Evaluating the cutting rate (CR) of stones is important in the cost estimation and the planning of the stone processing plants. This research used regression models to estimate the stones’ CR based on their physico-mechanical characteristics. Stone processing factories in Mahallat City (Markazi province, Iran) were visited, and the CR of diamond circular saws was recorded on six different travertine stones. Next, the stone block samples were collected from the quarries for laboratory tests. Stones’ porosity (n), uniaxial compressive strength (UCS), and Schmidt hammer hardness (SH) were determined in the laboratory as their physico-mechanical characteristics. Correlation relationships of CR with physico-mechanical characteristics were evaluated using simple and multiple regression analyses, and estimator models were developed. Results showed that multiple regression models are more reliable than simple regression for estimating the stones’ CR. The validity of the developed multiple regression models was verified with the published data of one researcher. The findings indicated that these models are accurate enough for estimating the CR of stones. Consequently, the multiple regression models provide practical advantages for estimating the CR and save time and cost during the planning and design of the stone processing factories.

This study aimed to estimate the genetic parameters of body weight traits in Markhoz goats, using B-spline random regression models. The data used in this study included 19549 records collected during 29 years (1992-2021) in Markhoz goat Breeding Research Station, located in Sanandaj, Iran. The model used to analyze data included fixed effects (year of birth, sex, type of birth and age of dam) and random effects including direct additive genetic, maternal additive genetic, permanent environmental and maternal permanent environmental assuming homogeneous and heterogeneous residual variance during the time. Akaike (BIC) and Bayesian (BIC) information criteria were used to compare the models and bspq.4.4.4.4 was selected as the best model. The direct heritability values for birth, 3-month, 6-month, 9-month and 12-month weights were estimated to be 0.14, 0.16, 0.08, 0.28 and 0.26, respectively. Genetic correlation between body weights at birth and 3-month, birth and 6-month, birth and 9-month, birth and 12-month, 3-month and 6-month, 3-month and 9-month, 3-month and 12-month, 6-months and 9-month and 9-month and 12-month were 0.22, 0.38, 0.21, 0.56, -0.26, 0.30, 0.62, 0.86 and 0.77, respectively. The highest phenotypic correlation was between the weight of 9-month and 12-month (0.82) and the lowest correlation was between birth weight and 3-month and 6-month (0.12). The results showed that the 9-month weight is a good criterion for selection in Markhoz goats.

Streptococcusis is the one of the most important bacterial fish diseases with outbreak in rainbow trout farms in Iran. The fish farmers have been largely suffered from huge economic losses due to the Streptococcusis outbreaks in different rainbow trout farms in Iran. The present study assessed the effects of some environmental risk factors on incidence of streptococcusis in rainbow trout farms in Haraz River in Mazandaran Province, Iran. A suit of environmental factors including water temperature, nitrite, nitrate, ammonium, water turbidity, DO, water Debi and total count of bacteria were explored as influential factors. Fish and water samples were randomly collected from 10 farms on a monthly basis throughout a year. Isolation and recognition of strep strains were made using biochemical and PCR tests and the data were analyzed by logistic regression method. According to the results, 20% of the differences were explained by the logistic model. Management of these factors might decline the rate of disease outbreak.

‎The high-dimensional data analysis using classical regression approaches is not applicable, and the consequences may need to be more accurate. This study tried to analyze such data by introducing new and powerful approaches such as support vector regression, functional regression, LASSO and ridge regression. On this subject, by investigating two high-dimensional data sets (riboflavin and simulated data sets) using the suggested approaches, it is progressed to derive the most efficient model based on three criteria (correlation squared, mean squared error and mean absolute error percentage deviation) according to the type of data.

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.

Introduction: Powerful and practical statistical packages have simplified the analysis and thus developed the application of data science in all research fields. Accordingly, regression has been applied to almost all aspects of the life sciences. However, misuse of this model has been reported in the past decades. This article aims to examine modeling with this important statistical method and introduce readers to the correct use of this method. Materials and methods: This review article uses real data, and the supplementary materials provide the method for performing the regression analysis in SAS and R statistical software and their related codes. Results: In the required assumptions of the regression model, the residuals of the model must be normally distributed, but performing the normality test for the actual values ​​of the response variable or any of the explanatory variables is not mandatory. Therefore, researchers should not obsess more than necessary about the normal distribution of real data. On the other hand, almost all normality test methods, such as Kolmogorov-Smirnov, are designed for large numbers of data, typically more than a thousand samples. This suggests that using such methods to test the normality of model residuals estimated from a small number of data, mostly less than a hundred cases, would be inaccurate. Another issue regarding applying the regression model is related to the co-linearity of the explanatory variables. There are still signs of correlation in a data set where all variables are generated separately and randomly in a statistical package. This means that it is very hard to find a correlation coefficient equal to zero (r = 0) even between any pair of separate, random variables. Therefore, in all regression models, there are some kinds of correlation between explanatory variables, but the important issue here is that only high correlation causes severe problems in the model. For collinearity test it would be better to use specialized methods such as Variance Inflation Factor (VIF) or Principal Component Analysis (PCA). The linearity of the model is one other assumption of regression model. Data transformation might be helpful under the situation of non-linearity of the model. However, transformation changes the variables unit, altering the array direction in a geometric space. Researchers should be careful regarding the use of modeling a large number of data affects the probability values ​​in variance analysis due to increasing the value of the degree of freedom of the model. Conclusion: As the number of data points increases, the degree of freedom of the error term increases rapidly. Therefore, the final error mean squared significantly reduces. In contrast, the scatter of data points around the regression line may be too wide. For this reason, using the coefficient of determination, usually called (R-Squared), is a suitable criterion for testing the model's fit. High coefficient values indicate a suitable model for the data set used. It should be noted that in a multiple regression model, the higher the number of explanatory variables used in the model, the higher the value of this coefficient increases. For such conditions, when the number of explanatory variables is large, another form of this coefficient, called the adjusted coefficient of determination (adjusted R2), has been introduced. The use of this coefficient in the approximations creates a limit on the number of variables used in the regression model. Accordingly, the number of variables in the model as explanatory variables should not exceed the number of samples (or the number of tens) in a set, and researchers should avoid using more variables than the number of samples.