitatively analyze the connections between green gentrification and variations in these socioeconomic variables across different neighborhoods. Our findings reveal noteworthy associations, highlighting positive correlations between green spaces and well-being, life expectancy, and house prices, while also noting a negative correlation with the unemployment rate. These insights contribute to a comprehensive understanding of the complex dynamics between urban development, environmental enhancements, and societal well-being, emphasizing the potential advantages of green gentrification and endorsing inclusive policies. Grounded in the OLS method, our research strengthens the empirical foundation for informed decision-making among policymakers, urban planners, and researchers dedicated to cultivating sustainable and equitable urban environments.

Transfer learning across datasets with different input dimensions: An algorithm and analysis for the linear regression case

With the development of new sensors and monitoring devices, more sources of data become available to be used as inputs for machine learning models. These can on the one hand help to improve the accuracy of a model. On the other hand, combining these new inputs with historical data remains a challenge that has not yet been studied in enough detail. In this work, we propose a transfer learning algorithm that combines new and historical data with different input dimensions. This approach is easy to implement, efficient, with computational complexity equivalent to the ordinary least-squares method, and requires no hyperparameter tuning, making it straightforward to apply when the new data is limited. Different from other approaches, we provide a rigorous theoretical study of its robustness, showing that it cannot be outperformed by a baseline that utilizes only the new data. Our approach achieves state-of-the-art performance on 9 real-life datasets, outperforming the linear DSFT, another linear transfer learning algorithm, and performing comparably to non-linear DSFT.11The code for reproducing the results of this paper is available at https://github.com/lpsilvestrin/incremental_input_tl.

Estimating the Returns to Education Using a Machine Learning Approach – Evidence for Different Regions

Abstract This article revisits the Mincer earnings function and presents comparable estimates of the average monetary returns associated with an additional year of education across different regions worldwide. In contrast to the traditional Ordinary Least Squares (OLS) method commonly employed in the literature, this study applied a cutting-edge approach known as Support Vector Regression (SVR), which belongs to the family of machine learning (ML) algorithms. SVR is specifically chosen to address the bias arising from underfitting inherent in OLS. The analysis focuses on recent data spanning from 2010 to 2018, ensuring temporal homogeneity across the examined regions. The findings reveal that each additional year of education, on average, yields a private rate of returns of 10.4%. Notably, Sub-Saharan Africa exhibits the highest returns to education at 17.8%, while Europe demonstrates the lowest returns at 7.2%. Moreover, higher education is associated with the highest returns across the regions, with a rate of 12%, whereas primary education yields returns of 10%. Interestingly, women generally experience higher returns than men, with rates of 10.6 and 10.1%, respectively. Over time, the returns to education exhibit a modest decline, decreasing at a rate of approximately 0.1% per year, while the average duration of education demonstrates an increase of 0.16 years per year (1% per year). The application of the state-of-the-art ML technique, SVR, not only improves the accuracy of estimates but also enhances predictive performance measures such as the coefficient of determination (R 2) and Root Mean Square Error (RMSE) when compared to the OLS method. The implications drawn from these findings emphasize the need for expanding university education, as well as investments in primary education, along with significant attention toward promoting girls’ education. These findings hold considerable importance for policymakers who are tasked with making informed decisions regarding education expenditure and the implementation of education financing programs.

Financial distress and stock price crash risk in Egyptian firms

Economic policy uncertainty intensified as a result of the global financial crisis. To overcome these obstacles, firms handle issues with financial distress and crash risk more proactively. This paper offers new insights into the relationship between financial distress and crash risk on the Egyptian stock market during the period of 2014–2021 and presents how managers strengthen the bad news hoarding mechanism to their advantage. Data were collected via financial statements and reports obtained from the Thomson Reuters database using 824 annual observations of 103 Egyptian firms via the generalized method of moments and ordinary least squares. Results show a strong positive impact of financial distress on crash risk using OLS and GMM. Results support the role of managerial opportunism to cover up bad news that undermines a firm’s economic fundamentals. The findings support an agency theory of how financial distress affects crash risk. The findings support conducting robust tests for alternative financial distress and crash risk measures.

