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.

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.