Statistical Adequacy Research Articles

Johansen’s Cointegration Analysis of Some Factors of Economic Growth and Exports of Products from the Republic of Azerbaijan to Ukraine

In the present paper, a Johansen’s cointegration analysis is carried out considering the volume of exports from Azerbaijan to Ukraine, GDP per capita of Ukraine, the openness of the economy of Ukraine and the economically active population of Azerbaijan for the period 1996-2022, also a comparative analysis of the above indicators is carried out, the characteristics of joint short-term and long-term movements are determined. In the course of research the author used the methodology of modified gravitational modeling, the econometric methodology of time series analysis, including tests for checking stationarity, the extended Dickey-Fuller test, the Granger test for the detection of causality, determining the cointegration dependence using the Johansen’s test, a Vector Error Correction Model (VECM) has been built. First, a basic modified model of gravity has been built, and the statistical adequacy of this model has been checked. A comparative analysis of two regression models was carried out after the inclusion of the trend component in one of them. The dynamic structure of regression residuals was studied and the test for heteroscedasticity and autocorrelation was carried out. It is shown that the most suitable specification for cointegration is the quadratic trend in the initial levels with a linear trend in cointegration relationships, which has led to the emergence of two cointegration vectors. As a result of the completed analysis, two cointegration relationships are obtained. The results of the impulse response functions, decomposition of dispersions and the VECM model in the form of combinations of two cointegrating vectors with the expected signs of the adjustment integers showed that the economic indicators used in the analysis for the specified period maintain cointegration in the long term with the not stable equilibrium joint movements of the factors under study.

Encapsulation of Bioactive Compounds from Germinated Mung Bean by Freeze-Drying, Release Kinetics, and Storage Stability.

This research explores the application of germinated mung bean extract, rich in GABA (Gamma-aminobutyric acid) and polyphenols, in enhancing human health. Recognizing the instability of these bioactive compounds in environmental conditions, encapsulation emerges as a pivotal technique to broaden their applications in food and pharmaceuticals. Utilizing response surface methodology and Box-Behnken design, the freeze-drying formulation for encapsulating the aqueous extract was optimized. Second-order polynomial models were developed, exhibiting statistical adequacy in predicting key variables such as encapsulation efficiency for GABA (EE-GABA) and total polyphenol content (EE-TPC), as well as encapsulation yield for GABA (EY-GABA) and total polyphenol content (EY-TPC). The established optimal formulation was validated, resulting in predicted values for EE-GABA, EE-TPC, EY-GABA, and EY-TPC. The release kinetics of encapsulated particles were investigated, highlighting the suitability of the Korsmeyer-Peppas and Higuchi models. Assessing the stability of the encapsulated powder under varying temperatures and humidities revealed degradation rates, half-life, and activation energy, with moisture equilibrium established at 4.70%, indicative of long-term stability. In conclusion, the encapsulated germinated mung bean powder demonstrates high stability, making it a promising candidate for integration into food products and functional ingredients.

Revisiting the Large n (Sample Size) Problem: How to Avert Spurious Significance Results

Although large data sets are generally viewed as advantageous for their ability to provide more precise and reliable evidence, it is often overlooked that these benefits are contingent upon certain conditions being met. The primary condition is the approximate validity (statistical adequacy) of the probabilistic assumptions comprising the statistical model Mθ(x) applied to the data. In the case of a statistically adequate Mθ(x) and a given significance level α, as n increases, the power of a test increases, and the p-value decreases due to the inherent trade-off between type I and type II error probabilities in frequentist testing. This trade-off raises concerns about the reliability of declaring ‘statistical significance’ based on conventional significance levels when n is exceptionally large. To address this issue, the author proposes that a principled approach, in the form of post-data severity (SEV) evaluation, be employed. The SEV evaluation represents a post-data error probability that converts unduly data-specific ‘accept/reject H0 results’ into evidence either supporting or contradicting inferential claims regarding the parameters of interest. This approach offers a more nuanced and robust perspective in navigating the challenges posed by the large n problem.