Mapping site index in coniferous forests using bi-temporal airborne laser scanning data and field data from the Swedish national forest inventory

Recent advancements in remote sensing of forests have demonstrated the capabilities of three-dimensional data acquired by airborne laser scanning (ALS) and, consequently, have become an integral part of enhanced forest inventories in Northern Europe. In Sweden, the first national laser scanning revolutionised forest management planning through low-cost production of large-scale and spatially explicit maps of forest attributes such as basal area, volume, and biomass, compared to the earlier practice based on field survey data. A second scanning at the national level was launched in 2019, and it provides conditions for the estimation of height growth and site index. Accurate and up-to-date information about site productivity is relevant for planning silvicultural treatments and for the prognosis of forest status and development over time. In this study, we explored the potential of bi-temporal ALS data and other auxiliary information to predict and map site productivity by site index according to site properties (SIS) of Norway spruce (Picea abies (L.) Karst) and Scots pine (Pinus sylvestris L.) in even-aged stands in Sweden. We linked ground survey data of SIS from more than 11,500 plots of the Swedish National Forest Inventory (NFI) to bi-temporal ALS data to predict and map site index using an area-based method and two regression modelling strategies: (1) a multiple linear regression (MLR) model with an ordinary least-squares parameter estimation method, and (2) a non-parametric random forests (RF) model optimised for hyper-parameter tuning. For model development, permanent plots were used, whereas the validation was done on the temporary plots of the Swedish NFI and an independent stand-level dataset. Species-specific models were developed, and the root mean square error (RMSE) metric was used to quantify the residual variability around model predictions. For both species, the MLR model gave precise and accurate estimates of SIS. The RMSE for SIS predictions was in the range of 1.96 – 2.11 m, and the relative RMSE was less than 10 % (7.68 – 9.49 %) of the reference mean value. Final predictors of site index include metrics of 90th percentile height and annual increment in the 95th percentile height, altitude, distance to coast, and soil moisture. Country-wide maps of SIS and the corresponding pixel-level prediction errors at a spatial resolution of 12.5 m grid cells were produced for the two species. Independent validations show the site index maps are suitable for use in operational forest management planning in Sweden.

Effect of government intervention in relation to COVID-19 cases and deaths in Malawi

The COVID-19 pandemic affected the world in various ways. In response to this, countries set up various interventions such as lockdowns, physical distancing, and mandatory face covering, among others. Governments also put in place measures to ensure compliance. However, the extent to which the various responses impacted the deaths and confirmed cases remains debatable. This paper explores this question by looking at how government stringency measures impacted deaths and cases in Malawi. We employ an instrumental variable (IV) approach to assess the impact of government action on confirmed COVID-19 cases and deaths. We measure government policy by the stringency index. By leveraging the IV approach, we circumvent potential endogeneity concerns between our main policy variable and the outcome variables. Our data comes from the University of Oxford COVID-19 project and spans a daily frequency from 20 February 2020 to 25 April 2022, covering multiple waves of the pandemic. Overall, the findings show that despite Malawi never having implemented a full lockdown, the government policies may have helped to reduce both cases and deaths related to COVID-19. Specifically, the IV shows that a unit increase in the government stringency index results in a drop of 179 cases and 6 deaths. All the results are statistically significant at 1% level and remain robust to the use of the ordinary least-squares method. This study demonstrates the efficacy of non-pharmaceutical tools implemented by the government to fight COVID-19. Thus, policymakers need to place more emphasis on the need for the public to adhere to these stringency measures in the event of new waves of the pandemic or similar outbreaks.

The Impact of Female Directors on the Relationship Between Corporate Social Responsibility and Capital Structure: Evidence From Egypt

This paper examines how corporate social responsibility affects capital structure. The sample consists of 58 non-financial companies listed on the Egyptian Stock Exchange, with 464 firm-year observations made between 2014 -2021 using the generalized method of moments and ordinary least squares. Data was gathered from reports and financial statements from an Egyptian information dissemination firm. This paper demonstrates that firms with female directors explain the negative impact of the association between corporate social responsibility and capital structure. Female directors and CSR disclosure improve manager oversight and reduce information asymmetry and agency conflicts. Results support agency and gender theories that expect different behavior from women in leadership posts.

An empirical study of Credit Policy Determinants of Algerian Banks/ During the period (1989-2009)

The study aimed to test the effect of size of deposits, the real interest rate, population, economic reforms on the credit policy of commercial banks of Algeria represented by the size of credit facilities. The study Used annual data for the period from 1989 to 2009. Where the Multi regression model was estimated using a method of Ordinary Least Squares OLS.Results of the analysis showed that there is a positive relationship with a statistically significant between the credit facilities and the deposits and the variable of economic reforms, while the real interest rate and population size have been linked by significant negative relationship

Bayes' approach of linear regression to modeling the human development index in Indonesia

Regression analysis is one of the data analysis techniques that can be used to examine the correlation between two variables, namely dependent variable and independent variable. It’s can be used to determine the parameter estimation of linear regression models are; the method of least squares or ordinary least square (OLS), Maximum likelihood estimation (MLE), and the Bayes method. Bayes' method defines the parameter as a random variable that describes the initial comprehension of the parameter before the observation was initiated and elucidated in an initial distribution refer as the prior distribution. The prior distribution used in this study is the pseudo prior distribution. The Data used in this study is secondary data, namely human development index (HDI) data in 2020, which was obtained from the website of the Central Statistics Agency (BPS). This study aims to estimate the regression model parameters using the Bayes method on the HDI data and the population data which adepts with information and communication technology (ICT) in Indonesia in 2020. The results of the specimen and analysis showed that population variables with ICT adepts have a significant effect on HDI variables. The results of the determination coefficient showed that 78.42% of HDI variables are affected by the population variables with ICT adepts while the remaining 21.58% are affected by other factors that have not been studied.&#x0D; Keywords: Bayes method, human development index, information communication and technology, linear regression, pseudo prior.MSC2020: 62F15

