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Exercise

Modeling SAT scores

We've trained three models relating school expenditures to SAT scores and computed bootstrap replications of effect size for each:

# Train models
mod_1 <- lm(sat ~ expend, data = SAT)
mod_2 <- lm(sat ~ expend + frac, data = SAT)
mod_3 <- lm(sat ~ expend * frac, data = SAT)

# Bootstrap replications of effect size
sizes_1 <- effect_size(ensemble(mod_1, nreps = 100), ~ expend)
sizes_2 <- effect_size(ensemble(mod_2, nreps = 100), ~ expend)
sizes_3 <- effect_size(ensemble(mod_3, nreps = 100), ~ expend)

The results are available in your workspace. Compare the models using:

  • Cross-validated prediction error
  • Inflation due to collinearity
  • The standard error of effect size of expend on sat

Which of these statements is true?

  1. Cross-validated prediction error favors mod_2 slightly over mod_3 and greatly over mod_1.
  2. Inflation due to collinearity is somewhat less in mod_1 than in mod_2, and much less than in mod_3.
  3. mod_3 has the narrowest confidence interval on the effect size of expend on sat.
Instructions
50 XP
Possible Answers