Linear regression.

This study focuses on optimizing the process of biofuel production from citrus peel using the Design of Experiments (DOE) technique. This study aims to determine the optimal values for the variables that have a significant impact on the production of biofuel. The variance within and between data groups was determined using the analysis of variance (ANOVA) table. The ANOVA table shows how much of the response variable's variation (biofuel production) can be explained by the independent variables (A, B, C, D, E, AB, AC, AD, AE, and BJ) and how much is caused by random error. The ANOVA table comprises of three primary parts: the F-statistic, the p-value, the df, the mean square (MS), the source of variation, and the sum of squares (SS). The wellspring of variety alludes to the beginning of the information variety, which can be either the lingering or the model. The amount of squares estimates the information's changeability, with the absolute amount of squares addressing the amount of the squared deviations of the genuine qualities from the mean worth. The residual is the sum of the squared deviations from the predicted values of the actual values, while the model's sum of squares is the sum of the squared deviations from the mean of the predicted values. The model has 10 degrees of freedom (the number of independent variables) and the residual has 4 degrees of freedom (the number of observations minus the number of independent variables). These degrees of freedom represent the number of independent pieces of information used to estimate a parameter. The mean square, which indicates the typical amount of variation for each variation source, is calculated by dividing the sum of squares by the degrees of freedom. The degree to which the model explains the variation in the data is indicated by the F-statistic, which is the ratio of the model's mean square to the residual's mean square. The probability of obtaining an F-statistic that is as large as the one observed if the null hypothesis is true is represented by the p-value. The independent variables' insignificant impact on biofuel production is the null hypothesis in this instance. The model's p-esteem in this study is under 0.05, demonstrating that the free factors essentially affect biofuel creation and that the model is genuinely huge. In addition, the model is significant because the F-statistic is relatively large in comparison to the F-distribution for the 10 and 4 degrees of freedom, respectively. The estimated coefficients for the linear regression model used to investigate the production of biofuel from citrus peel can be found in the ANOVA coefficients table. The table provides a list of the intercept and independent variables' coefficients, standard errors, t-values, and p-values. When all of the independent variables are zero, the intercept has a coefficient of 0.0672, indicating the estimated value of the response variable. The fact that the intercept does not differ significantly from zero is supported by the fact that its p-value is not significant. The fact that the coefficients of the independent variables A, E, AC, AD, AE, and BJ are not statistically significant indicates that these variables have little impact on the response variable. On the other hand, the positive coefficients and significant p-values of the independent variables B and C suggest that an increase in their values could result in an increase in the production of biofuel from citrus peel. In conclusion, the key variables that influence the production of biofuel from citrus peel have been identified thanks to the use of the Design of Experiments (DOE) method. According to the findings of this study, an increase in the production of biofuel from citrus peel may result from an increase in the values of the independent variables B and C. The development of environmentally friendly energy sources and the optimization of biofuel production processes will benefit greatly from these findings

The results from an analysis of balanced data are frequently summarized in an analysis of variance (AOV) table. Each sum of squares (SS) in the AOV table is uniquely associated with testing a particular hypothesis in the linear model. These hypotheses are well known and cause no confusion among statisticians as to what is being tested. Results from an analysis of unbalanced data, however, cannot be uniquely summarized in an AOV table, and, consequently, statisticians are often confused about the hypotheses being tested. Some statisticians prefer an orthogonal partitioning of the SS (paralleling the balanced case) as the appropriate analysis; others prefer various forms of nonorthogonal analyses. The purpose of this paper is to show (and, hopefully, clarify) the hypotheses that are being tested in various unbalanced AOV tables.

Recent widespread criticism of the lack of statistical rigor in science journals has focused attention on the need to improve the standards for statistical design and analysis in research. This study examined the role of analysis of variance (ANOVA) in the context of current concerns regarding the validity and appropriateness of statistics in scientific publications. One objective was to suggest how ANOVA tables can be constructed to enhance the transparency and scientific integrity of scientific journals and better assist the interpretation of data. The broader goal of this study was to generate new discussion, debate, and ideas regarding ANOVA. The history and current status of ANOVA as the context for assessing the practical and statistical relevance of ANOVA tables for students, authors, reviewers, editors, and readers of scientific journals is discussed. Each component of an ANOVA table (sources of variation, degrees of freedom, sums of squares, mean squares, F values, and P values) is critiqued for its information and value. Using a criterion of including the components that provide essential information on key details of the experimental design and validating the appropriateness of the analysis, guidelines are provided for constructing an ANOVA table that is SIMPLE—Simple, Informative, Meaningful, Powerful, Logical, and Effective. A prototype SIMPLE ANOVA table is presented to encourage further consideration and debate regarding best practices for ANOVA tables.

