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On Choosing an Adequate Linear Model for the Experiment and Dropping of Structurally Stable Observations

Written by A. M. Revyakin, I. V. Bardushkina

The authors did consider the task of choosing an adequate model for the experiment data. For the most accurate estimates of the model parameters and optimization of calculations they have proposed to make the columns of the experiment matrix orthogonal. For determination of the model dimension the authors did use confidence intervals for the selected model. The hypothesis about the outlier presence is verified using the criteria of L. N. Bolshev. This type of task is offered to students as a course work and is performed using MATLAB, Excel or specialized packages for statistical data analysis (STATISTICA, STATGRAPHIC, STADIA and SPSS).

Keywords: Regression Analysis; adequate model; Ordinary Least Squares; condition number; outlier; orthogonal matrix; orthogonalization process; course work.

References

  1. Revyakin A. M., Bardushkina I. V. Ob osobennostyakh vypolneniya kursovoi raboty po statistike s primeneniem elektronnogo komponenta (On the Specifics of Statistics Coursework Realization with the Use of Electronic Components for the Students’ Independent Work), Ekonomicheskie i sotsial’no-gumanitarnye issledovaniya, 2017, No. 1 (13), pp. 112—122.
  2. Bardushkina I. V., Revyakin A. M. K voprosu o povyshenii kachestva samostoyatel’noi raboty studentov po vysshei matematike (Towards Improving Quality of Students’ Independent Work on the Higher Mathematics), Ekonomicheskie i sotsial’no-gumanitarnye issledovaniya, 2015, No. 4 (8), pp. 57—62.
  3. Zadaniya dlya vypolneniya laboratornykh i individual’nykh rabot po kursu “Teoriya veroyatnostei i matematicheskaya statistika” s ispol’zovaniem paketa MATLAB (Tasks for Laboratory and Independent Work in “Theory of Probability and Mathematical Statistics” Course Using MATLAB Software), by V. V. Bardushkin, I. V. Bardushkina, V. V. Lesin, A. M. Revyakin, Proektirovanie inzhenernykh i nauchnykh prilozhenii v srede MATLAB: Mat-ly V Mezhdunar. nauch. konf. (g. Khar’kov, 11—13 maya 2011 g.), Sost. V. V. Zamaruev, Khar’kov, BET, 2011, pp. 471—533.
  4. Teoriya i praktika statisticheskikh issledovanii (Theory and Practice of Statistical Investigations), Pod red. A. M. Revyakina, V. V. Kostyleva, M., MGADA, 2007, 354 p.
  5. Draiper N., Smit G. Prikladnoi regressionnyi analiz, v 2 kn. (Applied Regression Analysis, in 2 Books), M., Finansy i statistika, 1986.
  6. Revyakin A. M. Vysshaya algebra (Higher Algebra), M., MIET, 2007, 504 p.
  7. Osobennosti vychisleniya tenzora po difraktometricheskim izmereniyam prodol’noi deformatsii (Peculiarities of Tensor Calculation by Diffractometric Measurement of Longitudinal Strains), D. M. Gulidov, M. O. Vargulevich, K. A. Tuzovskii, A. M. Revyakin, B. Malyukov, Zavodskaya laboratoriya, 1989, No. 2, pp. 57—59.
  8. Bol’shev L. N. Ob isklyuchenii grubykh nablyudenii (On Dropping of Structurally Stable Observations), Teoriya veroyatnostei i ee primenenie, M., Nauka, 1961, T. 6, Vyp. 4, pp. 482—484.
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