The fuzzy LINEAR REGRESSION MODEL with fuzzy input-output data and crisp coefficients is studied in this paper. A LINEAR programming MODEL based on goal programming is proposed to calculate the REGRESSION coefficients. In contrast with most of the previous works, the proposed MODEL takes into account the centers of fuzzy data’s an important feature as well as their spreads in the procedure of constructing the REGRESSION MODEL. Furthermore, the MODEL can deal with both symmetric and non-symmetric triangular fuzzy data as well as trapezoidal fuzzy data which have rarely been considered in the previous works. To show the efficiency of the proposed MODEL, some numerical examples are solved and a simulation study is performed. The computational results are compared with some earlier methods.

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.

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.

Background: Since women spend about one-third of their lifespan in menopause, accurate prediction of the age of natural menopause and its effective parameters are crucial to increase women’ s life expectancy. Objective: This study aimed to compare the performance of generalized LINEAR MODELs (GLM) and the ordinary least squares (OLS) method in predicting the age of natural menopause in a large population of Iranian women. Materials and Methods: This cross-sectional study was conducted using data from the recruitment phase of the Shahedieh Cohort Study, Yazd, Iran. In total, 1251 women who had the experience of natural menopause were included. For MODELing natural menopause, the multiple LINEAR REGRESSION MODEL was employed using the ordinary least squares method and GLMs. With the help of the Akaike information criterion, rootmean-square error (RMSE), and mean absolute error, the performance of REGRESSION MODELs was measured. Results: The mean age of menopausal women was 49. 1 ± 4. 7 yr (95% CI: 48. 8-49. 3) with a median of 50 yr. The analysis showed similar Akaike criterion values for the multiple LINEAR MODELs with the OLS technique and the GLM with the Gaussian family. However, the RMSE and mean absolute error values were much lower in GLM. In all the MODELs, education, history of salpingectomy, diabetes, cardiac ischemic, and depression were significantly associated with menopausal age. Conclusion: To predict the age of natural menopause in this study, the GLM with the Gaussian family and the log link function with reduced RMSE and mean absolute error can be a good alternative for MODELing menopausal age.