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Consider the following hypothetical. Let $y$ be the height of a child and $x$ be the height of their parent, and consider a regression of
Consider the following hypothetical. Let $y$ be the height of a child and $x$ be the height of their parent, and consider a regression of $y$ on $x$, performed in in a large population. Suppose that we estimate the regression coefficients separately for male and female parents (two separate regressions) and we find that the slope coefficient from the former regression $\hat\beta_1^{\text{dad}}$ is smaller than that from the latter $\hat\beta_1^{\text{mom}}$. Suppose however that we find (in this same population) the sample correlation between a father's height and their child's height is larger than that between a mother's height and their child's height. What is a plausible explanation for what is happening here
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