TESTING OF THE MATHEMATICAL MODEL OF THE WORK OF THE DISPENSER OF THE SEEDING APPARATUS OF THE SELECTION SEEDER OF SMALL SEED CULTURES

In Ukraine, the most common selection planters are "Maple" planters with electromechanical seeding devices. These planters are designed for accurate row sowing of small-seeded crops on the plots of preliminary and production competitive variety testing, as well as for conducting agrotechnical research. They are equipped with a reliable electromechanical drive and a rotary seed distributor. The analysis of the operation of the "Maple" electromechanical seeding system made it possible to identify the main directions for its improvement. It is necessary to improve the working body of the seeding device in order to ensure the accuracy of sowing small-seeded crops at the level of 95.0%. The purpose of the research is the development of a mathematical model of the operation of the dispenser of the seeding apparatus of the selection seeder of small-seeded crops and its production verification. For the operation of the seeder, a program was compiled in the Arduino IDE environment, which was based on the developed mathematical model of the operation of the dispenser of the seeder of the selection seeder of small-seeded crops. A program was compiled in the Wolfram Cloud to determine the mode parameters of the seeding machine dispenser (valve rotation angle α, the time interval when the valve is open or closed Δt) taking into account the given average effective seed diameter Dμ, the seeding rate N and the movement speed of the planter V. In the following, the given program will be used when creating a production sample of the seeding machine dispenser. The results of testing the experimental sample of the improved seeding device in production conditions show that its sowing accuracy is higher (89.3–95.1%) than that of the basic planter "Klen-4.2" (85.2–92.0%). Also, the quality of sowing is indicated by the obtained plant stand density: for the improved seeding device – 982.0–1057.5 thousand units/ha, and for the basic one – 940.9–1029.8 thousand units/ha. This is at the established rate of sowing - 1,000 thousand units/ha. The yield of winter mustard was: for the improved seeding apparatus - 0.92–1.07 t/ha, and for the basic one - 0.89–1.03 t/ha. The smallest significant difference for productivity was 0.03 t/ha, which confirms the statistical adequacy of the measurement results.

An introduction to the significance of sample size in particle analyses for nuclear forensics and radiological investigations

Particulate isotopic analysis in nuclear forensics has developed rapidly during the past two decades due to technical advances in determining the isotopic composition of individual particles. This paper introduces basic statistical concepts that can be applied by analysts to understand the importance of statistical adequacy when interpretating particle data. While these basic statistical methods provide a useful point-of-entry to particle data analysis, more sophisticated statistical and modeling approaches are needed to extract maximal information from such datasets in the future.

Conditional feature importance for mixed data

Despite the popularity of feature importance (FI) measures in interpretable machine learning, the statistical adequacy of these methods is rarely discussed. From a statistical perspective, a major distinction is between analysing a variable’s importance before and after adjusting for covariates—i.e., between marginal and conditional measures. Our work draws attention to this rarely acknowledged, yet crucial distinction and showcases its implications. We find that few methods are available for testing conditional FI and practitioners have hitherto been severely restricted in method application due to mismatched data requirements. Most real-world data exhibits complex feature dependencies and incorporates both continuous and categorical features (i.e., mixed data). Both properties are oftentimes neglected by conditional FI measures. To fill this gap, we propose to combine the conditional predictive impact (CPI) framework with sequential knockoff sampling. The CPI enables conditional FI measurement that controls for any feature dependencies by sampling valid knockoffs—hence, generating synthetic data with similar statistical properties—for the data to be analysed. Sequential knockoffs were deliberately designed to handle mixed data and thus allow us to extend the CPI approach to such datasets. We demonstrate through numerous simulations and a real-world example that our proposed workflow controls type I error, achieves high power, and is in-line with results given by other conditional FI measures, whereas marginal FI metrics can result in misleading interpretations. Our findings highlight the necessity of developing statistically adequate, specialized methods for mixed data.

