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A linear regression model and M-estimator of its regression coefficients are considered. We present a derivation of a weak consistency of the M-estimator together with a rate. Derivation is made under general conditions set on the error term, say “asymptotic stationarity” property. The results are proved by means of L2-convergence and cover the cases as the error term is ARMA, ARCH, GARCH process or it is attracted by an ARMA, ARCH, GARCH process. We do not separate random and deterministic covariates. Both cases are treated in one general setting.
properties and yarn strength relationship. Textile Research Journal, 65(9), 495–500.  Üreyen, M. E.; & Gürkan, P. (2008). Comparison of Artificial Neural Network and LinearRegression Models for Prediction of Ring Spun Yarn Properties. I. Prediction of Yarn Tensile Properties, Fibers and Polymers, 9(1), 87-91.  Üreyen, M. E.; & Gürkan, P. (2008). Comparison of Artificial Neural Network and LinearRegression Models for Prediction of Ring Spun Yarn Properties. II. Prediction of Yarn Hairiness and Unevenness. Fibers and Polymers, 9(1), 92-96.  Demiryürek, O
A simple linear regression model is one of the pillars of classic econometrics. Despite the passage of time, it continues to raise interest both from the theoretical side as well as from the application side. One of the many fundamental questions in the model concerns determining derivative characteristics and studying the properties existing in their scope, referring to the first of these aspects. The literature of the subject provides several classic solutions in that regard. In the paper, a completely new design is proposed, based on the direct application of variance and its properties, resulting from the non-correlation of certain estimators with the mean, within the scope of which some fundamental dependencies of the model characteristics are obtained in a much more compact manner. The apparatus allows for a simple and uniform demonstration of multiple dependencies and fundamental properties in the model, and it does it in an intuitive manner. The results were obtained in a classic, traditional area, where everything, as it might seem, has already been thoroughly studied and discovered.
Background and aims: To explore the most influential variables of fasting blood sugar (FBS) with three regression methods, to identify the existence chance of type 2 diabetes based on influential variables with logistic regression (LR), and to compare the three regression methods according to Mean Squared Error (MSE) value.
Material and Methods: In this cross-sectional study, 270 patients suffering from type 2 diabetes for at least 6 months and 380 healthy people were participated. The Linear regression, Ridge regression, and Least Absolute Shrinkage and Selection Operator (Lasso) regression were used to find influential variables for FBS.
Results: Among 15 variables (8 metabolic, 7 characteristic), Lasso regression selected HbA1c, Urea, age, BMI, heredity, and gender, Ridge regression selected HbA1c, heredity, gender, smoking status, and drug use, and Linear regression selected HbA1c as the most effective predictors for FBS.
Conclusion: HbA1c is the most influential predictor of FBS among 15 variables according to the result of three regression methods. Controlling the variation of HbA1c leads to a more stable FBS. Beside FBS that should be checked before breakfast, maybe HbA1c could be helpful in diagnosis of Type 2 diabetes.
This paper aims to provide rapid and precise methods to allow industrials to predict the amount of sewing thread needed to sew a garment using different lockstitches of class 300 (301, 301/301, 304, 308, 309, 310, 311, 312, and 315). To avoid unused stocks for each stitch type, a sewing consumption value was determined using a geometrical method of different lockstitch shapes. Furthermore, the relationships between overall geometrical models of the studied lockstitches of class 300 were developed. Indeed, based on the geometrical model of lockstitch type 301, all theoretical models proposed were investigated and proved to be accurate. Moreover, referring to the findings, the prediction of the sewing thread consumption relative to each investigated lockstitch was proposed as a function of the studied input parameters. To improve the established models using geometrical technique, a statistical method was conducted. In addition, based on multi-linear regression, compared geometrical and statistical results were discussed and the coefficient R2 value was determined to evaluate the accuracy of the tested methods. By comparing the estimated thread consumption with the experimental ones, we concluded that the accuracy of the models is significant (R2 ranged from 93.91% to 99.10%), which encourages industrialists to use geometrical models to predict thread consumption. Therefore, the accuracy of prediction using the geometrical method is more accurate than the statistical method regarding the range of R2 (from 92.84% to 97.87%). To classify the significance of all studied parameters, their contributions to the sewing thread consumption behavior were analyzed in the experimental design of interest. It was concluded that the most important parameters affecting thread consumption are stitch width, stitch density, and the gap between two needles. The thickness of fabric has a low contribution to the thread consumption value, whereas the effect of yarn count can be neglected.
The district heating (DH) system consists of three basic elements – a heat source, heating network and heat consumers. All of these elements have a definite role in the overall development of the DH system. The transition to 4th generation DH (4GDH) involves changes in each of those elements that interact with each other. Therefore, various related processes form the potential energy savings and reduction of CO2 emissions when introducing 4GDH as whole system in all elements. To estimate the potential outcome from such projects it requires complex engineering calculations, which is not always possible without relevant expertise. The article describes a novel simplified methodology for evaluating the potential GHG emission reduction when implementing 4GDH. Thus, it is proposed to use a simplified calculation formula from linear regression model for the calculation of CO2 reduction.
A new interpretative approach is proposed to best-estimate of gravity parameters related to simple geometrical shaped structures such as a semi-infinite vertical cylinder, an infinite horizontal cylinder, and a sphere like structures. The proposed technique is based on the multiple-linear regression oriented towards estimating the model parameters, e.g., the depth from the surface to the center of the buried structure (sphere or infinite horizontal cylinder) or the depth from the surface to the top of the buried object (semi-infinite vertical cylinder), the amplitude coefficient, and the horizontal location from residual gravity anomaly profile. The validity of the proposed approach is firstly demonstrated through testing different synthetic data set corrupted and contaminated by a white Gaussian random noise level. The theoretical synthetic obtained results obviously show that the estimated parameters values, derived by the proposed technique are close to the assumed true parameters values. This approach is applied on five real field residual gravity anomalies taken from Cuba, Sweden, Iran, USA, and Germany, where the efficacy of this new approach is consequently proven. A comparable and acceptable agreement is noticed between the results derived by this proposed approach and those obtained from the real field data information.
Rapid and precise methods (geometrical and statistical), which aim to predict the amount of sewing thread needed to sew a garment using different over-edge stitches of class 500 (501, 503, 504, 505, 512, 514, 515, and 516), have been provided. Using a geometrical method of different over-edge stitch shapes, sewing consumption value was determined to avoid the unused stocks for each stitch type. The prediction of the sewing thread consumption relative to each investigated over-edge stitch was proposed as a function of the studied input parameters, such as material thickness, stitch density, yarn diameter, and seam width (distance between the needle and the cutter and the distance between two needles). To improve the established models using a geometrical method, a statistical method based on multi-linear regression was studied. Geometrical and statistical results were discussed, and the coefficient R2 value was determined to evaluate the accuracy of the tested methods. By comparing the estimated thread consumption with the experimental ones, we concluded that the geometrical method is more accurate than the statistical method regarding the range of R2 (from 97.00 to 98.78%), which encourages industrialists to use geometrical models to predict thread consumption.
All studied parameters contributing to the sewing thread consumption behavior were investigated and analyzed in the experimental design of interest. It was concluded that the most important parameter affecting thread consumption is the stitch density. The material thickness and the seam width (B1) have a little impact on thread consumption values. However, the seam thread diameter has a neglected effect on thread consumption.