The t-test of a regression coefficient for imprecise data

Year 2024, , 1130 - 1140, 27.08.2024

Muhammad Aslam

https://doi.org/10.15672/hujms.1342344

Abstract

The existing t-test for testing the significance of the regression coefficient is applied when cent percent observations of the data are precise, exact and certain. In practice, the measurement data or data recorded in an uncertain environment do not have all precise observations. The imprecise data cannot be analyzed using the existing t-test for testing the significance of the regression coefficient. In this paper, we will present the design of a t-test for testing the significance of the regression coefficient under neutrosophic statistics. The proposed t-test for testing the significance of the regression coefficient can be applied to imprecise data. The effect of the degree of uncertainty on the power of the test will be studied. The proposed t-test for testing the significance of the regression coefficient will be applied using the imprecise data. From the analysis, it is concluded that the proposed t-test for testing the significance of the regression coefficient will be informative, flexible and adequate to be applied to imprecise data.

Keywords

t-test, inference, power of the test, simulation, level of significance

References

• [1] R. Alhabib and A. Salama, The neutrosophic time series-study its models (linearlogarithmic) and test the coefficients significance of its linear model, Neutrosophic Sets Syst. 33, 105-115, 2020.
• [2] M. Aslam, Neutrosophic F-Test for two counts of data from the Poisson distribution with application in climatology, Stats 5 (3), 773-783, 2022.
• [3] V. Bewick, L. Cheek and J. Ball, Statistics review 7: Correlation and regression, Crit. Care 7, 1-9, 2003.
• [4] S. Broumi, S. Krishna Prabha and V. Uluçay, Interval-valued Fermatean neutrosophic shortest path problem via score function, Neutrosophic syst. appl. 11, 1-10, 2023.
• [5] S. Broumi, S. Mohanaselvi, T. Witczak, M. Talea, A. Bakali and F. Smarandache, Complex fermatean neutrosophic graph and application to decision making, Decis. Mak. Appl. Manag. Eng. 6 (1), 474-501, 2023.
• [6] S. Broumi, P.K. Raut and S.P. Behera, Solving shortest path problems using an ant colony algorithm with triangular neutrosophic arc weights, Int. J. Neutrosophic Sci. 20 (4), 128-128-137, 2023.
• [7] S. Broumi, R. Sundareswaran, M. Shanmugapriya, A. Bakali and M. Talea, Theory and applications of Fermatean neutrosophic graphs, Neutrosophic Sets Syst. 50, 248- 286, 2022.
• [8] S. Broumi, R. Sundareswaran, M. Shanmugapriya, P.K. Singh, M. Voskoglou and M. Talea, Faculty performance evaluation through multi-criteria decision analysis using interval-valued Fermatean neutrosophic sets, Mathematics 11 (18), 3817, 2023.
• [9] C.C. Chen, C.M. Lai and W.C. Sun, Fuzzy testing for regression coefficient of Fuzzy numbers, J. Test. Eval. 41 (1), 116-121, 2013.
• [10] J. Chen, J. Ye and S. Du, Scale effect and anisotropy analyzed for neutrosophic numbers of rock joint roughness coefficient based on neutrosophic statistics, Symmetry 9 (10), 208, 2017.
• [11] J. Chen, J. Ye, S. Du and R. Yong, Expressions of rock joint roughness coefficient using neutrosophic interval statistical numbers, Symmetry 9 (7), 123, 2017.
• [12] M. Fischer, B.T. West, M.R. Elliott and F. Kreuter, The impact of interviewer effects on regression coefficients, J. Surv. Stat. Methodol. 7 (2), 250-274, 2019.
• [13] K.A. Frank, Impact of a confounding variable on a regression coefficient, Sociol. Methods Res. 29 (2), 147-194, 2000.
• [14] A.R. Ives, For testing the significance of regression coefficients, go ahead and logtransform count data, Methods Ecol. Evol. 6 (7), 828-835, 2015.
• [15] G.K. Kanji, 100 Statistical Tests, Sage, 2006.
• [16] S. Li and X. Yuan, Application of linear regression mathematical model in the evaluation of teachers informatization quality. Complexity 1, 1-10, 2021.
• [17] K. Mu, Q. Shi, Y. Ma and J. Tan, Exploration of entrepreneurship education by linear regression and psychological factor analysis, Front. Psychol. 11, 2045, 2020.
• [18] J. Mulder and A. Olsson-Collentine, Simple Bayesian testing of scientific expectations in linear regression models, Behav. Res. Methods 51, 1117-1130, 2019.
• [19] D. Nagarajan, S. Broumi, F. Smarandache and J. Kavikumar, Analysis of neutrosophic multiple regression, Neutrosophic Sets Syst. 43, 44-53, 2021.
• [20] P. Nieminen, Application of standardized regression coefficient in meta-analysis, BioMedInformatics 2 (3), 434-458, 2022.
• [21] A. Polymenis, A neutrosophic Studentsttype of statistic for AR (1) random processes, J. Fuzzy. Ext. Appl 2 (4), 388-393, 2021.
• [22] T. Ramanathan and M. Rajarshi, Rank tests for testing randomness of a regression coefficient in a linear regression model, Metrika 39, 113-124, 1992.
• [23] F. Smarandache, New types of Soft Sets: HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, and TreeSoft Set, Int. J. Neutrosophic Sci. 20 (4), 58-64, 2023.
• [24] F. Smarandache, Neutrosophic Statistics is an extension of Interval Statistics, while Plithogenic Statistics is the most general form of statistics (second version), Int. J. Neutrosophic Sci. 19 (1), 148-165, 2022.
• [25] F. Smarandache, Introduction to Neutrosophic Statistics, Sitech and Education, Craiova, Romania-Educational Publisher, Columbus, Ohio, USA, 123, 2014.