A New Method to Estimate Parameters in the Simple Regression Linear Equation

Abstract

Linear regression is widely used in various fields. Research on linear regression uses the OLS and ML method in estimating its parameters. OLS and ML method require many assumptions to complete. It is frequently found there is an unconditional assumption that both methods are not successfully used. This paper proposes a new method which does not require any assumption with a condition. The new method is called SAM (Simple Averaging Method) to estimate parameters in the simple linear regression model. The method may be used without fulfilling assumptions in the regression model. Three new theorems are formulated to simplify the estimation of parameters in the simple linear regression model with SAM. By using the same data, the simple linear regression model parameter estimation is conducted using SAM. The result shows that the obtained regression parameter is not quite far different. However, to measure the accuracy of both methods, a comparison of errors made by each method is conducted using Root Mean Square Error (RMSE) and Mean Averaged Error (MAE). By comparing the values of RMSE and MAE for both methods, SAM method may be used to estimate parameters in the regression equation. The advantage of SAM is free from all assumptions required by regression, such as error normality assumption while the data should be from the normal distribution.

Mathematical Model for 100- and 200-meter Olympic Games Running Championship Time Records

“…Therefore, it is possible to model the data used in this research by building a reverse logistic model that is opposite to the existing logistic model. Furthermore, the SA method [13] and the ISA method [12] can be used to generate the regression equation in the problem discussed in this article.…”

“…Likewise, Mishra and Kaur [7] used a simple linear regression model in their research. Agung et al [13] and Jetsada et al [12] offer a new method for estimating linear regression parameters when classical methods for estimating regression parameters cannot be used. Agung et al [13] used the Simple Averaging (SA) method based on the mean value in estimating the regression parameters.…”

“…Agung et al [13] used the Simple Averaging (SA) method based on the mean value in estimating the regression parameters. While Jetsada et al [13]. Estimation of regression parameters using the Improved Simple Averaging (ISA) method based on the median value.…”

An Improved Simple Averaging Approach for Estimating Parameters in Simple Linear Regression Model

“…Sometimes, the assumption may be violated. An alternative for estimating parameter on simple linear regression model proposing by Agung et al [1] presents an approach to estimating parameters in simple linear regression model under unconditional assumption which is simple averaging (SA) approach. SA approach is a process for estimating parameter supporting by Cliff et al [3] where have developed a new method in solving the simple and multiple linear regression equation.…”