Classical Linear Regression Model Research Articles

A Treatise on Ordinary Least Squares Estimation of Parameters of Linear Model

This research article primarily focuses on the estimation of parameters of a linear regression model by the method of ordinary least squares and depicts Gauss-Mark off theorem for linear estimation which is useful to find the BLUE of a linear parametric function of the classical linear regression model. A proof of generalized Gauss-Mark off theorem for linear estimation has been presented in this memoir. Ordinary Least Squares (OLS) regression is one of the major techniques applied to analyse data and forms the basics of many other techniques, e.g. ANOVA and generalized linear models [1]. The use of this method can be extended with the use of dummy variable coding to include grouped explanatory variables [2] and data transformation models [3]. OLS regression is particularly powerful as it relatively easy to check the model assumption such as linearity, constant, variance and the effect of outliers using simple graphical methods [4]. J.T. Kilmer et.al [5] applied OLS method to evolutionary and studies of algometry.

Wavelet-based multi station disaggregation of rainfall time series in mountainous regions

Abstract Hybrid models development by combining the data-driven method of artificial neural network (ANN) and wavelet decomposition for disaggregation of rainfall time series is the purpose of this paper. In this study, for disaggregating the Tabriz and Sahand rain-gauges time series, according to nonlinear characteristics of observed time scales, a wavelet-artificial neural network (WANN) hybrid model was suggested. For this purpose, 17 years of daily data of four rain-gauges and monthly data of six rain-gauges from the mountainous basin of Urmia Lake were decomposed with wavelet transform and then using mutual information and correlation coefficient criteria, the sub-series were ranked and superior sub-series were used as input data of ANN model for disaggregating the monthly rainfall time series to the daily time series. Results obtained by the WANN disaggregation model were compared with the results of ANN and classic multiple linear regression (MLR) models. The efficiency of the WANN model compared with the ANN and MLR models at validation stage in the optimized case for Tabriz rain-gauge showed up to a 22 and 41.2% increase and in the optimized case for Sahand rain-gauge it showed up to a 21.1 and 40.8% increase, respectively.

Women’s Empowerment and Its Determinants in Bangladesh: Evidence from a National Survey

The potential factors associated with women‟s empowerment in household decision making as well as attitudes toward wife beating were determined in the study. The Bangladesh Demographic Health Survey (BDHS), 2014 data were used to get the determinants of women‟s empowerment. To measure the women‟s empowerment, the principal component analysis was used in the study. The ordinal logistic regression model was applied to determine the potential factors for women‟s empowerment. Results were also compared with the results obtained from classical linear regression model. The study revealed that lower difference of spousal ages and lower number of daughters were more likely to increase women‟s empowerment. Similar to other studies, early marriage and living in rural area gave the women lower empowerment but education, 1-4 family members, having at least one child, exposed to media, belonging to NGO and working outside home had greater positive influence on women‟s empowerment.
 Dhaka Univ. J. Sci. 66(2): 129-134, 2018 (July)

SPATIAL CONVERGENCE OF THE GROSS VALUE OF PRODUCTION OF FIREWOOD IN THE MESOREGIONS OF THE BRAZILIAN NORTHEAST

ABSTRACT This paper analyzed the process of convergence in the gross value of wood production in mesoregions of Northeast Brazil, in the period of 1994 and 2013. The object of study was the Gross Value of Production (GVP) of firewood per km2 of the mesoregions of the Northeast of Brazil. In the methodology the Absolute Convergence Model was applied and estimated through the classical model and spatial models. In the spatial approach we used the Spatial Autoregressive Model (SAR) and the Spatial Error Model (SEM). From the results obtained, the following conclusions were reached: The mesoregions of the Northeast of Brazil had an average fall of 3.94% a.a. of the GVP/km2 of native wood for the period 1994 to 2013. Considering the classical linear regression model, convergence was verified and also the presence of spatial dependence for GVP/km2 of firewood. In order to correct the spatial dependence, the SAR and SEM Models were adequate and according to Akaike's Information Criterion and used the rook matrix the SEM was configured the best model. This study showed the importance of the involvement of the spatial question in the models, either by the overlap of information of the GVP and in the development of public policies that positively affect the neighborhood.

