Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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A linearity test statistic in a simple linear regression

단순회귀모형에서 선형성 검정통계량

  • Received : 2014.01.20
  • Accepted : 2014.02.10
  • Published : 2014.03.31
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Abstract

In a simple linear regression, a linear relationship between an explanatory variable and a response variable can be easily recognized in the scatter plot of them. The lack of fit test for the replicated data is commonly used for testing the linearity but it is not easy to test the linearity when the explanatory variable is not replicated. In this paper, we propose three new test statistics for testing the linearity regardless of replication using the principle of average slope and validate them through several simulations and empirical studies.

전통적으로 단순선형회귀모형에서 설명변수와 반응변수의 선형성 평가는 산점도로 쉽게 파악되었다. 보통 반복수가 존재하는 자료에서 적합결여검정은 선형성을 평가하는데 사용되었다. 하지만 반복수가 오직 하나인 경우에 선형성 검정이 수월하지 않다. 본 연구에서는 반복수가 오직 하나인 단순선형회귀모형의 선형성을 검정하는 통계량을 제안하고 모의실험 및 실증연구를 통하여 신뢰성을 파악한다.

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References

  1. Anscombe, F. J. (1973). Graphs in statistical analysis. The American Statistician, 27, 17-21.
  2. Barnett, V. and Lewis, T. (1984). Outliers in statistical data, 2nd ed., Wiley, New York.
  3. Belsley, D. A., Kuh, E. and Welsch, R. E. (1980). Regression diagnostics: Identifying influential data and sources of collinearity, Wiley, New York.
  4. Chatterjee, S. and Hadi, A. S. (2012). Regression analysis by example, Wiley, New York.
  5. Hocking, R. R. (2003). Methods and applications of linear models: Regression and the analysis of variance, Wiley, New York.
  6. Lee, H. Y. (2013). Goodness-of-fit tests for a proportional odds model. Journal of the Korean Data & Information Science Society, 24, 1465-1475. https://doi.org/10.7465/jkdi.2013.24.6.1465
  7. Park, H. C. (2013). Non-linear regression model considering all association thresholds for decision of association rule numbers. Journal of the Korean Data & Information Science Society, 24, 267-275. https://doi.org/10.7465/jkdi.2013.24.2.267
  8. Seo, H. S. and Yoon, M. (2013). Regression diagnostics for response transformations in a partial linear model. Journal of the Korean Data & Information Science Society, 24, 33-39. https://doi.org/10.7465/jkdi.2013.24.1.33
  9. Stewart, J. (2007). Calculus, 6th ed., Cengage Learning, Stamford.
  10. Weisberg, S. (1985). Applied linear regression, Wiley, New York.

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