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On common linear regression problems and their solutions
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Zahra Jafarian Moorakani   , Heydar Ali Mardani-Fard * |
| Yasouj University |
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Abstract: (620 Views) |
| The ordinary linear regression model is $Y=Xbeta+varepsilon$ and the estimation of parameter $beta$ is: $hatbeta=(X'X)^{-1}X'Y$. However, when using this estimator in a practical way, certain problems may arise such as variable selection, collinearity, high dimensionality, dimension reduction, and measurement error, which makes it difficult to use the above estimator. In most of these cases, the main problem is the singularity of the matrix $X'X$. Many solutions have been proposed to solve them. In this article, while reviewing these problems, a set of common solutions as well as some special and advanced methods (which are less favored by someone, but still have the potential to solve these problems intelligently) to solve them. |
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| Keywords: Colliniarity, dimension reduction, measurement error, ridge regression, psuedo estimation, SIR regression |
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Full-Text [PDF 259 kb]
(583 Downloads)
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Type of Study: Research |
Subject:
Special
Received: 2022/10/12 | Accepted: 2023/03/1 | Published: 2023/03/10
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