1. Here we explore the maximal margin classifier on a toy data set.
  1. We are given \(n = 7\) observations in \(p = 2\) dimensions. For each observation, there is an associated class label. Sketch the observations.
  2. Sketch the optimal separating hyperplane, and provide the equation for this hyperplane in the form of textbook equation 9.1.
  3. Write the classification rule for the maximal margin classifier.
  4. On your sketch, indicate the margin for the maximal margin hyperplane.
  5. Indicate the support vectors for the maximal margin classifier.
  6. Argue that a slight movement of observation 4 would not affect the maximal margin hyperplane.
  7. Sketch a separating hyperplane that is not the optimal separating hyper- plane, and provide the equation for this hyperplane.
  8. How would the separating hyperplane change if an 8th observation (8, 2, 2.5, 1) as added to the data? List the support vectors, and write the equation of the plane.
  1. Bagging and boosting on the ISLR caravan data set. Questions 1-4 from lab 8.

  2. Now scramble the response variable (Purchase) using permutation. The resulting data has no true relationship between the response and predictors. Re-do Q2 with this data set. Write a paragraph explaining what you learn about the true data from analysing this permuted data.