Identifying Good System Administrators. A management consultant is studying the roles played by experience and training in a system administrator’s ability to complete a set of tasks in a specified amount of time. In particular, she is interested in discriminating between administrators who are able to complete given tasks within a specified time and those who are not. Data are collected on the performance of 75 randomly selected administrators. They are stored in the file SystemAdministrators.csv.

Using these data, the consultant performs a discriminant analysis. The variable Experience measures months of full-time system administrator experience, while Training measures number of relevant training credits. The dependent variable Completed is either Yes or No, according to whether or not the administrator completed the tasks.

a. Create a scatter plot of Experience vs. Training using color or symbol to differentiate administrators who completed the tasks from those who did not complete them. See if you can identify a line that separates the two classes with minimum misclassification.

b. Run a discriminant analysis with both predictors using the entire dataset as training data. Among those who completed the tasks, what is the percentage of administrators who are classified incorrectly as failing to complete the tasks?

c. Given the decision function shown below with the coefficients for Experience and Training, respectively, compute the classification score for an administrator with 4 months of experience and six credits of training. Based on this classification score, how would you classify this administrator?

Coefficients [[1.44469947 0.14427824]]

Intercept [-13.60512707]

d. How much experience must be accumulated by an administrator with four training credits before his or her estimated probability of completing the tasks exceeds 0.5? 

e. Compare the classification accuracy of this model to that resulting from a logistic regression with cutoff 0.5.