Sir Francis Galton (1822-1911), an Anthropologist and Cousin of Charles $\widehat { \text { Studenth } } = 19.6 + 0.73 \times \text { Midparh, } R ^ { 2 } = 0.45 , \text { SER } = 2.0$

question 30

Essay

Sir Francis Galton (1822-1911), an anthropologist and cousin of Charles Darwin, created
the term regression.In his article "Regression towards Mediocrity in Hereditary Stature,"
Galton compared the height of children to that of their parents, using a sample of 930
adult children and 205 couples.In essence he found that tall (short)parents will have tall
(short)offspring, but that the children will not be quite as tall (short)as their parents, on
average.Hence there is regression towards the mean, or as Galton referred to it,
mediocrity.This result is obviously a fallacy if you attempted to infer behavior over time
since, if true, the variance of height in humans would shrink over generations.This is not
the case.
(a)To research this result, you collect data from 110 college students and estimate the
following relationship: $\widehat { \text { Studenth } } = 19.6 + 0.73 \times \text { Midparh, } R ^ { 2 } = 0.45 , \text { SER } = 2.0$
$(7.2) \quad(0.10)$ where Studenth is the height of students in inches and Midparh is the average of the
parental heights.Values in parentheses are heteroskedasticity-robust standard errors.
Sketching this regression line together with the 45 degree line, explain why the above
results suggest "regression to the mean" or "mean reversion."

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