hw-11

Homework 11 in STAT400 @ CSU

Assignment

Be sure to set.seed(400) at the beginning of your homework. Please use \(2000\) bootstrap samples in the problems below.

1. This data set is the cars data in R. The goal is to create a regression model about the relationship between stopping distance (dist) and speed (speed) in cars.

   1. Create a scatter plot of speed vs. dist in mpg and describe the relationship.
   2. Fit a simple linear model of dist on speed. Describe the result, including diagnostic plots, and create 95% CIs for the coefficients.
   3. Perform the paired bootstrap and compute the bootstrap bias and standard error for the coefficients. Construct 4 types of intervals that we discussed in class by using type=c("norm","basic", "perc", "bca") in the boot.ci command.
   4. Perform the bootstrap using the residuals and compute the bootstrap bias and standard error for the coefficients. Construct 4 types of intervals that we discussed in class by using type=c("norm","basic", "perc", "bca") in the boot.ci command.
   5. Which method (simple linear regression, paired bootstrap, or bootstrap using the residuals) would you use for this dataset and why?

Turn in in a pdf of your homework to canvas. Your .Rmd file on the server will also be used in grading, so be sure they are identical and reproducible.