Enhancing Concept Inventory Analysis by Using Indexes, Optimal Histogram Idea, and the Likert Analysis

Since the introduction of the Force Concept Inventory (FCI) in 1992, the CI tests have been widely used for measuring conceptual knowledge and for studying teaching issues in almost all disciplines and levels of study. A standard concept inventory analysis includes the design of a qualitative test, adequate realization of testing, calibration procedure, and comprehensive analysis of its findings. Usually, the CI test calibration is carried out through the Rasch sociometric technique, which is also used for calculating crucial indicators of knowledge such as item difficulties, students’ abilities, and many more. Whereas the quality of the tests’ design can be guaranteed by using certified and professional CI tests, the statistical adequacy of the testing merits critical attention before going on to the final step of the analysis. Also, the analysis of CI outcomes can be advanced by contemplating auxiliary tools and complementary techniques. In this framework, we propose to enforce the test index validity requirement for qualifying the CI outcomes as local or global. Specifically, the conclusions of CI analysis are acceptable for the whole population from which the sample has been extracted if the test's indexes comply with the validity requirements provided by the index theory. In the case when test indexes are out of validity range and re-conducting them is impractical for some objective circumstances or research specifics, we suggest injecting some new records into the existing one or mixing the data gathered from different samples until the new indexes are in the desired range. Using this methodology, we have reviewed our previous FCI tests, which were initially intended to demonstrate the impairment of learning in the physics discipline triggered by online learning during the pandemic closure. Through this renormalization procedure, we obtained a credible assessment of the understanding of mechanics and electromagnetism in high school students who followed online lectures during the pandemic closure. Also, by using indexes’ validity as an auxiliary tool, we identified that for measuring the knowledge of electromagnetism in students enrolled in branches where physics is a basic discipline, a shortened version of the BEMA test was a better instrument than the corresponding shortened EMCI test. Next, we used the optimal histogram idea borrowed from distribution fitting procedures to identify the natural levels of students’ abilities for solving a certain CI test. Another intriguing proposal presented in this work consists of combining an ad-hoc Likert scale assignment for usual errors in physics exams with the FCI designation of the basic commonsense confusion in mechanics for identifying their pairing features in common exams. We believe that the methods proposed herein can improve CI analysis in more general senses. Doi: 10.28991/HEF-2023-04-01-08 Full Text: PDF

Determinants of the investments: a case study of Côte d Ivoire

Purpose- Based on the importance of investments in supporting the economic growth in the country, the main objective of this study is to investigate the determinants of the investment in Cote d’Ivoire over the period 1980-2020. In order to achieve the objective, this study examines the interactive effect of external debt, communication infrastructures, imports and inflation on the investments in Cote d’Ivoire. Methodology- Annual time series data over the period 1980-2020 were employed in this study. The data are obtained from the World Bank. The ADF unit root test, Johansen cointegration test, OLS model, Granger causality test, and CUSUM test were applied to analyze the data. Ordinary Least Squares (OLS) model has been used in this study to estimate the coefficient of the variables, and it has been subjected to a number of statistical diagnostic tests, namely, the normality, serial correlation, and heteroscedasticity tests to ascertain its statistical adequacy. Findings- The ADF unit root test results indicated that all variables in the model are not stationary at the level but became stationary after first differencing. The Cointegration test pointed to a significant long-run relationship among the variables. Besides, the results of OLS model showed that investment is positively and significantly related with communication infrastructures, importing and inflation, but it is related negatively and insignificantly with external debt. Imports have the biggest effect on the investment. The Granger causality test shows that there are no short-run causality relationships between the variables. However, there are bidirectional long-run causality relationships between investment, external debt and importing, and unidirectional long-run causality relationships running from communication infrastructures and inflation to investment. Lastly, CUSUM test indicated that there are no structural changes in the model. Conclusion- The study therefore recommends that the government should use external debt more efficiently, reduce corruption, improve the infrastructure and create an attractive investment climate, as well as reducing most tariff and nontariff barriers, which will support the investment in the country.

