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.

The objective of this study was to develop a forecast model to determine the rate of generation of municipal solid waste in the municipalities of the Cuenca del Cañ ó n del Sumidero, Chiapas, Mexico. Multiple linear regression was used with social and demographic explanatory variables. The compiled database consisted of 9 variables with 118 specific data per variable, which were analyzed using a multicollinearity test to select the most important ones. Initially, different regression models were generated, but only 2 of them were considered useful, because they used few predictors that were statistically significant. The most important variables to predict the rate of waste generation in the study area were the population of each municipality, the migration and the population density. Although other variables, such as daily per capita income and average schooling are very important, they do not seem to have an effect on the response variable in this study. The model with the highest parsimony resulted in an adjusted coefficient of 0. 975, an average absolute percentage error of 7. 70, an average absolute deviation of 0. 16 and an average root square error of 0. 19, showing a high influence on the phenomenon studied and a good predictive capacity.

Background: Citrus is among the cold temperature (freezing) susceptible plants. The performance of storage and breeding of horticultural crops is mainly dependent on the correlation among the traits. Objectives: The present study was conducted to identify the physiological and biochemical traits of some citrus cultivars with the greatest influence on stress tolerance and determine the direct and indirect effects of these traits on the median Lethal Time (LT50) using integrated pathway analysis (i. e., stepwise regression and causality coefficient). Methods: Pathway analysis (i. e., stepwise regression and causality coefficient) based on additive models, which is among the robust statistical methods to describe the relationship among the traits, was used to investigate the physiological and biochemical charac, teristics of four citrus cultivars (i. e., Japanese mandarin, Thomson orange, Ruby Star grapefruit, and Lisbon lemon) at temperature levels (-8,-4, and +4°, C) in a completely randomized design with three replications in 2021. Results: The results showed that Japanese mandarin and Thomson orange cultivars had the highest stress tolerance (LT50). The results of the correlation coefficient demonstrated that the highest positive and significant correlations belonged to the LT50 with total flavonoid (0. 443**), chlorophyll a with chlorophyll b (0. 613**), carotenoid with chlorophyll a (0. 929**), chlorophyll b (0. 573**), and total chlorophyll (0. 849**), relative moisture content with malondialdehyde (0. 559**), glycine-betaine with catalase (0. 919**), hydrogen peroxide with total flavonoid (0. 405**), and catalase (0. 611**). Conclusions: The results of stepwise regression for all traits indicated the importance and critical role of total flavonoid, proline, and LT50 characteristics.

This paper describes 3D-QSAR analysis and biological evaluation of 1, 5- benzodiazepine analogues. Benzodiazepine nucleus with its simple structure gives a good opportunity for further modification regarding an increase of its antimicrobial activity.We synthesized a series of benzodiazepine analogues from condensation of various chalcones and halo substituted o-phenelynene diamines. All compounds were assayed in vitro against, E. coli, P. aeruginosa, S. aureus. The models were generated on the Vlife MDS 3.5; selected models showed a correlation coefficient (r2) above 0.9 with cross-validated correlation coefficient (q2) above 0.8, respectively, for all the selected organisms. The 3D-QSAR models generated were externally validated for all models using a test set of 6 molecules for which the predictive r 2 (r2 -pred) was found to be above 0.45. The results of 3D-QSAR indicate that contours can be used to design some potent antibacterial agents.