Estimate Family Proportions and Explain Regression Anomalies
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Estimate Family Proportions and Explain Regression Anomalies evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.
Scenario
On-site statistics round
Question
Population contains one-, two- and three-child families. Estimate the proportion of each family type from a sample of 100 children. Construct a 95 % confidence interval. Explain why the OLS coefficient of YX differs from XY and relate to causal direction. A regression model shows all coefficients statistically insignificant yet high predictive performance. Provide a statistical explanation and propose a fix.
Hints
Multinomial proportions, bootstrap CI; reverse causality; multicollinearity and LASSO/ridge.
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