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17 May 2022 To measure the influence of collinearity effectively: the deficiency of condition number and an improvement of main squared error
Weili Wang
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Proceedings Volume 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022); 1225920 (2022) https://doi.org/10.1117/12.2638802
Event: 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing, 2022, Kunming, China
Abstract
We frequently use condition number ( ) to judge the collinearity of a linear regression model. If the is large, we tend to believe the result of the least square estimate (LSE) is unreliable. However, in this article, we will give an example to show that is not a perfect indicator to reflect the influence of collinearity. In some cases, a model with high collinearity is quite likely to give an ideal LSE. Therefore, we put forward relative mean squared error ( ) to judge whether the collinearity significantly influences the LSE. Though is not theoretically perfect now, it indeed does better than when tested by the data we generate.
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Weili Wang "To measure the influence of collinearity effectively: the deficiency of condition number and an improvement of main squared error", Proc. SPIE 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), 1225920 (17 May 2022); https://doi.org/10.1117/12.2638802
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KEYWORDS
Condition numbers
Error analysis
Data modeling
Statistical modeling
Mathematics
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