Analysis of Variance Through Examples

In a factorial experiment involving two factors, one quantitative and one qualitative, one may simply treat both factors as qualitative and obtain an analysis of variance table by straightforward methods. The sum of squares due to the quantitative factor can then be partitioned into sums of squares due to the linear, quadratic, etc. orthogonal contrasts, while the sum of squares due to the qualitative factor can be partitioned into meaningful orthogonal contrasts. If, however, one of the levels of the quantitative factor is zero, the analysis is complicated by the fact that a zero amount of each level of the qualitative factor is the same treatment. It is clear, for example, that if one applies a zero amount of six different fertilizers to six experimental units, one treats each experimental unit in exactly the same way. The foregoing situation arises frequently in biological assay and detailed analyses have been derived under the assumption that the quantitative factor follows a particular response law for each level of the qualitative factor. A short summary of this type of analysis is given in Kempthorne [1, Sec. 18.8]. I have been unable to find in the literature any description of how to compute the analysis of variance table for the situation where one of the levels of the quantitative factor is zero. The computations for the analysis of variance table which is appropriate for experiments involving quantitative and qualitative factors including zero amounts are presented in the remainder of this paper. Suppose that a factorial experiment involves one quantitative factor, A, having a levels and one qualitative factor, B, having b levels. When none of the levels of the quantitative factor A is a zero amount, the usual analysis of variance table for a two-way classification with one observation per experimental unit applies. If yij denotes the yield of the experimental unit that receives level i of factor A and level j of factor B, the sum of squares due to factor B,

Inferential Statistics

Clinical features of vitiligo associated with comorbid autoimmune disease: A prospective survey

C-regression models are known as very useful tools in many fields. Since now, many trials to construct c-regression models for data with uncertainty in independent and dependent variables have been done. However, there are few c-regression models for data with uncertainty in independent variables in comparison with dependent variables now. The reason is as follows. The models are constructed using optimal solutions which is derived by solving an optimization problem “analytically”. The problem for data with uncertainty in dependent variables can be easily solved but it is very difficult to solve the problem for data with uncertainty in independent variables “analytically”. Therefore, most of the models for data with uncertainty in independent variables are constructed in which the solutions are calculated “numerically”. By the way, we have proposed “tolerance” of a convenient tool to handle data with uncertainty and applied it to some of clustering algorithms. This concept of tolerance is very useful. The reason is that we can handle data with uncertainty in the framework of optimization to use the concept, without introducing some particular measure between intervals. Especially when we handle the data with missing values of its attributes in the framework of optimization like as fuzzy c-means clustering, this tool is effective. Besides, we think that the tolerance is also available when we consider to construct a regression model for data with uncertainty in independent and dependent variables. In this paper, we first derive the optimal solutions for c-regression models for data with uncertainty in independent and dependent variables “analytically” by using the concept of tolerance. Second, we construct hard and fuzzy c-regression models for data with tolerance in independent and dependent variables. Moreover, we estimate effectiveness of the algorithms through some numerical examples.

Various computational methods exist for generating sums of squares in an analysis of variance table. When the ANOVA design is balanced, most of these computational methods will produce equivalent sums of squares for testing the significance of the ANOVA model parameters. However, when the design is unbalanced, as is frequently the case in practice, these sums of squares depend on the computational method used.- The basic reason for the difference in these sums of squares is that different hypotheses are being tested. The purpose of this paper is to describe these hypotheses in terms of population or cell means. A numerical example is given for the two factor model with interaction. The hypotheses that are tested by the four computational methods of the SAS general linear model procedure are specified. Although the ultimate choice of hypotheses should be made by the researcher before conducting the experiment, this paper PENDLETON,VON TRESS,AND BREMER presents the following guidelines in selecting these hypotheses: When the design is balanced, all of the SAS procedures will agree. In unbalanced ANOVA designs when there are no missing cells. SAS Type III should be used. SAS Type III tests an unweighted hypothesis about cell means. SAS Types I and II test hypotheses that are functions of the ceil frequencies. These frequencies are often merely arti¬facts of the experimental process and not reflective of any underlying frequencies in the population. When there are missing cells, i.e. no observations for some factor level combinations. Type IV should be used with caution. SAS Type IV tests hypotheses which depend

This study analyzes the effect of Computer Aided Innovation (CAI) to improve R&D Capabilities empirically. Survey was distributed by e-mail and Google Docs, targeting CTO of 235 SMEs. 142 surveys were returned back (rate of return 60.4%) from companies. Survey results from 119 companies (83.8%) which are effective samples except no-response, insincere response, estimated value, etc. were used for statistics analysis. Companies with less than 50billion KRW sales of entire research ed companies occupy 76.5% in terms of sample traits. Companies with less than 300 employees occupy 83.2%. In terms of the type of company business Partners (called 'partners with big companies' hereunder) who work with big companies for business occupy 68.1%. SMEs based on their own business (called 'independent small companies') appear to occupy 31.9%. The present status of holding IT system according to traits of company business was classified into partners with big companies versus independent SMEs. The present status of ERP is 18.5% to 34.5%. QMS is 11.8% to 9.2%. And PLM (Product Life-cycle Management) is 6.7% to 2.5%. The holding of 3D CAD is 47.1% to 21%. IT system-holding and its application of independent SMEs seemed very vulnerable, compared with partner companies of big companies. This study is comprised of IT infra and IT Utilization as CAI capacity factors which are independent variables. factors of R&D capabilities which are independent variables are organization capability, process capability, HR capability, technology-accumulating capability, and internal/external collaboration capability. The highest average value of variables was 4.24 in organization capability 2. The lowest average value was 3.01 in IT infra which makes users access to data and infor mation in other areas and use them with ease when required during new product development. It seems that the inferior environment of IT infra of general SMEs is reflected in CAI itself.