Model Validation and DSGE Modeling

The primary objective of this paper is to revisit DSGE models with a view to bringing out their key weaknesses, including statistical misspecification, non-identification of deep parameters, substantive inadequacy, weak forecasting performance, and potentially misleading policy analysis. It is argued that most of these weaknesses stem from failing to distinguish between statistical and substantive adequacy and secure the former before assessing the latter. The paper untangles the statistical from the substantive premises of inference to delineate the above-mentioned issues and propose solutions. The discussion revolves around a typical DSGE model using US quarterly data. It is shown that this model is statistically misspecified, and when respecified to arrive at a statistically adequate model gives rise to the Student’s t VAR model. This statistical model is shown to (i) provide a sound basis for testing the DSGE overidentifying restrictions as well as probing the identifiability of the deep parameters, (ii) suggest ways to meliorate its substantive inadequacy, and (iii) give rise to reliable forecasts and policy simulations.

Evaluation of Control Priorities Based on a Matrix of Paired Comparisons

The article contains a description of the model and approach for determining the weights of controls (other objects) based on a matrix of pairwise comparisons. The initial data in the matrix of paired comparisons implicitly specify interval estimates for comparison of controls. Interval estimates can be constructed relatively easily using Harrington's fuzzy metric scale. A heuristic method for determining the priorities of controls is proposed, which seeks to obtain weights (priorities) of controls that deviate minimally from the boundary values of the weight intervals.The latter are easy to find using the system of relations, on the basis of which the matrix of pairwise comparisons of controls is built. To assess the statistical adequacy of the found control priorities, the determination coefficient is used, the value of which at the level of 80 % and above is considered practically acceptable for applications. The critical value of the coefficient of determination can be determined, for example, using the Fisher criterion. If the conditions of statistical adequacy are not met, the initial data in the matrix of paired comparisons should be revised. An example is provided to illustrate the method described in the article. The main advantages of the approach described in the article are the flexibility of the choice of interval estimates for pairwise comparison of controls, the relative simplicity of computational calculations, and the ability to control the calculation results using statistical criteria. The described method develops the authors' approach to the adoption of anti-crisis management by adapting management priorities to the conditions of the production system and its environment.

Milling of Inconel 718: an experimental and integrated modeling approach for surface roughness

Inconel 718, a hard-to-cut superalloy is reputed for having poor machining performance due to its low thermal conductivity. Consequently, the surface quality of the machined parts suffers. The surface roughness value must fall within the stringent limits to ensure the functional performance of the components used in aerospace and bioimplant applications. One doable way to enhance its machinability is the adequate dissipation of heat from the machining zone through efficient and ecofriendly cooling environment. With this perspective, an experimental and integrated green-response surface machining-based-evolutionary optimization (G-RSM-EO) approach is presented during this investigation. The results are compared with two base-line techniques: the traditional flooded approach with Hocut WS 8065 mineral oil, and the dry green approach. A Box-Behnken response surface methodology (RSM) is employed to design the milling tests considering three control parameters, i.e., cutting speed (vs), feed/flute (fz), and axial depth of cut (ap). These control parameters are used in the various experiments conducted during this research work. The parametric analysis is then accomplished through surface plots, and the analysis of variance (ANOVA) is presented to assess the effects of these control parameters. Afterwards, a multiple regression model is developed to identify the parametric relevance of vs, fz, and ap, with surface roughness (SR) as the response attribute. A residual analysis is performed to validate the statistical adequacy of the predicted model. Lastly, the surface roughness regression model is considered as the objective function of the particle swarm optimization (PSO) model to minimize the surface roughness of the machined parts. The optimized SR results are compared to the widely employed genetic algorithm (GA) and RSM-based desirability function approach (DF). The confirmatory machining tests proved that the integrated optimization approach with PSO being an evolutionary technique is more effective compared to GA and DF with respect to accuracy (0.05% error), adequacy, and processing time (3.19 min). Furthermore, the study reveals that the Mecagreen 450 biodegradable oil-enriched flooded strategy has significantly improved the milling of Inconel 718 in terms of eco-sustainability and productivity, i.e., 42.9% cost reduction in cutting fluid consumption and 73.5% improvement in surface quality compared to the traditional flooded approach and the dry green approach. Moreover, the G-RSM-EO approach presents a sustainable alternative by achieving a Ra of 0.3942 μm that is finer than a post-finishing operation used to produce close tolerance reliable components for aerospace industry.

