Bootstrap Sampling for Multiple Linear Regression (Lecture Notes for Lecture 17)

1. Describe the Case Resampling Bootstrap in the context of Multiple Linear Regression.
2. Use functions from confcurve to construct confidence curves, confidence intervals, and perform hypothesis testing for single coefficients for a Multiple Linear Regression model via bootstrapping.

The Problem of Multiple Comparisons (Lecture Notes for Lecture 17)

1. State the problem of multiple comparisons in the context constructing more than one confidence interval for population coefficients for a multiple linear regression model.
2. Perform computations for a toy model of multiple comparisons where \(m\) independent samples are used to construct confidence intervals for a collection of \(m\) population parameters.

The Bonferroni Correction for Multiple Comparisons (Lecture Notes for Lecture 17)

1. State the Bonferroni correction for adjusting the confidence levels of individual confidence intervals to attain an overall coverage of at least \(1 - \alpha\).
2. Construct Bonferroni corrected confidence curves, confidence intervals, and coefficient plots in R.

Confidence Ellipses for Multiple Comparisons (Lecture Notes for Lecture 17)

1. Define a confidence level \(c\) confidence ellipse for two population parameters.
2. Explain what the confidence level \(c\) for a confidence ellipse means.
3. Given a two or more confidence ellipses for the same population parameters constructed from the same sample and the confidence levels used to construct those confidence ellipses, match a confidence ellipse with its confidence level.
4. Construct confidence ellipses for two coefficients at a time using car::confidenceEllipse.