The board of directors influence on the information quality of financial reporting through accounting conservatism – Empirical evidence on Vietnamese listed enterprises

The information quality contained in financial reporting has practical implications for stakeholders. Accounting conservatism is a criterion that affects the authentication of the value of assets and liabilities related to the financial reporting of enterprises. The role of the board of directors is to supervise the information quality of an enterprise. The purpose of the paper is to examine how the board of directors influences the information quality of financial reporting through accounting conservatism. The survey sample includes 100 listed enterprises that have the highest capitalization in Vietnam’s stock market. Time series data taken for the last five years are published by enterprises from 2018 to 2022. The paper implements the quantitative method of ordinary least squares to test the hypotheses. The results explore that board size, board independence, and audit organization affect the information quality of financial reporting through accounting conservatism. Accordingly, board size has the strongest influence, and board independence has the weakest effect on the information quality of financial reporting through accounting conservatism. The research suggests some policies for Vietnamese listed enterprises to have appropriate regulations for the board of directors and strengthen control of the information quality of financial reporting.

Validation of the EPACODI-1 Scale: University Students' Perceptions of Inclusive Education.

In the last fifteen years, changes have been taking place in education systems at the international and national levels that aim to achieve, in the near future, the objectives set by the UN International Convention on the Rights of Persons with Disabilities (hereafter CRPD). Spain is no stranger to these objectives, as recognized in the new Organic Law for the Modification of the Law on the Organization of Education. This situation makes it necessary to know the perceptions that professionals in training (about to graduate) from faculties of education have about the legal content established by articles 4.1.i and 24 of the CRPD on inclusive education. In order to ascertain these perceptions, the EPACO-DI-1 instrument was used in a quantitative and confirmatory study by means of a multivariate factor analysis (CFA), applying the parallel estimation method of ordinary least squares (OLS) and principal axes with polychoric correlation and promax oblique rotation. This study involved 552 fourth-year students between the ages of 21 and over 45 from the specializations offered by the Faculty of Education of the University of Murcia. The obtained results are consistent and show the validity of the EPACODI-1 scale for determining the perceptions of professionals in training on inclusive education.

Analysis of Urbanization and Energy Consumption Using Time Series Data: Evidence from the SAARC Countries

Urbanization has posed some tremendous challenges which are related to environmental stresses through increased energy consumption. These challenges have drawn attention to the need to implement urbanization with sustainable energy consumption globally. The present study aims to identify the urbanizing factors that cause energy consumption in the SAARC countries. The South Asian Association for Regional Cooperation is considered in the study during the period of 1975-2014. The data are analyzed by using simple statistics and econometric techniques, such as the ordinary least squares (OLS) method for the country level. The study has found that all urbanizing variables significantly affect energy consumption with different levels in different countries, as shown by the OLS method. The coefficient of GDP is statistically significant at 1% level of significance for Bangladesh, Pakistan and Sri Lanka, while at 5% and 10% levels for India and Nepal, respectively. The coefficient of the industrial sector share in GDP is statistically significant at 1% level of significance for Bangladesh, Nepal and Pakistan. The result shows that a 1% increase in the service sector’s share in GDP leads to a reduction in energy consumption of 0.15%, 0.34% and 1.61%, respectively, in Bangladesh, Nepal and Sri Lanka. The result for urban population indicates that a 1% increase in urban population leads to an increase in energy consumption by 1.94%, 2.32%, 0.85% and 3.87%, respectively, for Bangladesh. India, Nepal and Sri Lanka. Green technology and energy efficiency technologies to use in the industries, encourage using public transportation, sustainable energy and urbanization are potential policy recommendations.