27 - Analysis of Variance and Statistical Design of Experiments

Employees are considered as the key determinants of the success of an organization that shall have different training and development so as to cope up with the fast-changing business world. Training and development programs are essential for every organization for its long term planning that requires careful preparation if they are to be successful and help to achieve its objectives in time and enhance the knowledge, skills, and competencies of its workforce. The overall objective of this study is to assess the practices and challenges of training and development at the Ethiopian Textile Industry Development Institute(ETIDI). The study adopted a mixed approach and used both primary and secondary data sources. The primary data collected from ETIDI through self-administered questionnaire for 116 selected operating employees and middle-level managers using a purposive sampling method to make sure that they have gone through the training program or understand the training and development program in the institute and semi-structured interview question employed for top managers(directors and deputy directors and training coordinator) through interview. The collected data were analyzed by using statistical tools (SPSS-Version 22). Both descriptive and inferential statistics were used for the data analysis. The descriptive statistics such as frequency and percent were used for describing the demographic characteristics of respondents and the dependent and independent variables. Qualitative data obtained through interviews were analyzed using content analysis. Inferential statistics like Pearson correlation coefficient(r) and multiple linear regression were used to determine if there is a relationship existed between independent and dependent variables. The study shows that 62.5% of the variation in the dependent variable was explained by independent variables. The findings also indicated that the relationship between the dependent variable was positively correlated and claimed to be a statistically significant relationship with the independent variables. The findings of the study indicated that there is no series of attention to allocate enough time, sufficient budget and resource for the training and development; in ETIDI there is no SMART manual and instrument of need assessment; training and development need assessment is not prepared by considering the need of prospective trainees; the organized training by the Institute is for the sake of refreshment or to collect allowance with less attention to the outcome of the training; training and development objectives are not set in advance; training and development program of the organization is not designed in line with the actual job to be performed and training and development program not followed by a reward. Hence, the researcher recommended that the management of the institute, the board, and other stakeholders should define an appropriate training and development policy and programs that bring or capacitate the organization as well as the employee, Staff in the institute should be helped to grow into more responsibility by systematic training and development rather than consider it training as means to make themselves free from staff routine and receive allowance without considering the objective and benefits of training for themselves and for their institute so that they will be confident enough to carry out the responsibility of the job and the management of the institute, the board, and other concerned bodies should come up with training and development practices and policies for their ETIDI because they are the strategic link between the institute’s vision and its day-to-day operations. Keywords : SMART manual, training and development, reward DOI: 10.7176/JAAS/68-02 Publication date: September 30 th 2020

The present study deals with male’s attitude towards contraceptive use behavior and fatalism in Peshawar city, Pakistan. Pakhtoon mostly inhabitsPeshawar city, which has its own culture, highly strict in terms of women emancipation and considered women freedom as a sin and culturallyasking for severe punishment even in some cases death for the offenders. A sample size of 613 married male respondents (15-49 years old) wasinterviewed through cluster sampling procedure from five randomly selected bazaars out of total fifteen. Likert and Semantic Differential Scales were used in devising independent and dependent variables while constructing interview schedule. At first stage univariate analysis and then bivariate analysis were carried out to reach into logical outcome. Both dependent variable (Contraceptive Use Behavior) and independent variable (Fatalism) were indexed and reliability analysis was carriedout through Cronbach’s alpha test. The reliability coefficients were found lying between .7 to .8. Both dependent and independent variables were indexed and cross-tabulated for conducting bi-variate analysis. Gamma, Chi-square and Fisher Exact Test was used to determine the strength, direction and level of association between dependent and independent variables. Majority of the respondents had a clear vision of family planning and found to be moderately consistent of contraceptive use behavior. Moreover, respondents negated that fate prescribes the final number of children, a childless woman is a handicapped person, a sonless womanis a sign of misfortune, more children ensure perpetuation of family; bring husband and wife closer and sign of prestige. Results based onindexation of variables showed a low intensity of fatalistic behavior amongst the respondents of the study area. Efforts are needed on part of the policy makers to properly portray the complexities involved in the bareness of a woman by recognizing more rights for women than just producing children. Moreover, Peshawar city needs to be declared as model to other parts of the country, which is still in the grip of fatalism.

STILL SEARCHING FOR A TRUE RACE? REPLY TO KRAMER ET AL. AND ALBA ET AL.

fourteen - STATISTICS FOLLOWING SIGNIFICANCE