Mathematics and Statistics Vol. 8(2), pp. 75 - 81
DOI: 10.13189/ms.2020.080201
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A New Method to Estimate Parameters in the Simple Regression Linear Equation

Agung Prabowo ^1,*, Agus Sugandha ¹, Agustini Tripena ¹, Mustafa Mamat ², Sukono ³, Ruly Budiono ^4
1 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Jenderal Soedirman, Indonesia
² Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Malaysia
³ Department of Mathematics, Faculty of Mathematics and Natural Science, Padjadjaran University, Indonesia
⁴ Department of Biology, Faculty of Mathematics and Natural Science, Padjadjaran University, Indonesia

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.

KEYWORDS
Linear Regression, Parameter, Ordinary Least Square Method, Simple Average Method

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Agung Prabowo , Agus Sugandha , Agustini Tripena , Mustafa Mamat , Sukono , Ruly Budiono , "A New Method to Estimate Parameters in the Simple Regression Linear Equation," Mathematics and Statistics, Vol. 8, No. 2, pp. 75 - 81, 2020. DOI: 10.13189/ms.2020.080201.

(b). APA Format:
Agung Prabowo , Agus Sugandha , Agustini Tripena , Mustafa Mamat , Sukono , Ruly Budiono (2020). A New Method to Estimate Parameters in the Simple Regression Linear Equation. Mathematics and Statistics, 8(2), 75 - 81. DOI: 10.13189/ms.2020.080201.