Bootstrapping to Approximate the Sampling Distribution of a Statistic (Lecture Notes for Lecture 8)

1. Explain why inferential statistics derived under the SLRGN model become “junk numbers” when the SLRGN model fails to hold.
2. Identify when inferential statistics derived under the SLRGN model are likely to be “junk numbers”.
3. Explain how a resampling-based inferential method replaces a model-based sampling distribution with a sampling distribution based on the sample itself.

The Case Resampling Bootstrap for Simple Linear Regression (Lecture Notes for Lecture 8)

1. Describe the procedure for the Case Resampling Bootstrap.
2. Given a scatter plot, explain how you could generate a bootstrap sample using the Case Resampling Bootstrap.
3. Explain the tradeoffs between small and large values for \(B\), the number of bootstrap samples.

The Percentile Bootstrap (Lecture Notes for Lecture 8)

1. Describe how to compute a percentile bootstrap confidence interval from bootstrapped estimates of parameter values.
2. State the name of the improved confidence interval method implemented in confcurve.

Confidence Curves from the Bootstrap Distribution (Lecture Notes for Lecture 8)

1. Explain how one can construct a bootstrapped confidence curve for a parameter value using the percentile bootstrap confidence interval.

\(P\)-values from the Bootstrapped Confidence Curve (Lecture Notes for Lecture 8)

1. Explain how one can compute a bootstrapped \(P\)-value for a two-sided hypothesis test using a bootstrapped confidence curve.

confcurve in R (Lecture Notes for Lecture 8)

1. Use bootcurve.lm to generate bootstrapped parameter estimates from a dataframe.
2. Use confcurve to compute a BCa bootstrap confidence interval for the population slope and intercept using an output from bootcurve.lm.
3. Use plot.confcurve to compute a BCa bootstrap confidence curve for the population slope and intercept using an output from bootcurve.lm.
4. Use confpvalue to compute bootstrapped two-sided \(P\)-values for the population slope and intercept using an output from bootcurve.lm.
5. Compare and contrast SLRGN-based and bootstrap-based confidence curves for the same data set in terms of how violations of the SLRGN model impact the properties of its inferential statistics.