Understanding Regression: Predicting Heights of Sons Based on Father's Height
This analysis, based on the work of Pearson and Lee in 1906, explores the concept of regression by examining the relationship between fathers' and sons' heights. It reveals that, on average, tall fathers tend to have sons who are not as tall, and short fathers have sons who are not as short. This regression effect highlights how extreme traits in parents may be moderated in their offspring. Additionally, the text warns against the regression fallacy, which is the misconception of attributing causal meaning to the observed regression effects.
Understanding Regression: Predicting Heights of Sons Based on Father's Height
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Presentation Transcript
Heights of sons Pearson & Lee, Biometrika 2:357-462, 1906 average = 69.2 in.
Heights of fathers and sons average = 68.4 in.
Heights of fathers and sons average = 69.5 in.
Summary • Regression concerns predicting Y from X. • There are two regression lines. • The regression effect: • Tall fathers, on average, have sons who are not so tall. • Short fathers, on ave., have sons who are not so short. • The regression fallacy: assigning some deeper (causal) meaning to the regression effect.
