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| Format: | Recurso digital |
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Zenodo
2023
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| Online Access: | https://doi.org/10.5281/zenodo.20177750 |
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| _version_ | 1866901757568745472 |
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| author | Maccallini, Paolo |
| author_facet | Maccallini, Paolo |
| contents | <p>This Italian paper proves two key relationships linking multiple linear regression coefficients to simple linear regression coefficients. Working in mean-centered (normalized) coordinates, it shows that the multiple regression slope vector <strong>B</strong> can be expressed as a linear transformation of the simple regression slopes <strong>A</strong> via the matrix (Ξᵀ Ξ)⁻¹Ξ_D, and equivalently that the simple slopes satisfy <strong>A</strong> = Γᵀ<strong>B</strong>, where Γ contains pairwise regression coefficients between the predictors. Variance formulas for both simple and multiple regression estimators are derived, and the paper closes with two reference synopses summarizing standard results for simple and multiple linear regression.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20177750 |
| institution | Zenodo |
| language | |
| publishDate | 2023 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Sul legame tra i coefficienti di regressione lineare multipla e quelli di regressione lineare semplice Maccallini, Paolo <p>This Italian paper proves two key relationships linking multiple linear regression coefficients to simple linear regression coefficients. Working in mean-centered (normalized) coordinates, it shows that the multiple regression slope vector <strong>B</strong> can be expressed as a linear transformation of the simple regression slopes <strong>A</strong> via the matrix (Ξᵀ Ξ)⁻¹Ξ_D, and equivalently that the simple slopes satisfy <strong>A</strong> = Γᵀ<strong>B</strong>, where Γ contains pairwise regression coefficients between the predictors. Variance formulas for both simple and multiple regression estimators are derived, and the paper closes with two reference synopses summarizing standard results for simple and multiple linear regression.</p> |
| title | Sul legame tra i coefficienti di regressione lineare multipla e quelli di regressione lineare semplice |
| url | https://doi.org/10.5281/zenodo.20177750 |