Improving parameter estimation efficiency of a non linear manoeuvring model of an underwater vehicle based on model basin data

In this work, a methodology is proposed for the improvement of the parameter estimation efficiency of a non-linear manoeuvring model of a torpedo shaped unmanned underwater vehicle. For this purpose, data from different tests, were carried out with the aforementioned vehicle at the facilities of the CEHIPAR (Canal de Experiencias Hidrodinámicas de El Pardo), Madrid. In the proposed methodology, the following aspects are taken into account in order to improve the parameter estimation efficiency: selection of the sampling period, smoothing of the data acquired in the tests, considering a compromise between bias and variance of the smoothing filter to be applied, analysis of the classical linear regression model proposed in each trial from the statistical point of view for the estimation of the parameters. Improvements in efficiency are verified by graphical and statistical methods.

High-dimensional multivariate posterior consistency under global–local shrinkage priors

We consider sparse Bayesian estimation in the classical multivariate linear regression model with p regressors and q response variables. In univariate Bayesian linear regression with a single response y, shrinkage priors which can be expressed as scale mixtures of normal densities are popular for obtaining sparse estimates of the coefficients. In this paper, we extend the use of these priors to the multivariate case to estimate a p×q coefficients matrix B. We derive sufficient conditions for posterior consistency under the Bayesian multivariate linear regression framework and prove that our method achieves posterior consistency even when p>n and even when p grows at nearly exponential rate with the sample size. We derive an efficient Gibbs sampling algorithm and provide the implementation in a comprehensive R package called MBSP. Finally, we demonstrate through simulations and data analysis that our model has excellent finite sample performance.

Investigating the trend of average changes of annual temperatures in Iran

Temperature is one of the key elements of climate formation and its changes can alter the climate structure of each region. To study the trend of temperature changes in Iran, the data from the three variables of average minimum temperature, average maximum temperature and average annual temperature of 43 synoptic stations were obtained from the Iranian Meteorological Organization for a 48-year statistical period (1966–2016). Moreover, in order to detect the trend of average changes of minimum, maximum and annual temperatures, fuzzy possibilistic regression and classical linear regression models were used. The comparison of the results of the slope of the change trend obtained from the two models clearly showed that, in most cases, the fuzzy possibilistic regression shows the slope of the change trend more than the classical linear regression. The statistics of root-mean-square error also showed that the function of classical linear regression was much better than fuzzy possibilistic regression. Therefore, based on the results of classical linear regression, the maximum amount of the average change trend of maximum annual temperatures of Iran is first observed in the west and northwest, and then in the northeastern of Iran. However, the average trend of minimum annual temperatures in Iran has shown more different spatial configurations than the average of maximum annual temperatures in Iran, with the highest rates of change in the east half, especially in the northeast. Finally, based on the classical linear regression model, it was observed that in the whole study period, 1.40 °C has been added to the average of maximum annual temperatures and 1.68 °C to the average of minimum annual temperatures in Iran.

OLS and IV estimation of regression models including endogenous interaction terms

ABSTRACTWe analyze a class of linear regression models including interactions of endogenous regressors and exogenous covariates. We show how to generate instrumental variables using the nonlinear functional form of the structural equation when traditional excluded instruments are unknown. We propose to use these instruments with identification robust IV inference. We furthermore show that, whenever functional form identification is not valid, the ordinary least squares (OLS) estimator of the coefficient of the interaction term is consistent and standard OLS inference applies. Using our alternative empirical methods we confirm recent empirical findings on the nonlinear causal relation between financial development and economic growth.

Modeling daily soil temperature over diverse climate conditions in Iran—a comparison of multiple linear regression and support vector regression techniques

The knowledge of soil temperature at different depths is important for agricultural industry and for understanding climate change. The aim of this study is to evaluate the performance of a support vector regression (SVR)-based model in estimating daily soil temperature at 10, 30 and 100 cm depth at different climate conditions over Iran. The obtained results were compared to those obtained from a more classical multiple linear regression (MLR) model. The correlation sensitivity for the input combinations and periodicity effect were also investigated. Climatic data used as inputs to the models were minimum and maximum air temperature, solar radiation, relative humidity, dew point, and the atmospheric pressure (reduced to see level), collected from five synoptic stations Kerman, Ahvaz, Tabriz, Saghez, and Rasht located respectively in the hyper-arid, arid, semi-arid, Mediterranean, and hyper-humid climate conditions. According to the results, the performance of both MLR and SVR models was quite well at surface layer, i.e., 10-cm depth. However, SVR performed better than MLR in estimating soil temperature at deeper layers especially 100 cm depth. Moreover, both models performed better in humid climate condition than arid and hyper-arid areas. Further, adding a periodicity component into the modeling process considerably improved the models’ performance especially in the case of SVR.

Testing for constancy in varying coefficient models

ABSTRACTWe consider varying coefficient models, which are an extension of the classical linear regression models in the sense that the regression coefficients are replaced by functions in certain variables (for example, time), the covariates are also allowed to depend on other variables. Varying coefficient models are popular in longitudinal data and panel data studies, and have been applied in fields such as finance and health sciences. We consider longitudinal data and estimate the coefficient functions by the flexible B-spline technique. An important question in a varying coefficient model is whether an estimated coefficient function is statistically different from a constant (or zero). We develop testing procedures based on the estimated B-spline coefficients by making use of nice properties of a B-spline basis. Our method allows longitudinal data where repeated measurements for an individual can be correlated. We obtain the asymptotic null distribution of the test statistic. The power of the proposed testing procedures are illustrated on simulated data where we highlight the importance of including the correlation structure of the response variable and on real data.

Financial fraud and the effect of insider abuse in Nigerian banking sector

The fundamental objective of this study is to scrutinize the effect of insider abuse in the Nigerian banking sector along with its rudimental causes. The Classical Linear Regression Model (CLRM) was adopted along with secondary data extracted from the Nigeria deposit insurance corporations (NDIC) annual account report 2000-2016. The Ordinary Least Square technique signifies the prime technique of analysis as recommended by the ADF unit root test result. The ADF unit test revealed dataset stationarity at first order difference I(1). The R2 explains that 76.32% of the variation in the dependent variable is explained by the principal regressors. Total cases of fraud and amount involved were established to have a positive link with the total expected loss while, staff involvement, and total expected loss established negative and non-significant link. The study established that fraud in relation to insider abuse is not peculiarly Nigerian. The results bare that insider abuse are breed where there is weak and faulty internal control, lack of job security and reward for excellence. Recommendations are that financial institutions must review their internal control system, along with staff salary, the quality of staffs recruited and the audit system of the bank

Automated General-to-Specific (GETS) Regression Modeling and Indicator Saturation for Outliers and Structural Breaks

This paper provides an overview of the R package gets, which contains facilities for automated general-to-specific (GETS) modeling of the mean and variance of a regression, and indicator saturation (IS) methods for the detection and modeling of outliers and structural breaks. The mean can be specified as an autoregressive model with covariates (an model), and the variance can be specified as an autoregressive log-variance model with covariates (a model). The covariates in the two specifications need not be the same, and the classical linear regression model is obtained as a special case when there is no dynamics, and when there are no covariates in the variance equation. The four main functions of the package are arx, getsm, getsv and isat. The first function estimates an AR-X model with log-ARCH-X errors. The second function undertakes GETS modeling of the mean specification of an 'arx' object. The third function undertakes GETS modeling of the log-variance specification of an 'arx' object. The fourth function undertakes GETS modeling of an indicator-saturated mean specification allowing for the detection of outliers and structural breaks. The usage of two convenience functions for export of results to EViews and Stata are illustrated, and LATEX code of the estimation output can readily be generated.

Mass appraisal of farmland using classical econometrics and spatial modeling

Mass appraisals of properties traditionally use classical linear regression models (CLRMs); however, there has been the need to model the data spatially. Such modeling of the geographic effects has been used mainly in appraisals of urban areas, but the values of the properties in rural areas are also affected by the geographic location. This paper aims to use spatial regression econometric models in a sample of rural properties to elaborate the plan of values for an area of the North Fluminense Region – RJ, Brazil. The proposed methodology is to investigate and model the effects caused by the spatial autocorrelation on the CLRMs, evaluate their performance comparing them with the spatial models and produce the plan of values through ordinary kriging. The utilized sample consisted of 113 observations and 25 samples of verification. The performance of the obtained surfaces of values was evaluated through the Root Mean Squared Error (RMSE). The results showed that the spatial autocorrelation can have its effects controlled by Spatial Regression Models, because the Spatial Error Model (CAR) allowed to model the spatial dependence present in the residuals. Using the metrics of Akaike information criterion (AIC), R2 and likelihood function (LIK), the CAR model showed better fit in comparison to the CLRM. The results showed that the surface generated by the CAR model showed the best performance with the lowest RMSE. The combination of the methodologies of classical and spatial regressions and the use of geostatistical techniques were adequate to elaborate and obtain the plan of values for rural areas, to be used for various purposes, such as taxation, financing, expropriations, indemnities (in case of creation of conservation units or even in environmental disasters), among others.

Testing the heteroscedastic error structure in quantile varying coefficient models

In mean regression the characteristic of interest is the conditional mean of the response given the covariates. In quantile regression the aim is to estimate any quantile of the conditional distribution function. For given covariates, the conditional quantile function fully characterizes the entire conditional distribution function, in contrast to the mean which is just one of its characteristic quantities. Regression quantiles substantially out-perform the least-squares estimator for a wide class of non-Gaussian error distributions. In this article we consider quantile varying coefficient models (VCMs) that are an extension of classical quantile linear regression models, in which one allows the coefficients to depend on other variables. We consider VCMs with various structures for the variance of the errors (the variability function) in order to allow for heteroscedasticity. For longitudinal data, the time (T) dependent coefficient functions in the signal and the variability functions are estimated with P-splines (Penalized B-splines). Consistency of the proposed estimators is proved. Further, likelihood-ratio-type tests are considered for comparing the variability functions. The performance of the testing procedure is illustrated on simulated and real data. The Canadian Journal of Statistics xx: 1–19; 2017 © 2017 Statistical Society of Canada

Income smoothing: a study of the health sector’s credit unions

Purpose – The aim of this study was to verify whether the credit unions affiliated to Brazilian Confederation of Central Cooperatives (UNICRED) manage their accounting results, in order to reduce the variability of the institution’s returns and transmit a sense of solidity to its members. Design/methodology/approach – The method adopted was the Classic Linear Regression Model with Panel Data, estimated by Feasible Generalized Least Squares for fixed effects and corrections for heteroscedasticity. The sample was made up of 113 credit unions affiliated to UNICRED systems, over the 2001-2011 period, and data was made available by Central Bank of Brazil. Findings – The analysis, carried out through non-discretionary results on credit operations in order to explain the changes in net expenses of provision on credit operations, indicated there was smoothing of results. Thus, we can infer that the credit unions affiliated to UNICRED make use of earnings management in the income smoothing modality. Originality/value – This study contributes to the issue of Accounting Results Management, and corroborates that there are indications that, in the occurrence of higher non-discretionary results, credit unions tend to maximize provisions. Similarly, in the occurrence of lower non-discretionary results, they tend to minimize provisions, making evident the search for smaller variability in results, thus signaling mitigation of risks.

Linear Model Selection When Covariates Contain Errors

ABSTRACTPrediction precision is arguably the most relevant criterion of a model in practice and is often a sought after property. A common difficulty with covariates measured with errors is the impossibility of performing prediction evaluation on the data even if a model is completely given without any unknown parameters. We bypass this inherent difficulty by using special properties on moment relations in linear regression models with measurement errors. The end product is a model selection procedure that achieves the same optimality properties that are achieved in classical linear regression models without covariate measurement error. Asymptotically, the procedure selects the model with the minimum prediction error in general, and selects the smallest correct model if the regression relation is indeed linear. Our model selection procedure is useful in prediction when future covariates without measurement error become available, for example, due to improved technology or better management and design of data collection procedures. Supplementary materials for this article are available online.

Evaluation of the spatial pattern of surface soil water content of a karst hillslope in Southwest China using a state-space approach

ABSTRACTThis study aims to evaluate the effects of soil physicochemical properties and environmental factors on the spatial patterns of surface soil water content (SWC) based on the state-space approach and linear regression analysis. For this purpose, based on a grid sampling scheme (10 m × 10 m) applied to a 90 m × 120 m plot located on a karst hillslope of Southwest China, the SWC at 0–16 cm depth was measured 3 times across 130 sampling points, and soil texture, bulk density (BD), saturated hydraulic conductivity (Ks), organic carbon (SOC), and rock fragment content as well as site elevation (SE) were also measured at these locations. Results showed that the distribution pattern of SWC could be more successfully predicted by the first-order state-space models (R2 = 67.5–99.9% and RMSE = 0.01–0.14) than the classic linear regression models (R2 = 10.8–79.3% and RMSE = 0.11–0.24). The input combination containing silt content (Silt), Ks, and SOC produced the best state-space model, explaining 99.9% of the variation in SWC. And Silt was identified as the first-order controlling factor that explained 98.7% of the variation. In contrast, the best linear regression model using all of the variables only explained 79.3% of variation.

Analysis of Foreign Direct Investment, Agricultural Sector and Economic Growth in Tanzania

This paper analyzes the effect of foreign direct investment (FDI) on agricultural sector in Tanzania. The paper also examines the declining contribution of agriculture to real GDP growth despite the fact that the sector employs more than 70 percent of the total labour force. Annual time series data spanning from 1990 to 2015 are used to test the significance of the relationship between FDI inflow and agriculture value added-to-GDP ratio on one hand and FDI inflows and economic growth on the other hand. Also, the relationship between agriculture value added and economic growth rate is empirically examined. Variables such as gross fixed capital formation, inflation rate, trade liberalization, real exchange rate and population are considered as control variables. For the purpose of inference, the paper employs classical linear regression model. Ordinary least squares methods are used for estimation. The diagnostic tests including RESET regression errors specification test, Breusch-Godfrey serial correlation LM test, Jacque-Bera-normality test and white heteroskedasticity test reveal that the models have no signs of misspecification and that, the residuals are serially uncorrelated, normally distributed and homoskedastic. Interestingly, empirical results suggest that there is no significant effect of FDI inflows on agriculture value added-to-GDP ratio in Tanzania despite the fact that FDI inflows in economy have been outstanding particularly in past two decades. Unsurprisingly, the results show that FDI inflows-to-GDP ratio and real GDP growth rate are positively correlated. Notwithstanding, agriculture sector, which constitutes the largest proportion of the total labour force, contributes, on average, less than 30 percent, to total GDP. This suggests that the sector is inefficient and therefore, effort towards attracting more FDI aiming at improving productivity in agriculture sector, which in turn may reduce poverty, is much needed.

Shape testing in varying coefficient models

We consider varying coefficient models which are an extension of the classical linear regression models in the sense that the regression coefficients are replaced by functions in certain variables (often time). Varying coefficient models have been popular in longitudinal data and panel data studies, and have been applied in fields, such as finance and health sciences. We estimate the coefficient functions by splines. An important question in a varying coefficient model is whether a coefficient function is monotone or convex. We develop consistent testing procedures for monotonicity and convexity. Moreover, we provide procedures to test simultaneously the shapes of certain coefficient functions in a varying coefficient model. The tests use constrained and unconstrained regression splines. The performances of the proposed tests are illustrated on simulated data. We also give a real data application.

Daily soil temperature modeling using ‘panel-data’ concept

ABSTRACTThe purpose of this research was to predict soil temperature profile using ‘panel-data’ models. Panel-data analysis endows regression analysis with both spatial and temporal dimensions. The spatial dimension pertains to a set of cross-sectional units of observation. The temporal dimension pertains to periodic observations of a set of variables characterizing these cross-sectional units over a particular time-span. This study was conducted in Khorasan-Razavi Province, Iran. Daily mean soil temperatures for 9 years (2001–2009), in 6 different depths (5, 10, 20, 30, 50 and 100 cm) under bare soil surface at 10 meteorological stations were used. The data were divided into two sub-sets for training (parameter training) over the period of 2001–2008, and validation over the period of the year 2009. The panel-data models were developed using the average air temperature and rainfall of the day before ( and , respectively) and the average air temperature of the past 7 days (Tw) as inputs in order to predict the average soil temperature of the next day. The results showed that the two-way fixed effects models were superior. The performance indicators (R2 = 0.94 to 0.99, RMSE = 0.46 to 1.29 and MBE = −0.83 and 0.74) revealed the effectiveness of this model. In addition, these results were compared with the results of classic linear regression models using t-test, which showed the superiority of the panel-data models.