The house is one of the main requirements of human to achieve comfort and relaxation. It plays an essential role in life’ s quality and is an index of welfare in a society. According to the central bank of Iran reports, the housing share in households has increased by more than 30 percent from 2008 to 2017. This rate increased by 43 percent in 2017. These values are also higher for lower deciles. In 2016, 78% of low-income households’ income was spent on housing and food. Therefore, these families unable to enjoy urban amenities. Also, due to the annual movements which cause many problems of hiring and stresses, the priority of citizens is house purchasing. Therefore, families search in the city to find suitable Apartments according to their needs and budget. Awareness of property Prices is important for both homeowners and customers. If buyers know the Prices of Apartments in the area, not only find the most suitable unit based on their needs and budget but may not also be defrauded by some individuals. Researches show that residents of each area look for Apartments around the previous areas for purchase or rental of residential units. The Price information gives people more freedom and confidence to find the best cases, and save time and money instead of limit themselves to the surrounding area.

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.

Although computational strategies for taking care of Non-linear Regression Based on Hybrid Algorithms (EPNRHA) to Estimation of Parameters have always been available for years, the further application of Evolutionary Algorithms (EAs) to such difficulties provides a framework for addressing a wide range of Multi-Objective Conflicts (MOPs).  NRPSOGSA is an Estimation of Parameters of Non-linear Regression Gravitational Search Algorithm with Practical Swarm Optimization that involves the synthesis of hegemony by using the hybrid algorithm (PSOGSA) approach is utilized. Whilst Gravitational Search Algorithm with Practical Swarm Optimization Since the leader hiring process uses the Tchebycheff Strategy as a criterion, simplifying the multi-objective problem (MOP) by rewriting it as a set of Tchebycheff Approach, solving these issues at the same time within the GSA context may lead to rapid resolution. Dominance is important in constructing the leader's library because it allows the chosen leaders to encompass fewer dense places, reducing global optimization problems and producing a more diverse approximated Pareto front. 6 non-linear standard functions yielded this result. PSOGSA appears to be more productive than GSA, PSO, and BAT. All of the outcomes were completed. by MATLAB (R2020b).

Introduction In this study, we addressed parameter Estimation in the linear Regression model in the presence of multicollinearity when there exists some prior information about predictor variables that appears as a linear restriction on the model parameters. We estimated the parameters based on Liu-type linear shrinkage, preliminary test, Stein, and positive Stein strategies. The performance of the proposed estimators is compared to the Liu-type estimator in terms of their relative efficiency via a Monte Carlo simulation study and an actual data set. Material and Methods In the linear Regression model, the ordinary least squares (OLS) estimator is the best linear unbiased estimator for model parameters when the predictor variables are independent. The multicollinearity problem arises when there exists near linear dependence among the predictor variables. This problem leads to variance inflation of the OLS estimator. Thus the interpretations based on it are not true. The ridge and Liu-type estimators are two methods to combat multicollinearity. The Liu-type estimator is more efficient than the ridge estimator when there is a strong correlation between the predictor variables. We suppose that there is some prior information about parameter vector ,under a linear restriction as R,= r where R is a p2 ,p matrix and r is a p2 ,1 vector. The restricted estimator of ,is obtained by maximizing the log-likelihood function of the linear Regression model under the linear restriction. The Liu-type restricted estimator can be defined in the presence of multicollinearity under the linear restriction. We propose the Liu-type shrinkage estimators using the Liu-type and Liu-type restricted estimators to improve the Estimation of parameters. We compare the performance of the Liu-type shrinkage estimators and the Liu-type estimator in terms of their relative efficiency using a Monte Carlo simulation study. The simulation is conducted under different sample sizes, n = 30,50, the correlation level between the predictor variables ,= 0: 80,0: 90,0: 95, p1 = 5, and p2 = 3,5,7. To investigate the behavior of the proposed estimators, we define Δ,= ∥, ,􀀀, , 0∥, 2, where ∥, : ∥,is the Euclidean norm, ,is the parameters vector in the simulated model and , 0 is the true parameters vector in the candidate sub-model. We also apply the proposed Estimation methods to a real data set. Results and Discussion The simulation results show that all estimators’,performances become better when p2 and ,increase for fixed n. For all combinations of p2, , , and n, the Liu-type restricted estimator has the best performance at Δ,= 0. As Δ,moves away from zero, all estimators’,simulated relative efficiencies (SREs) decrease. As ,approaches one, the performance of the Liu-type linear shrinkage estimator increases. Conclusion This paper suggested the Liu-type shrinkage estimators in the linear Regression model in the presence of multicollinearity under the subspace information. A Monte Carlo simulation was conducted to compare the proposed estimators’,performance with the Liu-type estimator. The simulation results confirm that the proposed estimators perform better than the Liu-type estimator when Δ,= 0 and near it for all p2, , , and n.

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.

One of the most fundamental aspects of any country is the housing economy. Because its Price changes will cause numerous effects on the national economy in the short and long periods; therefore, it is essential to obtain a model which can assess housing Prices. In this regard, the objectives of this research are to compare multiple linear Regression and random forest Regression to evaluate the Price of residential units and extract the important factors in relation to the Price of them. The statistical population included four north valiasr neighborhoods (n=30, 272 units) and the sample size was estimated to be 379 units using the cochran formula at 95% confidence level and with a 5% error. But 400 samples considered. To eliminate the effect of time, only the data of september, 2020 were used. Also, arcmap, spss and rstudio software were used to analyze the data. According to the results, area, Apartment floors, construction year, proximity to health centers, urban facilities, green spaces, religious land-use, medical centers, military land-uses and floor level, are the ten most important variables in relation to housing Prices in the north valiasr neighborhoods, respectively. Further, according to the findings, random forest Regression has a superior capability in predicting housing Prices in north valiasr of tabriz compared to multiple linear Regression.

Background and Objective: Ground level ozone (O3) is one of most dangerous pollutants for human health in urban areas. The aim of this study was to identify the factors affecting the formation of ozone and modeling the spatial and temporal variations of ozone concentration in Tehran metropolitan area.Materials and Methods: The data used in this research included meteorological data and pollution concentration data for 2014. First, we studied the impact and correlation of parameters to ozone concentration using the coefficient of Pearson, and then we did modeling of ozone concentration using a multivariate linear Regression method.Results: The developed model had the ability to describe 79% of the data changes for 2014. The temporal analysis of the ozone concentration showed that the best coefficient of determination of the model was R2=0.771 in the summer and R2=0.778 in July. These results also showed that among the air quality monitoring station of Tehran, station 4 had the lowest coefficient of determination (R2=0.6) and Aqdasieh station had the highest coefficient of determination (R2=0.79). Finally, the spatial distribution of the estimated ozone concentration was consistent with the measured ozone concentration at the station level.Conclusion: According to the results, all the parameters related to air pollution concentration and meteorological parameters were effective parameters on modeling of ozone concentration on the ground level. The spatial distribution of ozone concentration in Tehran showed a greater concentration of ozone in the South and East than the North and West of the city.