Uticaj berzanskog prometa na BDP u Republici Srbiji

Stock exchange turnover growth increases the capital performance of a country. This paper examines the stock exchange turnover trends after the global financial crisis while considering the novel COVID-19 global crisis in the Republic of Serbia. Moreover, this paper estimates the correlation between the stock exchange turnover and GDP indicators. Since the COVID-19 crises is recent, the available official data for the last two years are not complete yet. Therefore, the aim of this research is to measure the impact of stock exchange turnover on economic growth in the Republic of Serbia for the period 2006-2020, with respective predictions. The methodological approach consists of the application of linear regression model, with previous statistical adequacy tests. The final results of this research indicate that the growth of stock exchange turnover has positive and statistically significant impact on GDP in this country. However, the prediction analysis indicates that the stock exchange turnover may have a negative impact on GDP in the next years, which is why there are several suggestions for decision makers and further research.

Statistical modeling and inference in the era of Data Science and Graphical Causal modeling

AbstractThe paper discusses four paradigm shifts in statistics since the 1920s with a view to compare their similarities and differences, and evaluate their effectiveness in giving rise to ‘learning from data' about phenomena of interest. The first is Fisher's 1922 recasting of Karl Pearson's descriptive statistics into a model‐based [] statistical induction that dominates current statistics (frequentist and Bayesian). A crucial departure was Fisher's replacing the curve‐fitting perspective guided by goodness‐of‐fit measures with a model‐based perspective guided by the statistical adequacy: the validity of the probabilistic assumptions comprising . Statistical adequacy is pivotal in securing trustworthy evidence since it underwrites the reliability of inference. The second is the nonparametric turn in the 1970s aiming to broaden by replacing its distribution assumption with weaker mathematical conditions relating to the unknown density function underlying . The third is a two‐pronged development initiated in Artificial Intelligence (AI) in the 1990s that gave rise to Data Science (DS) and Graphical Causal (GC) modeling. The primary objective of the paper is to compare and evaluate the other competing approaches with a refined/enhanced version of Fisher's model‐based approach in terms of their effectiveness in giving rise to genuine “learning from data;” excellent goodness‐of‐fit/prediction is neither necessary nor sufficient for statistical adequacy, or so it is argued.

Examination and Optimization of Machining Parameters in Electrical Discharge Machining of UNS T30407 Steel

Electrical discharge machining (EDM) is a non-conventional process utilized for machining electrically conductive materials which cannot be machined by conventional processes. This paper is focused on modeling and optimization in electrical discharge machining (EDM) of UNS T30407 steel. The variables such as pulse on time (Ton), pulse off time (Toff), and current will influence the material removal rate (MRR) and surface roughness (Ra) which were taken as response variables. Experimental data were collected as per the central composite design (CCD) matrix of response surface methodology (RSM) approach and mathematical models have been developed for both the response variables. The analysis of variance (ANOVA) was employed to determine the significant machining parameters and optimize the input parameters for both the responses (MRR and Ra). The statistical adequacy of the models is tested with the help of ANOVA. The optimum parametric combination for maximum MRR and smaller Ra (highest surface finish) was found. The surface characteristics of the machined surface were investigated by a scanning electron microscope (SEM).

