In a multiple linear regression model, there are instances where one has to update the regression parameters. In such models as new data become available, by adding one row to the design matrix, the least-squares estimates for the parameters must be updated to reflect the impact of the new data. We will modify two existing methods of calculating regression coefficients in multiple linear regression to make the computations more efficient. By resorting to an initial solution, we first employ the Sherman-Morrison formula to update the inverse of the transpose of the design matrix multiplied by the design matrix. We then modify the calculation of the product of the transpose of design matrix and the design matrix by the Cholesky decomposition method to solve the system. Finally, we compare these two modifications by several appropriate examples.

Regression is a statistical technique used in finance, investment, and several other domains to assess the magnitude and precision of the association between a dependent variable (often represented as Y) and a set of other factors (referred to as independent variables). This work introduces a linear programming approach for constructing regression models for Neutrosophic data. To achieve this objective, we use the least absolute deviation approach to transform the regression issue into a linear programming problem. Ultimately, the efficacy of the suggested approach in resolving such problems has been shown via the presentation of a concrete illustration.

Background: Linear-regression analysis is a well-known statistical technique that serves as a basis for understanding the relationships between variables. Its simplicity and interpretability render it the preferred choice in healthcare research, including vision science, as it enables researchers and practitioners to model and predict outcomes effectively. This article presents the fundamentals of linear-regression modeling and reviews the applications and interpretations of the main linear-regression analysis. Methods: The primary objective of linear regression is to fit a linear equation to observed data, thus allowing one to predict and interpret the effects of predictor variables. A simple linear regression involves a single independent variable, whereas multiple linear regression includes multiple predictors. A linear-regression model is used to identify the general underlying pattern connecting independent and dependent variables, prove the relationship between these variables, and predict the dependent variables for a specified value of the independent variables. This review demonstrates the appropriate interpretation of linear-regression results using examples from publications in the field of vision science. Results: Simple and multiple linear regressions are performed, with emphasis on the correct interpretation of standardized and unstandardized regression coefficients, the coefficient of determination, the method for variable selection, assumptions in linear regression, dummy variables, and sample size, along with common mistakes in reporting linear-regression analysis. Finally, a checklist is presented to the editors and peer reviewers for a systematic assessment of submissions that used linear-regression models. Conclusions: Medical practitioners and researchers should acquire basic knowledge of linear-regression such that they can contribute meaningfully to the development of technology by accurately interpreting research outcomes. Incorrect use or interpretation of appropriate linear-regression models may result in inaccurate results. Appointing an expert statistician in an interdisciplinary research team may offer added value to the study design by preventing overstated results.

In the simulated binary crossover, offspring are generated from parents with a coefficient of variation and uses a probability distribution function for the coefficient and there is a linear relationship between parents and offspring. Most existing methods of crossover operators generate offspring on the solution on the decision space during the search and so far, no suggestion has been proposed on making a regression model for generating the offspring on the objective space. In this paper, a Gaussian linear regression crossover has been proposed. The idea is to apply linear regression to model a relationship between parents and offspring in crossover operations through the Gaussian process. The reason for using this process is that the probability distribution of the simulated binary operator is based on the parent in the mating pool on decision space, while the probability distribution of the proposed method is on objective space in the mating pool. To optimize problems on the combinatorial sets, the proposed method is applied. The performance of the proposed algorithm was tested on Computational Expensive Optimization benchmark tests and indicates that the proposed operator is a competitive and promising approach.