Model A \( \widehat{Y}=\widehat{\alpha}+\widehat{\beta}\cdotp X \) |
Model B \( \widehat{Y}=\widehat{\alpha}+\widehat{\beta}\cdotp { \log}_b(X) \) |
Model C \( \widehat{{ \log}_a(Y)}=\widehat{\alpha}+\widehat{\beta}\cdotp X \) |
Model D \( \widehat{{ \log}_a(Y)}=\widehat{\alpha}+\widehat{\beta}\cdotp { \log}_b(X) \) | ||
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Beta-hat coefficient and standard error from regression model |
\( \widehat{\beta} \) = 0.288 se(\( \widehat{\beta} \)) = 0.015 |
\( \widehat{\beta} \) = 1.517 se(\( \widehat{\beta} \)) = 0.133 |
\( \widehat{\beta} \) = 0.005 se(\( \widehat{\beta} \)) = 0.0003 |
\( \widehat{\beta} \) = 0.028 se(\( \widehat{\beta} \)) = 0.003 | |

Absolute change in Y for an absolute change of c units in X
| Effect size | 0.288 | 0.145 | 0.263 | 0.133 |

95% CI | (0.259–0.317) | (0.120–0.169) | (0.236–0.291) | (0.109–0.156) | |

Absolute change in Y for a relative change of k times in X
| Effect size | 0.288 | 0.145 | 0.263 | 0.133 |

95% CI | (0.259–0.317) | (0.120–0.169) | (0.236–0.291) | (0.109–0.156) | |

Relative change in Y for an absolute change of c units in X
| Effect size | 1.0058 | 1.0029 | 1.0053 | 1.0027 |

95% CI | (1.0052–1.0063) | (1.0024–1.0034) | (1.0047–1.0058) | (1.0022–1.0031) | |

Relative change in Y for a relative change of k times in X
| Effect size | 1.0058 | 1.0029 | 1.0053 | 1.0027 |

95% CI | (1.0052–1.0063) | (1.0024–1.0034) | (1.0047–1.0058) | (1.0022–1.0031) |