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In a statistical decision problem, the risk function is an indicator that reflects the merits of the decision function. Admissibility is one of the best decision criteria to minimize risk, which is to analyze the results of estimation and plays an important role to select a better decision function. Therefore, there are many different loss functions and admissibility studies have been done in the literature. The key point of this article is to use the extended balanced loss functions (EBLF) which is more flexible compared to other loss functions to discuss the admissibility. Our study will be carried out by following steps, firstly, characterized the admissibility of linear estimators (AOLE) in different types of linear regression model (LRM)' s. Moreover, the admissibility of some known estimator and their properties under the EBLF are discussed. In the next step, a new more comprehensive loss function is proposed and under it, the linear admissibility of different types of regression coefficients (RC) is investigated. After that, some estimators are compared under the mean squares error (mse). Finally, a minimum matrix-valued risk estimator is proposed that combines the restricted least squares (RLS) and ordinary least squares (OLS) estimators. The results are supported by numerical examples and Monte Carlo simulation.