Underpricing of IPOs (Initial Public Offering) in Borsa Istanbul: The effect of Covid-19 Pandemic Period

Purpose- This research has both theoretical and practical implications. The study's findings will provide valuable insights into the impact of the COVID-19 pandemic on IPO mispricing in the Turkish IPO market. The study delves into the behavior of IPOs that were issued between 2010 and 2022, with a focus on how they were affected by the COVID-19 pandemic. The results may help investors and issuers understand the pandemic's effects on IPO pricing and inform their investment decisions. The study will also provide valuable insights to investors, regulators, and market participants, allowing them to make more informed decisions during market volatility and uncertainty periods. Methodology- The study involves employing two methods: the traditional ordinary least squares (OLS) and the more appropriate quantile regression (QR). The OLS method focuses on assessing the average impact of independent variables on mispricing, disregarding the unexplored latent characteristics of the mispricing distribution, especially when it deviates from a normal distribution. In contrast, the QR method allows us to investigate the diverse effects of independent variables at different levels of mispricing due to the asymmetric distribution of returns. By employing the QR approach, it can be identified the specific impacts of each variable on IPOs within particular levels of mispricing. This robust method is capable of handling potential heterogeneity in the distribution, which was observed in the sample. The QR method also facilitates the examination of various segments of the mispricing distribution, including the tail regions, enabling a comparison of the effects of explanatory factors on IPOs that range from extremely overpriced to extremely underpriced. Due to the constraints of the project, the paper has been done with a limited number of shares. Findings- The study investigates the impact of the COVID-19 pandemic on Initial Public Offering (IPO) mispricing in financial markets, examining changes in mispricing levels before, during, and after the pandemic. The results indicate a significant increase in IPO mispricing during the COVID-19 period, consistent with expectations due to factors such as heightened asymmetric information, reduced IPO volume, and decreased demand. The analysis tests the hypothesis that Covid-19 has a significant impact on IPO results. The results show that the null hypothesis (H0) cannot be rejected, supporting the notion that the pandemic has a substantial effect on IPO mispricing. This is particularly evident in equations examining 1-year returns. Furthermore, the study explores the influence of various factors on IPO mispricing, including stock market indices and dummy variables representing different years. While some index values are found to be insignificant, the Borsa Istanbul-All Index and dummy variables for 2020, 2021, and 2022 are significant in specific equations. Notably, the persistence of the impact of COVID-19 beyond the relevant period suggests a lasting effect on IPO mispricing. Examining sector-specific effects, the study finds that, based on first-day returns, all sector values, except for SEC 3 (Consumer Non-Cyclicals), are significant. However, for 1-year returns, only SEC 5 (Financials) and SEC 4 (Energy) exhibit significance, with the latter being slightly above the 10% limit. The increasing demand for energy companies in recent times is identified as a potential driver for higher levels of "IPO underpricing" in specific IPOs within these sectors. Conclusion- The study provides robust evidence of increased IPO mispricing during the COVID-19 pandemic, highlighting the persistent impact of the crisis on financial markets, as well as sector-specific nuances influencing mispricing levels. Keywords: IPOs (Initial Public Offerings), mispricing, pandemic, initial returns, long-term returns JEL Codes: C21, C23, D81, E44, G14

Evaluation of the Impact of Regional Trade Agreements on Indian Exports

This article scrutinises the repercussion of the regional trade agreements on Indian exports. The gravity model has been used for the analysis of two decades of panel data from 30 countries, spanning from 2001 to 2019. The gravity equation is estimated by the Ordinary Least Square (OLS) and Poisson pseudo-maximum likelihood (PPML) techniques using panel data regression. The PPML approach addresses the heteroskedasticity bias that is typically present in the OLS method. The study has revealed that the PPML results are more encouraging than those obtained based on the traditional OLS approach. According to the empirical findings, India’s trading partners in South Asia benefit more from its economic integration than India does. However, the measurement of country-specific degrees of globalisation has a negligible effect on fostering trade across select nations. JEL Codes: C1, F1, F2, F6

Application of the method of ordinary least squares in the calibration of temperature, pressure and mass meters

The goal of this paper is applied the Ordinary Least Squares (OLS) method as a strategy in order to reduce the uncertainty measurement associated to the relevant physical quantities. Methodology or method: This work was motivated due to the efforts made in the measurement sciences to investigate alternative methods that allow obtaining greater metrological reliability of the results, that is, reducing the uncertainty associated with the measurement. Thus, the applied methodology consisted of the development of a computational code using the MatLab tool, in which an algorithm was programmed that supports the application of the OLS method. Three of the most used physical magnitudes at an industrial level were evaluated: temperature, pressure and mass. These magnitudes were evaluated from the calibration of three measuring instruments: thermistor, manometer and digital scale. Results: The applied methodology allowed to: (i) obtain the matrix of the coefficients for polynomials of degrees 1, 2, 3 and 4 that adjust the experimental data; (ii) to draw the calibration curves for each of the obtained polynomials and (iii) to estimate the fit uncertainty (i.e.: the mean squared deviation) to specify the polynomial that best models the experimental data for a reliability level of 95.45 % (k = 2). The consolidated results confirmed a reduction in the uncertainty associated with the adjustment polynomial of 99.8% for the temperature measurement, 45.6% for the pressure measurement and 53.9% for the mass measurement. Conclusions: Finally, a discussion of the results is presented, confirming the effectiveness of the ordinary least squares method as a strategy to reduce the uncertainty associated with the calibration of measuring instruments.