Drop hier links of afbeeldingen om ze aan de editor toe te voegen.

This problem makes use of the Carseats dataset in he ISLR2 package.

Questions

  1. For each quantitative variable in the dataset besides Sales, fit a linear model to predict Sales using that quantitative variable. Report the p-values associated with the coefficients for the variables. That is, for each model of the form \(Y = \beta_0 + \beta_1 X + \epsilon\), report the p-value associated with the coefficient \(\beta_1\). Here, \(Y\) represents Sales and \(X\) represents one of the other quantitative variables. Store the p-values in a variable p.values. (check the example code below)

  2. Suppose we control the Type I error at level \(\alpha = 0.05\) for the p-values obtained in the first exercise. Which null hypotheses do we reject? Store your answer in the variable rejected.null.hypotheses. Hint: you can make use of the function which().

  3. Now suppose we control the FWER at level 0.05 for the p-values. There are 2 possible methods to do this.
    MC1: Which method is the least conservative?
    1. Bonferroni
    2. Holm

    Which null hypotheses do we reject using that least conservative method? Store the adjusted p-values in p.values.fwer and store your answer in the variable rejected.null.hypotheses.FWER.

  4. Finally, suppose we control the FDR at level 0.2 for the p-values. Which null hypotheses do we reject? Store the adjusted p-values in p.values.fdr and store your answer in the variable rejected.null.hypotheses.FDR.

Assume that: