Ordinary Least-squares Method Research Articles

Estimasi Parameter Model Regresi Linier Berganda dengan Pendekatan Bayes Menggunakan Prior Pseudo

The parameter estimation of a regression model can use the Ordinary Least Square (OLS) method which must fulfill the assumption of BLUE. Besides OLS, there is another method that can be used to estimate the regression parameters, namely the Bayes method. Parameter estimates using the OLS method and the Bayes method have been widely used in the field of development. One of them is on economic development, namely the Human Development Index (HDI). The purpose of this study is to know multiple linear regression models and interpretations that state the relationship between per capita expenditure, average length of school, life expectancy, and school length for the Human Development Index (HDI) with the Bayes approach using pseudo priors.

Indicadores financieros y rentabilidad en bancos grandes y medianos ecuatorianos, periodo: 2016-2019

Este estudio examina el impacto de los indicadores financieros en la rentabilidad de los bancos privados ecuatorianos, entregando una metodología útil para la identificación de los factores internos relevantes que influyen en el rendimiento de la entidad y permiten así, que la toma de decisiones del corto y largo plazo sea más eficiente. La investigación realizada utilizó un modelo de regresión lineal múltiple basado en mínimos cuadrados ordinarios, analizando indicadores de liquidez, morosidad, calidad de activos, y apalancamiento como variables independientes, mientras que el rendimiento sobre activos (ROA) y el rendimiento sobre patrimonio (ROE) constituyeron las variables dependientes. El estudio utilizó 192 observaciones provenientes de las entidades bancarias: Banco de Guayaquil, Produbanco, Banco Internacional, y Banco Bolivariano durante el periodo 2016-2019. Los resultados de este estudio demuestran (1) una relación negativa significativa entre los indicadores de liquidez y morosidad con el rendimiento y (2) una relación positiva significativa entre la calidad de activos y apalancamiento con el ROA y ROE. Con estos resultados, se concluye que las variables independientes son relevantes en el rendimiento bancario, por lo que se las debe monitorear continuamente para su control efectivo. Este manuscrito, complementa a la literatura financiera al introducir un análisis estadístico del periodo 2016-2019, entregando una investigación previa a la ocurrencia de la pandemia Covid19, de manera que, se recomienda que estudios futuros realicen un análisis posterior a la emergencia sanitaria y se comparen dichos resultados para determinar los efectos en la rentabilidad de los bancos provocados por la pandemia.

Chronic Kidney Disease Progression and Transition Probabilities in a Large Preventive Cohort in Colombia.

Background Variability in chronic kidney disease (CKD) progression is a well-known phenomenon that underlines the importance of characterizing the said outcome in specific populations. Our objectives were to evaluate changes in the estimated glomerular filtration rate (eGFR) over time and determine the frequency of dialysis admission and factors associated with this outcome, to estimate the rate of program's loss-to-follow-up and the probability of transition between CKD stages over time. Methods The study type was an observational analytic retrospective cohort in patients treated in a CKD prevention program in Bogota, Colombia, between January 1, 2009, and December 31, 2013, with follow-up until December 31, 2018. Adult participants of 18 years of age or older with diagnosed CKD stages G3 or G4 were enrolled into a prevention program. For each patient, the rate of progression of CKD in ml/min/1.73 m2/year was estimated using the ordinary least-squares method. Dialysis initiation and program's loss-to-follow-up rates were calculated. Heat maps were used to present probabilities of transitioning between various CKD stages over time. Survival model with competing risks was used to evaluate factors associated with dialysis initiation. Results A total of 2752 patients met inclusion criteria and contributed with 14133 patient-years of follow-up and 200 dialysis initiation events, which represents a rate of 1.4 events per 100 patient-years (95% CI 1.2 to 1.6). The median change of the eGFR for the entire cohort was −0.47 ml/min/1.73 m2 per year, and in the diabetic population, it was −1.55 ml/min/1.73 m2 per year. The program's loss-to-follow-up rate was 2.6 events per 100 patient-years (95% CI 2.3 to 2.9). Probabilities of CKD stage transitions are presented in heat maps. Female sex, older age, baseline eGFR, and serum albumin were associated with lower risk of dialysis initiation while CKD etiology diabetes, cardiovascular disease history, systolic blood pressure, blood urea nitrogen, and LDL cholesterol were associated with a higher likelihood of dialysis initiation. Conclusions A CKD secondary prevention program's key indicator is reported here, such as dialysis initiation, progression rate, and program drop-out; CKD progression appears to be correlated with diabetic status and timing of referral into the preventive program.

The Impact of Socioeconomic Factors on Cancer Survival Rate

Background: Socioeconomic status, as a major determinant of health, has a considerable impact on the cancer survival rate. The present study aimed to investigate the impact of socioeconomic factors on the 5-year survival rate for the most common cancer types in 56 countries. Methods: In this ecological study, 5-year survival data for gastric cancer, colon cancer, lung cancer, breast cancer, cervical cancer, ovarian cancer, prostate cancer, and leukemia during the period of 2005-2009 and socioeconomic factors including gross domestic product (GDP), life expectancy, literacy rate, urbanization and healthcare expenditure were extracted from the CONCORD-2 study and the World Bank database, respectively. multivariate regression analysis was used to estimate the model with the ordinary least-squares (OLS) method using Stata 14 software. Results: The GDP coefficient for breast cancer, cervical cancer, and leukemia was positive and significant. No correlation was identified between gastric, colon, lung, ovarian, and prostate cancer and GDP. Gastric, colon, breast, and prostate cancers had a positive and significant correlation with life expectancy. In contrast, no significant correlation was found between lung cancer, cervical cancer, ovarian cancer, leukemia and life expectancy. There was no correlation between cancer survival rate and literacy rate, or urbanization. There was only a positive correlation between prostate cancer and healthcare expenditure. Furthermore, there was no statistically significant relationship between gastric and ovarian cancers and socioeconomic variables. Finally, GDP and life expectancy had the most significant impact on cancer survival rates. Conclusion: Different countries can play a key role in increasing cancer survival rates by implementing policies to improve economic and social factors.

Predicting the rental value of houses in household surveys in Tanzania, Uganda and Malawi: Evaluations of hedonic pricing and machine learning approaches.

Housing value is a major component of the aggregate expenditure used in the analyses of welfare status of households in the development economics literature. Therefore, an accurate estimation of housing services is important to obtain the value of housing in household surveys. Data show that a significant proportion of households in a typical Living Standard Measurement Survey (LSMS), adopted by the Word Bank and others, are self-owned. The standard approach to predict the housing value for such surveys is based on the rental cost of the house. A hedonic pricing applying an Ordinary Least Squares (OLS) method is normally used to predict rental values. The literature shows that Machine Learning (ML) methods, shown to uncover generalizable patterns based on a given data, have better predictive power over OLS applied in other valuation exercises. We examined whether or not a class of ML methods (e.g. Ridge, LASSO, Tree, Bagging, Random Forest, and Boosting) provided superior prediction of rental value of housing over OLS methods accounting for spatial autocorrelations using household level survey data from Uganda, Tanzania, and Malawi, across multiple years. Our results showed that the Machine Learning methods (Boosting, Bagging, Forest, Ridge and LASSO) are the best models in predicting house values using out-of-sample data set for all the countries and all the years. On the other hand, Tree regression underperformed relative to the various OLS models, over the same data sets. With the availability of abundant data and better computing power, ML methods provide viable alternative to predicting housing values in household surveys.

Are most proposed ridge parameter estimators skewed and do they have any effect on MSE values?

Multicollinearity is a common problem in multiple regression that occurs whenever two or more explanatory variables are highly correlated. When multicollinearity exists, the method of Ordinary Least Square (OLS) is likely to produce poor parameter estimates. Furthermore, OLS estimates of regression coefficients can be inflated making them too large. Ridge regression is one of the most popular methods used in the presence of multicollinearity as an alternative. In this study, a comparison of all ridge regression estimators encountered in the literature is conducted in terms of their distributions and Mean Square Error (MSE) values. To this end, 80 different estimators have been studied with comparisons carried out using the Monte Carlo simulations. A distribution was obtained for each ridge parameter and showed, surprisingly, that most are skewed and only a few behave like the Gauss distribution. Interestingly, few of the ridge parameters are distributed within the zero to ten range.

A MGSTAR: An Extension of The Generalized Space-Time Autoregressive Model

Up to now, Generalized Space-Time Autoregressive (GSTAR) models are focused only for univariate spatial-temporal data. This research proposes an extension of GSTAR for multivariate spatial-temporal data, known as Multivariate GSTAR or MGSTAR. Three studies were conducted in this research, i.e., theoretical, simulation, and applied studies. These studies were initially developed based on bivariate spatial-temporal data. A theoretical study was done by developing MGSTAR based on the framework of Vector Autoregressive (VAR) models. In this proposed MGSTAR model, the parameter estimation was obtained by implementing Ordinary Least Square (OLS) method. The simulation study showed that OLS method yielded unbiased estimator. Furthermore, the MGSTAR models have applied for forecasting CO and PM10 at three stations in Surabaya City. The results showed that MGSTAR model could explain well the dynamic relationship between variables and locations. However, based on Root Mean Square Error Prediction (RMSEP), the results showed that MGSTAR model yielded less accurate forecast than ARIMA model due to MGSTAR employed simpler order of Autoregressive. Further research is needed to expand the MGSTAR model with a higher order of Autoregressive, particularly to handle trend and seasonal order.

EFFECT OF ENERGY UTILIZATION AND FINANCIAL DEVELOPMENT ON ECONOMIC GROWTH IN NIGERIA

The necessity for rapid economic growth has not only been of great concern to global institutions and agencies but has continued to dominate discussions at major economic conferences at the national and international levels. There is an implicit assumption of positive correlation between economic growth, as measured by increase in national output, and the welfare of citizens, with the effect that governments seek to understand the real causes of output growth to aid formulation and implementation of policies that promote the welfare of their citizens. The depth of academic research in this area of knowledge is a further indication of its relevance to humanity. This study builds on existing body of knowledge on the subject by estimating the contributions of the financial and energy sectors to the Nigerian economy between 1981 and 2018. Using the estimation method of dynamic ordinary least squares (DOLS), the study reveals electricity consumption, inflation and financial development as positive predictors of growth while oil price and gross fixed capital are negative predictors. From the above findings, we conclude that robust financial and energy sectors are major influencers of growth and therefore suggest that adequate attention be given to development of these sectors through formulation and implementation of supportive policies. In addition, we see the necessity for a need assessment of the infrastructure needs of the real sector in order to ensure that infrastructure critical to its performance is identified and addressed through targeted investment.Keywords: Energy consumption, Financial development, Economic growth, Endogenous growth theory.JEL Classifications: C22, G21, O47, Q43DOI: https://doi.org/10.32479/ijeep.10691

Company Income Tax and Unemployment in Nigeria

This paper focused on the impact of company income tax on unemployment in Nigeria from 1980 to 2019. The data for this study were sourced from the statistical bulletin of Nigeria’s apex bank. The Augmented Dickey-Fuller (ADF) unit root test and Ordinary Least Squares (OLS) methods were used as the main analytical tools. The ADF unit test result revealed stationarity of the variables at order zero which satisfied the requirement to employ the OLS method. The OLS regression result revealed that corporate income tax has positive and significant relationship with unemployment rate in Nigeria. Prime lending rate has negative and significant relationship with unemployment rate in Nigeria. Inflation rate has negative and insignificant relationship with unemployment rate in Nigeria. The study therefore concluded that tax revenue from company income has not been efficiently and effectively used to provide infrastructural facilities and social amenities that will help the different sectors of the economy to function very well thereby reducing unemployment in the country. Based on the results, the study suggested that government should ensure that revenue from corporate income tax and other sources are efficiently and effectively used to provide infrastructural facilities and social services that will help the different sectors of the economy to function very well, in so doing unemployment will be reduced. The management, administration and implementation of corporate income tax should be done in such a way that it will not hinder investment and employment in the economy. At the same time, ensure accountability and transparency from government officials on the management of revenue derived from company income tax.

ФИНАНСОВАЯ ПОДДЕРЖКА СОЦИАЛЬНО ОРИЕНТИРОВАННЫХ НЕКОММЕРЧЕСКИХ ОРГАНИЗАЦИЙ В РЕГИОНАХ РОССИИ

Currently, socially oriented nonprofit organizations (SO NPOs) in Russia are actively engaged in the process of social services provision. The support provided to them, including the financial support provided by the regional authorities, is extremely important for SO NPOs. This article describes the reasons why the state involves NPOs in social services provision and gives them support, and the advantages and disadvantages of NPOs in services provision. We analyze the size, structure and dynamics of financial support for nonprofit organizations at the regional level and factors related to the size of support, as well as the criteria for granting subsidies (one of the types of support). The criteria were analyzed based on the regional legislation of 52 regions of Russia. The analysis of the size, structure and dynamics of financial support was conducted on the data from registers of SO NPOs that received support of 43 regions of Russia for 2016-2018. Our analysis demonstrates an increase in the total amount of support and a significant intraregional and interregional differentiation in the size of support. Using the method of ordinary least squares, we found that the average per capita value of financial support provided to the SO NPOs at the regional level is positively associated with per capita regional budget revenues, the share of education expenditures in the total amount of regional budget expenditures and the quality of life in the region.

The GSp criterion on subset selection method for regression in the presence of outliers and multicollinearity

Linear regression models a relation between a response variable with regressor variables and produce regression model. Ordinary least squares (OLS) method is often utilized to estimate parameters of linear regression model. OLS method will produce the best linear unbiased estimates when all the assumptions are met. The “best” means the estimate is unbiased and has the minimum variance. However, in real data, those assumptions are often violated, such as the multicollinearity and outliers. Multicollinearity will produce a large variance of the regression parameters, while outliers will cause a biased estimate. Jackknife ridge M-estimator is recommended to be implemented in the model when these problems are present. Jackknife ridge M-estimator is a parameter estimation method of the regression with robust property, which makes robust to outliers, and ridge method is utilized to overcome multicollinearity. Whereas the jackknife method is utilized to reduce the bias from the result of the ridge method. In multiple linear regression, regression model could possibly contain many candidates for regressor variables. Subset selection method is utilized to select some of those regressors that best predicts the response variable. The selection criterion that can be utilized on the subset selection method when outlier and multicollinearity are present is the GSp criterion. The reason for this is because the GSp criterion is based on jackknife ridge M-estimator, which is able to solve the problem of outlier and multicollinearity. Furthermore, GSp criterion is implemented to obtain the best model on predicting IQ based on several predictors. It was found that IQ could be predicted by only doing 3 personality test which is test 1, test 3 and test 5 instead of all 5 different personality test.

Pengaruh Ketimpangan Distribusi Pendapatan Terhadap Persentase Penduduk Miskin Di Provinsi Banten Tahun 2000-2012

Poverty has always been a problem in every developing country, even in developed countries. In Indonesia, the high number of poor people is influenced by various factors, including the existence of inequality in the distribution of both per capita income between one provinces to another. This study aims to analyze how many influence the Gini Index and Williamson Index to the percentage of poor people in the province of Banten in 2000 - 2012. The method of analysis in this study using multiple linear regression analysis with the method of ordinary least squares (OLS). With the help of software Eviews 4.1. The results of this study indicate that the variable distribution of per capita income inequality (Gini index) is influencing positively and it gives a significant impact on the percentage of poor people in the province of Banten, while inequality of income distribution among districts / cities Williamson index does not affect the percentage of poor people in the province of Banten in 2000 - 2012.

A driver or a placebo? The role of financial support in farmer cooperative development in China

PurposeThis paper explores the effect of financial support on farmer cooperative development in the Chinese context, aiming to evaluate the effectiveness of public inputs and draw implications for the sustainable development of cooperatives. The variance of the effect in different sectors, i.e. crop, forestry, husbandry, fishery and services, is investigated.Design/methodology/approachProvincial-level panel data from 2007 to 2017 are used for this study. A linear dynamic panel regression model is estimated using multiple estimation methods, i.e. the generalized method of moments (GMMs), fixed-effect model and ordinary least squares (OLS) are applied.FindingsThe empirical analyses indicate that the role of the government is important for the development of farmer cooperatives but limited in some specific aspects. First, the coverage of financial support is positively associated with the growth of cooperative population and membership size, but the strength of financial support, measured by the total amount of financial support divided by local agricultural gross domestic product (GDP), has no statistically significant effects on the development of cooperatives. Second, financial support does not exhibit significant influence on the revenue of cooperatives. Third, the magnitude of the effect of government support on cooperative development is heterogeneous across different sectors.Originality/valueThe research study adds to the institutional economics literature on the association between institutional environment and organization development by focusing on a particular and an important type of organization, i.e. farmer cooperatives. It is one of the attempts and a most extensive study to empirically investigate the role of financial support in the development of farmer cooperatives.

Estimation of transmission line parameters by using two least‐squares methods

This work proposes two new approaches based on the ordinary least-squares method and the total least-squares method to estimate the parameters of a balanced three-phase transmission line using voltage and current measurements from phasor measurement unit. First, a new model for the steady-state phasorial equations of a medium-length transmission line is proposed. Then, the noises acting upon each measurement on the ordinary least-squares setup are considered, and for the total least-squares setup, noise acting upon the observation matrix in order to account for model uncertainties and non-linearities is also considered. The methods are tested in simulation data of a real medium-size transmission line.s The main goal is to compare both methods and show their complexities. The results show good performances for both methods and, indeed, the total least-squares setup had better performance than other reported total least-squares estimators, which use a different phasorial set of equations and oversimplified noise modelling. It is concluded that for the ordinary least-squares, the solution is well known and its behavior is predictable. While for the total least-squares, the solution requires more sophisticated methods of matrix decomposition and its behavior is not as predictable. Therefore the implications of these new approaches, where new considerations about the modelling of the noises are made and where a new phasorial set of equations is used are significant, given that the many works in the literature make use of these common-place tools.

Sensor-Based Degradation Prediction and Prognostics for Remaining Useful Life Estimation: Validation on Experimental Data of Electric Motors

Prognostics is an emerging science of predicting the health condition of a system and/or its components, based upon current and previous system status, with the ultimate goal of accurate prediction of the Remaining Useful Life (RUL). Based on this assumption, components/systems can be monitored to track the health state during operation. Acquired data are generally processed to extract relevant features related to the degradation condition of the component/system. Often, it is beneficial to combine several of these degradation parameters through an optimization process to develop a single parameter, called prognostic parameter, which can be trended to estimate the RUL. The approach adopted in this paper consists of a prognostic procedure which involves prognostic parameter generation and General Path Model (GPM) prediction. The Genetic Algorithm (GA) and Ordinary Least Squares (OLS) optimization methods will be used to develop suitable prognostic parameters from the selected features. Both time and frequency domain analysis will be investigated. Steady-state data obtained from electric motor accelerated degradation testing is used for method validation. Ten three-phase 5HP induction were run through temperature and humidity accelerated degradation cycles on a weekly basis. Of those, five presented similar degradation pathways due to bearing failure modes. The results show that the OLS method, on average, generated the best prognostic parameter performance using a combination of time domain features. However, the best single model performance was obtained using the GA methodology. In this case, the estimated RUL nearly coincided with the true RUL with an absolute percent error averaging under 5% near the end of life.

Estimating the price of apartments in Tehran using extracted compound variables

PurposeHousing price is a barometer of a national economy. In recent years, Iran experienced high inflation in its economy, which affects everything, including housing. The purpose of this study is the estimation of the value of residential apartments of Tehran using ordinary least square (OLS) and geographically weighted regression (GWR) methods.Design/methodology/approachThis paper proposed a method for determining the compound variables and used them to estimate and evaluate the prices in the district six of Tehran city. Also, this paper compared the GWR and OLS methods with different types of factors and their influences in house price estimations.FindingsDuring the high inflation period of the study period, the age of buildings, inflation, parking, storage room and their locations are the most critical factors that affect the price of apartments in district six of Tehran. Besides, compound variables have the most influence on the prediction of the prices.Research limitations/implicationsThe exact location of the apartments in the study area were unknown. Therefore, the positions are extracted from their addresses. The uncertainty of location forced us to ignore the neighborhood terms in the hedonic method.Practical implicationsThe exact locations of the apartments in the study area were unknown. Therefore, the positions are extracted from their addresses. The uncertainty of location forced us to ignore the neighborhood terms in the hedonic method.Originality/valueThe originality of the proposed method is that it used a different approach to determine the valid variables of the apartment prices. Also, the evaluation of the method showed that the proposed variables are significantly useful.

Bayesian model predicts the aboveground biomass of Caragana microphylla in sandy lands better than OLS regression models

Abstract Aims In forest ecosystems, different types of regression models have been frequently used for the estimation of aboveground biomass, where Ordinary Least Squares (OLS) regression models are the most common prediction models. Yet, the relative performance of Bayesian and OLS models in predicting aboveground biomass of shrubs, especially multi-stem shrubs, has relatively been less studied in forests. Methods In this study, we developed the biomass prediction models for Caragana microphylla Lam. which is a widely distributed multi-stems shrub, and contributes to the decrease of wind erosion and the fixation of sand dunes in the Horqin Sand Land, one of the largest sand lands in China. We developed six types of formulations under the framework of the regression models, and then, selected the best model based on specific criteria. Consequently, we estimated the parameters of the best model with OLS and Bayesian methods with training and test data under different sample sizes with the bootstrap method. Lastly, we compared the performance of the OLS and Bayesian models in predicting the aboveground biomass of C. microphylla. Important Findings The performance of the allometric equation (power = 1) was best among six types of equations, even though all of those models were significant. The results showed that mean squared error of test data with non-informative prior Bayesian method and the informative prior Bayesian method was lower than with the OLS method. Among the tested predictors (i.e. plant height and basal diameter), we found that basal diameter was not a significant predictor either in OLS or Bayesian methods, indicating that suitable predictors and well-fitted models should be seriously considered. This study highlights that Bayesian methods, the bootstrap method and the type of allometric equation could help to improve the model accuracy in predicting shrub biomass in sandy lands.

Analisa Pengaruh Asset (NPL) dan Likuiditas (LDR) Terhadap Return Saham Perbankan Go Public di Indonesia

Abstract - This study was conducted to examine the influence of fundamental factors (NPL, and LDR) on stock returns Banks listed in the Indonesia Stock Exchange for the period 2005-2014. The sampling technique used in this research is purposive sampling with criteria as follows, 1) Listed in Indonesia Stock Exchange in 2005-2014, 2) Always report the annual financial statements during the period from 2005 to 2014, 3) is engaged in the same relative industry. Data required in this study were taken from Indonesian Capital Market Directory (ICMD), during 2005-2014 has listings for 42 companies banking and samples taken 10 Bank. Multiple regression analysis of data by the method of ordinary least squares (OLS). Hypothesis test used t-statistic and f-statistics at 5% significance level. The results showed Non perfoming loan (NPL) and loan to deposit ratio (LDR) significantly affects stock returns. The results of this study indicate that the performance factors fundamental Non perfoming loan (NPL) and loan to deposit ratio (LDR) should be considered to increase the Return Stocks, because by keeping the balance between the funds raised to be channeled into loans and for NPL small or well then will produce maximum profit. Keywords: Non perfoming Loan, Loan to Deposit Ratio and Stock Return

The Effect of Wages, Investment, Number of Industrial Units, and Number of Job Opportunities on the Level of Migration to DKI Jakarta in 2008-2019

One of the cities in Indonesia that has quite rapid economic progress is DKI Jakarta. The high minimum wage, investment, number of industrial units, and job opportunities in DKI Jakarta are factors that attract people to migrate to this city. However, in reality, the growth of in-migration to DKI Jakarta in the 2008-2019 period tends to show a decline. This study aims to determine the influence and magnitude of the effect of wages, investment, number of industries, and employment opportunities on in-migration to DKI Jakarta in 2018-2019. The analysis method used is multiple linear regression analysis and the method of least squares Ordinary Least Square (OLS). While the types and methods of research used in this research are descriptive quantitative and verification methods. The data used are data on provincial minimum wages, investment, industrial units, job opportunities, and data on incoming migration in DKI Jakarta in the 2008-2019 timeframe. The data in this study came from the Central Bureau of Statistics. The results showed that the provincial minimum wage (UMP) and investment (INV) variables partially affected the incoming oil (MM) to DKI Jakarta in 2008-2019. Meanwhile, the industrial unit variable (UIN) and the variable number of job opportunities (KKJ) partially did not affect in-migration to DKI Jakarta (MM) in 2008-2019. This research implies that in dealing with the high rate of population movement, the government needs to implement policies to overcome it such as increasing the provincial minimum wage, investment, the number of industrial units.

Robust Regression Analysis Study for Data with Outliers at Some Significance Levels

Robust regression analysis is an analysis that is used if there is an outlier in a regression model. Outliers cause data to be abnormal. The most commonly used parameter estimation method is Ordinary Least Squares (OLS). However, outliers in models cause the estimator of the least-squares in the model to be biased, so handling of outliers is required. One of the regressions used for outliers is robust regression. Robust regression method that can be used is M-Estimation. By using Tukey's Bisquare weighted function, a robust M-estimation method can estimate parameters in a model, for example in malnutrition data in East Java Province 2017 to 2012. This study aims to compare the robust method of M-estimation and OLS method on data with several different levels of significance, which is 1%, 5%, and 10%. The predictor variables used in this study were the percentage of poor society, population density, and some health facilities. R2 is used to compare the OLS method and the robust method of M-estimation. The results obtained that robust regression is the best method to handle the model if there are outliers in the data. It was supported by almost all results of the value of R^2 on each data that M-estimation has a higher value than the OLS method.