Performance prediction and optimization of a photovoltaic thermal system integrated with phase change material using response surface method

Abstract In this study, a predictive model is developed based on the response surface method (RSM), to show the relationship between the operating factors (independent parameters) and some important response factors (dependent parameters) of a photovoltaic thermal system integrated with phase change material (PVT/PCM). The considered phase change material is the Rubitherm (RT) series of organic phase change materials. Moreover, both single and multi-objective optimization are conducted using RSM for different optimization objectives to recommend the optimal values of control factors for different operating conditions. The selected operating factors include PCM layer thickness, solar radiation, melting temperature of PCM and ambient temperature. Five response factors, including electrical power, thermal power, electrical exergy, thermal exergy and entropy generation are considered. To evaluate the model statistical adequacy, diagnostic analysis is performed for each response to indicate that the predictive model has a reasonable accuracy. The analysis of variance (ANOVA) test and perturbation analysis are also applied to evaluate the suitability and statistical importance of the recommended model and they show that the sensitivity of solar radiation on energy and exergy outputs is higher than that of other operating factors. According to the results, to maximize the electrical power, thermal power, electrical exergy, thermal exergy, and to minimize the entropy generation, simultaneously, it is recommended to select the PCM layer thickness of 1.5 cm, solar radiation of 901 W/m2, melting temperature of 25 °C, and the ambient temperature of 40 °C, based on the proposed method in this study.

Predictive modeling of material properties for aircraft control cables

PurposeThis study aims to investigate the relationship between material properties and alloying elements of carbon steels through predictive modeling. Aircraft control cables are usually made of steel materials and subjected to deformation because of the motion of control surfaces such as aileron, rudder, elevator and trailing edge flaps. Investigation of the relationship between material properties and alloying elements would therefore be explored.Design/methodology/approachThis study is focused on the modeling of mechanical properties of carbon steels concerning the content of alloying elements by using response surface methodology with false discovery rate (FDR) correction approach. SAS Institute JMP data analysis software was used to develop response and argument relationships in various carbon steels without including thermomechanical treatment effect. Mechanical properties were considered as tensile strength, yield strength, ductility, and Brinell hardness. Carbon (0.28 Wt.%-0.46 Wt.%) and manganese (0.7 Wt.%-0.9 Wt.%) proportions were gathered fromASM Handbook. Linear regression models were tested for the statistical adequacy by using analysis of variance and statistical significance analysis. A posterior probability, which refers to Benjamini–Hochberg FDR (BH-FDR), was embedded as multiple testing corrections of thet-testp-values.FindingsPredictive modeling of the material properties for aircraft control cables was successfully achieved by using the response surface method with BH-FDR significance level of 0.05.Originality/valueThe effect of statistically developed graphical interactions of alloying elements on the common mechanical properties of such steels would provide prompt comparison to material suppliers and part manufacturers except those subjected to thermomechanical treatment applications.

Experimental Analysis of the Function of a Window with a Phase Change Heat Accumulator.

The article presents the results of long-term field tests and their mathematical analysis regarding the impacts of innovative phase change materials on the energy efficiency of composite windows with various glazing parameters. Research was conducted on six glazing combinations throughout the heating season in a temperate climate in Rzeszów (Poland). The empirical results obtained during the spring months showed an improvement in the monthly heat balance for windows with phase change materials compared to the reference window by as much as 34.09%. In addition, the empirical results allowed the development and verification of a mathematical model describing the transport and distribution of heat within a window with a phase change heat accumulator. The model was made using equations of non-stationary heat flow and an explicit finite difference method using calorimetric thermograms describing the phase change eutectic mixture used in the research. Carrying out the Snedecor–Fischer test proved the statistical adequacy of the developed model in 4 out of 6 tested combinations of glazing units. Good matching of the empirical and theoretical quantities was also confirmed using the quasi-Newton method. The article is a solution to the problem of the effective use of solar energy within transparent building partitions, while presenting a useful mathematical tool that determines potential thermal gains in various climatic conditions.

Yule–Simpson’s paradox: the probabilistic versus the empirical conundrum

The current literature views Simpson’s paradox as a probabilistic conundrum by taking the premises (probabilities/parameters/ frequencies) as known. In such a context, it is shown that the paradox arises within a very small subset of the relevant parameter space, rendering the paradox unlikely to occur in real data. The problem, however, is that the probabilistic perspective, ignores certain crucial empirical (data, statistical) issues raised by the original Pearson and Yule papers on ‘spurious’ association reversals. Placing the paradox in a broader empirical framework that begins with the raw data $${\mathbf {z}}_{0}$$ and an appropriately selected statistical model $${\mathcal {M}}_{{\varvec{{\theta }}}}({\mathbf {x}})$$ , the discussion elucidates the original Yule–Pearson conundrum by formalizing its notion of ‘spurious or fictitious associations’ into ‘statistically untrustworthy associations’ stemming from a misspecified $${\mathcal {M}}_{{\varvec{{\theta }}}}( {\mathbf {x}})$$ ; invalid probabilistic assumptions imposed on $${\mathbf {z}}_{0}$$ . It is shown that several empirical examples used to illustrate Simpson’s paradox in the current literature constitute examples of the Yule–Pearson untrustworthy association reversals. The empirical perspective is used to revisit the causal explanation of the paradox and make a case that several widely accepted causal claims are questionable on statistical adequacy grounds. It is also used to propose a procedure to detect and account for the ‘third entity’ in the paradox, as well as (reliably) select among different potential causal explanations, such as collider, mediator or confounder, on empirical grounds.

In Àuence factors for enterprise free cash Àow: correlation and regression analysis

A specific informative indicator allowing judging enterprise movement through its life cycle stages is a Free Cash Flow (FCF). Differences in FCF determining considerably influence its calculation and further analysis methods. Thus the issue of FCF size determination algorithm formalization arises. The present time need in practical usage of certain applied aspects regarding the enterprise FCF management stipulates the research issues and thesis relevance as well. The aim – identification of both negative and positive influence factors for the confectionary enterprises FCF by means of correlation and regression analysis; checking of the selected influence factors statistical meaning and model adequacy. The article refers to the correlation and regression analysis, liner regression. It allows transferring from factors functional relation and effective indicator to scholastic dependence. The correlation and regression analysis allows the task solving: to determine the analytical form of relation between the effective and factor indicators as well as define their density relation level. The correlation analysis is held for 15 confectionary enterprises FCF size in 2002-2018 and 85 indicators of No1-3 financial accounting forms indicators in the first case. According to the correlation analysis results 10 influence factors possessing the close relation with FCF size are chosen. Pre-requisite availability of independent and not related factors in the regression modelresults in their reduction to 5. The greatest reverse influence makes the enterprise income from the capital assets sell and financial investments; its correlation coefficient is equal to -0.76. The other factors possess the correlation coefficient meaning at the visible and high level. The received empiric linear regression equation possesses multiple correlation effect on 0.9 level. The hypothesis on heteroscedastic model absence is confirmed. The model received according to the correlation and regression analysis results is adequate and statistically meaningful. The offered model application allows forecasting the general FCF indicator meaning for confectionary industry enterprises as well as determining tendencies in the future and managing it in general. Key words: free cash flow, NOPAT, financial result, cash flow report, confectionary enterprise, correlation analysis, regression analysis, model, heteroscedasticity.

Geometrical Parametric Optimisation of A356 Alloy Composite in a Two-Stage Casting Process for Automobile Wheel Covers using Response Surface Methodology

In recent years, novel products from out–of–use A356 alloy engine components are increasingly produced for the automobile industries. Despite being a promising method the sand casting of these products reveals an inadequately understood cast geometry phenomenon for the process. At present, there is no technical solution to the optimisation of cast geometries for A356 alloy reconfigured into composites through organic matter reinforcements. This paper models and analyse sand casting process product geometries in a two–phase method. It utilises the response surface methodology with data on inputs and outputs to create the regression. Volume and density of the first casting process and the weight loss were evaluated for the various groupings of casting process variables, including length, weight, height, width of product for the first casting, weight, length, breadth of the product for the second casting, and the total weight of organic materials. The input and output associations were established in two models of regression analysis representing the central composite design, CCD. The influences of the cast geometrical variables on the evaluated responses were analysed. Furthermore, the predictive accuracy of the two regression models was evaluated. Results revealed that the applied CCD and the regression models reveals statistical adequacy and are competent to predict accurately.