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Computer Simulates the Effect of Internal Restriction on Residuals in Linear Regression Model with First-order Autoregressive Procedures


  • Lee, Mei-Yu


This paper demonstrates the impact of particular factors – such as a non-normal error distribution, constraints of the residuals, sample size, the multi-collinear values of independent variables and the autocorrelation coefficient – on the distributions of errors and residuals. This explains how residuals increasingly tend to a normal distribution with increased linear constraints on residuals from the linear regression analysis method. Furthermore, reduced linear requirements cause the shape of the error distribution to be more clearly shown on the residuals. We find that if the errors follow a normal distribution, then the residuals do as well. However, if the errors follow a U-quadratic distribution, then the residuals have a mixture of the error distribution and a normal distribution due to the interaction of linear requirements and sample size. Thus, increasing the constraints on the residual from more independent variables causes the residuals to follow a normal distribution, leading to a poor estimator in the case where errors have a non-normal distribution. Only when the sample size is large enough to eliminate the effects of these linear requirements and multi-collinearity can the residuals be viewed as an estimator of the errors.

Suggested Citation

  • Lee, Mei-Yu, 2014. "Computer Simulates the Effect of Internal Restriction on Residuals in Linear Regression Model with First-order Autoregressive Procedures," MPRA Paper 60362, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:60362

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    Cited by:

    1. Mei-Yu LEE, 2014. "The Effect of Nonzero Autocorrelation Coefficients on the Distributions of Durbin-Watson Test Estimator: Three Autoregressive Models," Expert Journal of Economics, Sprint Investify, vol. 2(3), pages 85-99.

    More about this item


    Time series; Autoregressive model; Computer simulation; Non-normal distribution;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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