Instructions

In this lab, you will begin to get oriented with R and work with some data.

How to complete this assignment.

  • Attempt each exercise in order.

  • In each code chunk, if you see “# INSERT CODE HERE”, then you are expected to add some code to create the intended output (Make sure to erase “# INSERT CODE HERE” and place your code in its place).

  • If my instructions say to “Run the code below…” then you do not need to add any code to the chunk.

  • Many exercises may require you to type some text below the code chunk, interpreting the output and answering the questions.

  • Please follow the Davidson Honor Code and rules from the course syllabus regarding seeking help with this assignment.

How to submit this assignment.

  • When you are finished, click the “Knit” button at the top of this panel. If there are no errors, an word file should pop up after a few seconds.

  • Take a look at the resulting word file that pops up. Make sure everything looks correct, your name is listed at the top, and that there is no ‘junk’ code or output.

  • Save the word file (to your local computer, and/or to a cloud location) as: Lab 8 “Insert Your Name”.

  • Use this link to upload your word file to my Google Drive folder. Do not upload the original .Rmd version.

  • This assignment is due Thursday, August 4, 2022, no later than 9:30 am Eastern. Points will be deducted for late submissions.

  • TIP: Start early so that you can troubleshoot any issues with knitting to word.

Grading Rubric

There are 6 possible points on this assignment.

Baseline (C level work)

  • Your .Rmd file knits to word without errors.
  • You answer questions correctly but do not use complete sentences.
  • There are typos and ‘junk code’ throughout the document.
  • You do not put much thought or effort into the Reflection answers.

Average (B level work)

  • You use complete sentences to answer questions.
  • You attempt every exercise/question.

Advanced (A level work)

  • Your code is simple and concise.
  • Unnecessary messages from R are hidden from being displayed in the word.
  • Your document is typo-free.
  • At the discretion of the instructor, you give exceptionally thoughtful or insightful responses.

Exercise 1. (6 points)

We have seen that we can fit an SVM with a non-linear kernel in order to perform classification using a non-linear decision boundary. We will now see that we can also obtain a non-linear decision boundary by performing logistic regression using non-linear transformations of the features.

  1. Generate a data set with n = 500 and p = 2, such that the observations belong to two classes with a quadratic decision boundary between them. For instance, you can do this as follows:
  • \(x1 <- runif(500) - 0.5\)
  • \(x2 <- runif(500) - 0.5\)
  • \(y <- 1 * (x1^2 - x2^2 > 0)\)

  1. Plot the observations, colored according to their class labels. Your plot should display \(X_1\) on the x-axis, and \(X_2\) on the y-axis.

  2. Fit a logistic regression model to the data, using \(X_1\) and \(X_2\) as predictors.

  3. Apply this model to the training data in order to obtain a predicted class label for each training observation. Plot the observations, colored according to the predicted class labels. The decision boundary should be linear.

  4. Now fit a logistic regression model to the data using non-linear functions of \(X_1\) and \(X_2\) as predictors (e.g. \(X_1^2, X_1 \times X_2, log(X_2)\), and so forth).

  5. Apply this model to the training data in order to obtain a predicted class label for each training observation. Plot the observations, colored according to the predicted class labels. The decision boundary should be obviously non-linear. If it is not, then repeat (a)-(e) until you come up with an example in which the predicted class labels are obviously non-linear.

  6. Fit a support vector classifier to the data with \(X_1\) and \(X_2\) as predictors. Obtain a class prediction for each training observation. Plot the observations, colored according to the predicted class labels.

  7. Fit a SVM using a non-linear kernel to the data. Obtain a class prediction for each training observation. Plot the observations, colored according to the predicted class labels.

  8. Comment on your results

#insert code here

ANSWER: