Parameters Of Linear Regression Model Research Articles

Addressing Autocorrelation, Multicollinearity, and Heavy-Tail Errors in the Linear Regression Model

The most popular estimator for estimating parameters of linear regression models is the Ordinary Least Squares (OLS) Estimator. The OLS is considered the best linear unbiased estimator when certain assumptions are not violated. However, when autocorrelation, multicollinearity, and heavy-tail error are jointly present in the dataset, the OLS estimator is inefficient and imprecise. In this paper, we developed an estimator of linear regression model parameters that jointly handle multicollinearity, autocorrelation, and heavy tail errors. The new estimator, LADHLKL, was derived by combining the Hildreth-Lu (HL), the Kibria Lukman (KL), and the Least Absolute Deviation (LAD) estimators. The LADHLKL poses both the characteristics of the LAD, HL, and KL estimators which makes it resistant to both problems. We examined the properties of the proposed estimator and compared its performance with other existing estimators in terms of mean square error. An application to real-life data and simulation study revealed that the proposed estimator dominates other estimators in all the considered conditions in terms of mean square error.

The effect of the working correlation on fitting models to longitudinal data

AbstractWe present a detailed discussion of the theoretical properties of quadratic inference function estimators of the parameters in marginal linear regression models. We consider the effect of the choice of working correlation on fundamental questions including the existence of quadratic inference function estimators, their relationship with generalized estimating equations estimators, and the robustness and asymptotic relative efficiency of quadratic inference function and generalized estimating equations estimators. We show that the quadratic inference function estimators do not always exist and propose a way to handle this. We then show that they have unbounded influence functions and can be more or less asymptotically efficient than generalized estimating equations estimators. We also present empirical evidence to demonstrate these results. We conclude that the choice of working correlation can have surprisingly large effects.

Using Nonparametric Procedure to Develop an OCMT Estimator for Big Data Linear Regression Model with Application Chemical Pollution in the Tigris River

Chemical pollution is a very important issue that people suffer from and it often affects the nature of health of society and the future of the health of future generations. Consequently, it must be considered in order to discover suitable models and find descriptions to predict the performance of it in the forthcoming years. Chemical pollution data in Iraq take a great scope and manifold sources and kinds, which brands it as Big Data that need to be studied using novel statistical methods. The research object on using Proposed Nonparametric Procedure NP Method to develop an (OCMT) test procedure to estimate parameters of linear regression model with large size of data (Big Data) which comprises many indicators associated with chemical pollution and profoundly have an effect on the life of the Iraqi people. The SICA estimator were chosen to analyze data and the MSE were used to make a comparison between the two methods and we determine that NP estimator is more effective than the other estimators under Big Data circumstances.

Analysis of the role and influence of sight-singing and ear training on vocal learning skills

Abstract Sight-singing and ear training is one of the essential introductory courses for music majors, and the effectiveness of sight-singing and ear training teaching directly affects students’ growth and progress in music. In this paper, we have combined relevant contents of sight-singing, ear training, and vocal learning to construct a flipped classroom teaching model for sight-singing and ear training using the flipped classroom teaching process. Secondly, taking the students of L Conservatory of Music as the research object, two different questionnaires were designed for students and teachers, and the teaching experiment comparison method was used to test the role of sight-singing and ear-training flipped classroom on vocal music learning skills. Finally, the parameters of the multiple linear regression model were estimated using the least squares method, and the model was used to analyze the specific effects of sight-singing and ear training on vocal learning skills. It was found that after the flipped classroom teaching of sight-singing and ear-training, the ear-training scores of students in the experimental class were 90.43±9.26 points, which were 17.06 points higher than those of students in the control class, and there was no difference in the pre- and post-test scores of sight-singing and ear-training. The regression coefficient of students’ musical expression was 0.306. Every 1 percentage point increase in musical expression would enhance vocal learning skills by 0.306 percentage points. Sight-singing and ear-training can help students better master the basic skills of vocal music, cultivate their sense of rhythm, and enhance their vocal music learning skills.

A study on the integrated teaching model of core literacy in college physical education and health courses using multiple data fusion

Abstract This paper introduces an experiential teaching model for physical education and health courses. Secondly, the parameters of the multiple linear regression model were estimated and tested for significance based on the least squares method, and the integration of multiple data was carried out by using rough set simplification. Finally, an empirical analysis of the core literacy of physical education and health curriculum was conducted through three aspects: physical activity ability, health behavior and physical morality. The results showed that the p-values of physical exercise awareness, physical exercise habit, and health knowledge mastery and application were 0.015, 0.024, and 0.021, respectively, thus indicating that the experiential teaching model can effectively improve students’ core literacy in physical education and health curriculum.

Using Feasible Graphical Lasso Regression Method to Estimate the Parameters of General Linear Regression Model Under High Dimensional Data with Application

The high dimensions problem is one of the important problems that affect the data, and with company of high dimensional data in the general linear regression model, it becomes very difficult to use classical estimation methods such as maximum likelihood method and moments method because these methods lead to biased and inefficient estimates for parameters of the model. The necessity to use new methods to estimate the parameters of the general linear regression model. In this research, two methods were used, the Smooth Integration of Counting Absolute Deviation SICA method, as well as the Feasible Graphical Lasso method FGLasso. Simulation data were used, as well as real data representing the level of pollution in the Tigris River. The results compared using the Mean Square Error MSE and the results showed that the FGLasso estimator is the best

ANALISIS PENGARUH PEMBELAJARAN DARING TERHADAP PRESTASI BELAJAR SISWA DIMASA PANDEMI COVID-19 MENGGUNAKAN MODEL REGRESI BERGANDA (STUDI KASUS DI SMPN 33 BANJARMASIN)

The impact of the Covid-19 pandemic that occurred from 2019-2021 has had an impact on many sectors, one of which is the education sector. With this pandemic, learning takes place online which is possible for junior high school students is not an effective thing so that it has an impact on the final grades of student learning. This study aims to estimate the parameters of the multiple linear regression model formed in the analysis of the effect of online learning on student achievement at SMPN 33 Banjarmasin during the Covid-19 pandemic, and to explain the factors that significantly influence student achievement at SMPN 33 Banjarmasin during the pandemic. Covid-19. This study uses the independent variables of learning media and teacher teaching methods while the dependent variable uses student achievement. The population of this research is students at SMPN 33 Banjarmasin with a total sample of 120 respondents. Analysis was performed using multiple linear regression analysis. The results of the study showed that there was a significant influence between learning media and teacher teaching methods on student achievement at SMPN 33 Banjarmasin during the Covid-19 pandemic. Other results are shown based on testing the hypothesis that the variable that has the most influence is the teacher's teaching method variable. The teacher's teaching method variable (X2) has the largest relative contribution compared to the learning media variable (X1). Keywords: Online Learning, Learning Achievement, Multiple Linear Regression

KLKB1 and CLSTN2 are associated with HDL-mediated cholesterol efflux capacity in a genome-wide association study

Background and aimsHDL-mediated cholesterol efflux capacity (CEC) may protect from cardiovascular disease. Thus, we aimed to identify its genetic and non-genetic determinants. MethodsWe measured CEC to 2% apolipoprotein B-depleted serum using BODIPY-cholesterol and cAMP-stimulated J774A.1 macrophages using serum samples from 4,981 participants in the German Chronic Kidney Disease (GCKD) study. Variance of CEC explained by clinical and biochemical parameters in a multivariable linear regression model was calculated by proportional marginal variance decomposition. A genome-wide association study with 7,746,917 variants was performed based on an additive genetic model. The main model was adjusted for age, sex and principal components 1-10. Further models were selected for sensitivity analysis and to reduce residual variance by known CEC pathways. ResultsVariables that explained 1% and more of the variance of CEC were concentrations of triglycerides (12.9%), HDL-cholesterol (11.8%), LDL-cholesterol (3.0%), apolipoprotein A-IV (2.8%), PCSK9 (1.0%), and eGFR (1.0%). The KLKB1 (chr4) and APOE/C1 (chr19) loci were genome-wide significantly (p < 5x10−8) associated with CEC in our main model (p = 8.8x10−10 and p = 3.3x10−10, respectively). KLKB1 remained significantly associated after additional adjustment for either kidney parameters, HDL-cholesterol, triglycerides or apolipoprotein A-IV concentrations, while the APOE/C1 locus was not significantly associated anymore after adjustment for triglycerides. Adjustment for triglycerides also revealed an association with the CLSTN2 locus (chr3; p = 6.0x10−9). ConclusionsWe identified HDL-cholesterol and triglycerides as the main determinants of CEC. Furthermore, we newly found a significant association of CEC with the KLKB1 and the CLSTN2 locus and confirmed the association with the APOE/C1 locus, likely mediated by triglycerides.

Identification of parameters of a combined piece-linear regression model

Subject of research: the problem of estimating the parameters of a combined piecewise linear regression model.&#x0D; Purpose of research: to apply the apparatus of linear Boolean programming to identify its parameters. &#x0D; Methods and objects of research: the object of research is a set of indicators of inventive activity in the Russian Federation, the methods are regression analysis and mathematical programming.&#x0D; Main results of research: an approach to estimating the parameters of a combined piecewise linear regression model by using the method of least modules is described, which makes it possible to reduce this problem to a linear Boolean programming problem. A combined piecewise linear model of inventive activity in the Russian Federation has been constructed, which can be used in various analytical and predictive calculations. The output variable of the model is the number of patent applications, and the input variable is the volume of gross domestic product, the number of graduate students and teaching staff.

A Modified Two Parameter Estimator with Different Forms of Biasing Parameters in the Linear Regression Model

Despite its common usage in estimating the linear regression model parameters, the ordinary least squares estimator often suffers a breakdown when two or more predictor variables are strongly correlated. This study proposes an alternative estimator to the OLS and other existing ridge-type estimators to tackle the problem of correlated regressors (multicollinearity). The properties of the proposed estimator were derived, and six forms of biasing parameter k (generalized, median, mid-range, arithmetic, harmonic and geometric means) were used in the proposed estimator to compare its performance with five other existing estimators through a simulation study. The proposed estimator dominated existing estimators when the mid-range, arithmetic mean, and median versions of k were used. However, the proposed estimator did not perform well when the generalized, harmonic, and geometricmean versions were used.

Estimating the Parameters of a Simple Linear Regression Model Without Using Differential Calculus

To estimate the parameters of a simple linear regression model, students who already know calculus can minimize the total squared deviations by setting its first-order partial derivatives to zero and solving simultaneously. For students who do not know calculus, most teachers/textbooks simply state the formulas without justifying them. Students accept the formulas on faith; and for given data, they evaluate the estimates using a calculator or a statistical software. In this paper, we justify the formulas without invoking calculus. We hope the users of statistics will benefit from our proposed justifications.

The influence of age, waist circumference and smoking on the respiratory function indices on the example of employees of a chrome ore mine

Introduction. Employees engaged in mining are exposed to several harmful (hazardous) occupation factors: dust factor, industrial noise, general and local vibration, hard labour, heating or cooling microclimate. The paper aims at studying the influence of the length of employment in underground chrome ore mining coupled with biological (age, obesity) and behavioral (smoking) parameters on spirometric bronchial obstruction indices. Material and methods. The study included 134 employees of a chrome ore mine having underground experience from 1 to 33 years. The comparison group comprised of 404 people who had never worked in a mine. External respiration function was evaluated using the Spirometer SP-1 (Schiller). Statistical processing was carried out using the SPSS 22. One-factor and multi-factor linear regression models were built. Results. The construction of one-factor linear regression models of the dependence of FEV1%, FVC% considering the selected independent factors (age, waist circumference, smoking experience, underground experience) showed a statistically significant effect on the dependent variable of all factors in the model (R2 = 0.010-0.135; p = 0.026-0.0001). The variability of obstructive parameters in a multi-factor linear regression model occurs not often in terms of the studied factors (as for FEV1%, R2 = 0.163; as for FVC%, R2 = 0.107). Smoking experience and waist circumference are the most significant factors leading to the decrease in these indices. Age and underground work experience are less important, but statistically significant. Limitations. The limitation of the results of the study was that they characterize a specific set of certain working conditions and lifestyles of workers in chromium mines. Conclusion. A small part of the impact on the obstruction indices of underground work experience might be due to the use of modern engineering systems to eliminate the harmful effects of occupation factors, as well as personal respiratory protection from dust exposure.

WATER QUALITY PARAMETERS FOR POLLUTION SOURCE IDENTIFICATION IN WARWADE DAM WATER, DUTSE, JIGAWA STATE, NIGERIA: STATISTICAL AND SPATIOTEMPORAL EVALUATION

This study looked at the diminishing water quality of Warwade Dam, which is one of Dutse's largest dams. Statistical methodologies such as descriptive statistics, principal component analysis (PCA), regression analysis, correlation analysis, and cluster analysis were used to examine selected water quality characteristics. pH, conductivity, TDS, temperature, and DO captured the highest variability (98.94%) in the data set, according to the PCA scree plot. Ca and Mg were the most variable from the PCA scree plot among the metals studied (99.96 percent). The correlational analysis revealed that the characteristics differed in terms of spatio-temporal and/or limnological aspects. Variables within a cluster are relatively similar, whereas variables outside a cluster are very dissimilar, according to cluster analysis employing hierarchical dendrogram to establish linkages, relationships, and differences among parameters. The validation test was passed by 67 percent of the parameters in the general linear regression model (very strong fit at P value 0.05). The PCA scree plot of 99.39 percent variability revealed that the dam concentrations of nitrate, nitrite, and chloride were identical

Using Quadratic Form Ratio Multiple Test to Estimate Linear Regression Model Parameters in Big Data with Application: Child Labor in Iraq

The current paper proposes a new estimator for the linear regression model parameters under Big Data circumstances. From the diversity of Big Data variables comes many challenges that can be interesting to the researchers who try their best to find new and novel methods to estimate the parameters of linear regression model. Data has been collected by Central Statistical Organization IRAQ, and the child labor in Iraq has been chosen as data. Child labor is the most vital phenomena that both society and education are suffering from and it affects the future of our next generation. Two methods have been selected to estimate the parameter of linear regression model, one Covariate at a Time Multiple Testing OCMT. Moreover, the Euclidian Distance has been used as a comparison criterion among the three methods

A Gini estimator for regression with autocorrelated errors

Abstract The widely used Prais–Winsten technique for estimating parameters of linear regression model with serial correlation is sensitive to outliers. In this paper, an alternative method based on Gini mean difference (GMD) is proposed. A Monte Carlo simulation is used to show that the Gini estimator is more robust than the general least squares one when the data are contaminated by outliers.

User-assisted methodology targeted for building structure interpretable QSPR models for boosting CO2 capture with ionic liquids

Task-specific ionic liquid (IL) is an emerging class of compounds that may be environmentally friendly. Properly selected, these compounds may be green alternative to amine solutions and can replace them in post-combustion carbon dioxide (CO2) capture processes on an industrial scale. However, owing to the vast diversity of ions and their possible combinations, laboratory research is time consuming and expensive. Therefore, computational methods are preferred for assessing their potential applications. In this study, three quantitative structure–property relationship models based on six distinct descriptors were created to predict Henry’s law constant (HLC) of CO2 in 62 ILs. The statistical parameters of multiple linear regression, logistic regression, and partial least squares models were satisfactory. In all cases, the coefficients of determination (R2) exceeded 0,90, and both external and internal validation proved them to be reliable and predictive with Q2 and Rpred2 values exceeding 0,90 and 0,87, respectively. Three of the descriptors were attributed to cations, and three were attributed to anions. In contrast to many other models, the descriptors were chosen in a manner that ensured their interpretability. Each of the six descriptors was analyzed for its influence on HLC. On this basis, guidelines for designing the structure of ionic liquids with increased CO2 absorption capacity were developed.

Prediction of SPAD values for paddy leaves using smartphone-based direct contact imaging method

The Soil Plant Analysis Development (SPAD) value obtained from the SPAD meter is directly related to leaf chlorophyll content. The chlorophyll content is related to nitrogen content means the amount of fertilizer of a crop. Therefore, determining SPAD value is directly involved with crop health. Minolta SPAD meter can directly measure this value, and this is a well-established method in the research field for measuring chlorophyll content. Still, this instrument is too costly, which is beyond a farmers’ reach in the perspective of Bangladesh. The purpose of this study is to predict the SPAD value for paddy leaves using the smartphone-based direct contact imaging method to estimate the chlorophyll content of a paddy leaf. Numerous features were extracted from each image to predict the SPAD values. The features were then used as parameters in the multiple linear regression model. The models' performance was evaluated using images captured from a paddy field using a Minolta SPAD-502 Chlorophyll Meter. The multiple linear regression model's R2 and root mean square error (RMSE) values were 0.71 and 3.6512, respectively. Therefore, this result confirms that the direct digital contact imaging method has the potential to quantify the SPAD value of paddy leaves accurately. However, these results could be more accurate if the image acquisition was made from the seedling to mature stage of the paddy. In the future, an android app will be developed using this value which can directly measure the chlorophyll content of paddy leaves.

Bayesian Inference of a Non normal Multivariate Partial Linear Regression Model

This research includes the Bayesian estimation of the parameters of the multivariate partial linear regression model when the random error follows the matrix-variate generalized modified Bessel distribution and found the statistical test of the model represented by finding the Bayes factor criterion, the predictive distribution under assumption that the shape parameters are known. The prior distribution about the model parameters is represented by non-informative information, as well as the simulate on the generated data from the model by a suggested way based on different values ​​of the shape parameters, the kernel function used in the generation was a Gaussian kernel function, the bandwidth (Smoothing) parameter was according to the rule of thumb. It found that the posterior marginal probability distribution of the location matrix and the predictive probability distribution is a matrix-t distribution with different parameters, the posterior marginal probability distribution of the scale matrix is proper distribution but it does not belong to the conjugate family, Through the Bayes factor criterion, it was found that the sample that was used in the generation process was drawn from a population that does not belong to the generalized modified Bessel population.

An Improved Simple Averaging Approach for Estimating Parameters in Simple Linear Regression Model

This research is about estimating parameters in simple linear regression model. Regression model is applied for predictive in many filed. Ordinary lest square (OLS) approach and Maximum likelihood (ML) approach are employed for estimating parameter in simple linear regression model when the assumption is not violated. This research interested in simple linear regression model when the assumption is violated. Simple Averaging (SA) approach is an alternative for estimating parameters in simple linear regression model where assumptions are not successfully used. We improved SA approach based on the median which is called the improved Simple Averaging (ISA) approach. For comparing the two approaches for estimating parameter in simple linear regression model, ISA approach is compared with SA approach under Root Mean Square Error (RMSE) which reflected accuracy of prediction in simple linear regression. By using the sample, the results showed that ISA approach is better than SA approach where the value of RMSE of ISA approach is less than the value of RMSE of SA approach. Therefore, ISA approach is better than SA approach. Our study suggests ISA approach to estimating parameter on simple linear regression because ISA approach accuracy than SA approach and ISA approach simplify the estimation of parameters in the simple linear regression model. Hence, ISA approach an alternative for estimating parameters in simple linear regression model when the assumptions are not successfully used.

Modal linear regression models with additive distortion measurement errors

We consider modal linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with additive distortion measurement errors. Two calibration procedures are used to estimate parameters in the modal linear regression models, namely, conditional mean calibration and conditional mean calibration with exponential transformation. The asymptotic properties for the estimators based on two calibration procedures are established. Monte Carlo simulation experiments are conducted to examine the performance of the proposed estimators. The proposed estimators are applied to analyze a temperature forecast dataset for an illustration.