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Predictive Analytics
Published in Robert H. Chen, Chelsea Chen, Artificial Intelligence, 2022
The general linear model can be expanded to handle the effects of interdependent multiple correlations in a multivariate linear regression model, Y=XB+E where the dependent variable Y is a matrix with each column having a row of estimations of each of the dependent variables y as functions of the weighted independent variables, and the independent variable X is a matrix with each column being a set of observations on one of the independent variables x which is a function of the other independent variables, B is a matrix of parameters to be adjusted for fitting the data, and E is an error (noise) matrix that is assumed to be uncorrelated across observations and follows a multivariate normal distribution.
Multiple Regression Analysis
Published in William M. Mendenhall, Terry L. Sincich, Statistics for Engineering and the Sciences, 2016
William M. Mendenhall, Terry L. Sincich
Notice that the first column in the X matrix is a column of 1’s. Thus, we are inserting a value of x, namely, x0, as the coefficient of β0, where x0 is a variable always equal to 1. Therefore, there is one column in the X matrix for each β parameter. Also, remember that a particular data point is identified by specific rows of the Y and X matrices. For example, the y value y3 for data point 3 is in the third row of the Y matrix, and the corresponding values of x1, x2,..., xk appear in the third row of the X matrix. Using this notation, the general linear model can be expressed in matrix form as Y=Xβ+ε
Saving Money with Six Sigma Projects
Published in Kim H. Pries, Jon M. Quigley, Reducing Process Costs with Lean, Six Sigma, and Value Engineering Techniques, 2012
One of the principal tools in any approach to design for Six Sigma is the use of the designed experiment. To execute a designed experiment, we must know what we are trying to accomplish, the factors involved, a means of measuring effects, and some knowledge of some statistical tools. Two of the primary tools we use when designing experiments are analysis of variance or ANOVA and the general linear model when it is appropriate. In general, our goal is to design a robust product; that is, a product that is as immune to extraneous stimuli as we can design it. The designed experiment will reveal which factors are significant and subsequent mathematical analysis will show us how to increase the robustness of the product. Once we have gone as far as we can go in the robustness exercise, we can then assess the steps we need to take with regard to tolerancing. This approach originated with Taguchi and it is rational and appropriate to this day. While we may not choose to use the Taguchi form of designed experimentation, the steps of concept exploration, parameter design (see Figure 8.1), and tolerance design are all useful and reasonable.
Removal of orange G dye by Aspergillus niger and its effect on organic acid production
Published in Preparative Biochemistry & Biotechnology, 2023
Juana Lira Pérez, Refugio Rodríguez Vázquez
A 24-1 FFED was used to select the most significant conditions for the biosorption process, and the highest OG removal value (22.24%) was obtained in run 5 with 200 mg/L dye concentration, pH 2, 180 rpm and 90 min contact time. The relationship between the four independent variables and the percentage of discoloration can be approximated by the following polynomial response model: where y is the response variable DC (%), xi represent the independent variables and ε is the residual term that represents the experimental error. The parameter β0 is the overall mean of the response (discoloration), which is a constant of the model; βi is a linear coefficient. The obtained data were adjusted to the general linear model and, by means of a linear regression, the coefficients were determined. From this analysis, the response polynomial resulted in the following equation: where x1 is the dye concentration, x2 is the pH, x3 is the agitation and x4 is the contact time.
Spatial variations in the associations of mental distress with sleep insufficiency in the United States: a county-level spatial analysis
Published in International Journal of Environmental Health Research, 2023
In this study, we address previous limitations of insufficient sleep analyses through a study that examines regional variations in FMD in the United States. The primary objectives of this study are: 1) to compare results from the Hierarchical Linear Regression and the Complex Samples General Linear Model (CSGLM); 2) to investigate if FMD is distributed heterogeneously with respect to insufficient sleep; 3) to determine the association of FMD and insufficient sleep, after controlling for well-known demographic, socioeconomic, behavioral, and clinical confounding variables related to the mental distress. We hope that the findings gleaned from this study suggest a need for further investigation for more effective mental health prevention and intervention by elucidating regional variation of frequent mental distress in relation to inadequate sleep.
Specific smartphone uses and how they relate to anxiety and depression in university students: a cross-cultural perspective
Published in Behaviour & Information Technology, 2020
Tayana Panova, Xavier Carbonell, Andres Chamarro, Diana Ximena Puerta-Cortés
First, normality distribution was tested. Afterwards, the factor structure of questionnaires was examined using Confirmatory analysis (CFA), with generalised least squares (GLS) estimation and robust methods. Model fit was evaluated based on the comparative fit index (CFI), Tucker-Lewis index (TLI), root-mean-square error of approximation (RMSEA). As for CFA, CFI and TLI > .90, RMSEA < .08 typically reflect acceptable fit and CFI and TLI > .95, indicates excellent fit (Brown 2006; Marsh et al. 2014). Descriptive and correlational analyses were performed. To test country and sex differences in the study, a bifactorial (sex by country) Analysis of Variance (General Linear Model procedure) was performed. When main effects were significant, post-hoc comparisons (with Bonferroni adjustment for multiple comparisons) were computed. Finally, a hierarchical regression analysis was performed, where anxiety and depression were the dependent variables and sociodemographic data, uses and CERM were entered as the independent predictors. There were no missing values in the variables included.