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arXiv · 1508.02942

Galton's Family Heights Data Revisited

Hao Han·Yeming Ma·Wei Zhu
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Abstract

Galton's family heights data has been a preeminent historical dataset in regression analysis, on which the original model and basic results have survived the close scrutiny of statisticians for 125 years. However by revisiting Galton's family data, we challenge whether Galton's classic model and his regression towards mean interpretation are proper. Using Galton's data as a benchmark for different regression methods, such as least squares, orthogonal regression, geometric mean regression, and least sine squares regression - a newly developed nonparametric robust regression approach, we elucidate that his regression model has fundamental drawbacks not only in variable and model selection by "transmuting" women into men thus the simple linear model, but also a strong bias in least squares regression leading to otherwise alternative conclusions on the true relationships between the heights of the child and his or her parents.

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Hao Han, Yeming Ma, Wei Zhu. 2015-08-12. Galton's Family Heights Data Revisited. https://arxiv.org/abs/1508.02942

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