The Royalty Gold Corporation prospects for undiscovered gold deposits around the world. The company is currently investigating a possible site on the island of Milos off the coast of Greece in the Mediterranean. When prospecting, the company drills to collect soil and rock samples and then analyzes the chemical properties of the samples to help determine whether or not the site is likely to contain significant gold deposits. Gold is made up of various elements including calavarite, sylvanite, and petzite. Sites with higher concentrations of these elements are more likely to contain significant gold deposits. The company has collected the data found in the file RoyalGold.xlsm accompanying this book representing the average levels of calavarite, sylvanite, and petzite in samples collected from previous various sites examined in previous prospecting expeditions. These data are grouped according to whether or not significant gold deposits were found at the location (1 = significant, 2 = insignificant).

a. What are the coordinates of the centroids for the good students and the weak students?

b. Use XLMiner’s standard data partition command to partition the data into a training set (with 60% of the observations) and validation set (with 40% of the observations) using the default seed of 12345.

c. Use discriminant analysis to create a classifier for this data. How accurate is this procedure on the training and validation data sets?

d. Use logistic regression to create a classifier for this data. How accurate is this procedure on the training and validation data sets?

e. Use the k-nearest neighbor technique to create a classifier for this data (with normalized inputs and a k = 3). How accurate is this procedure on the training and validation data sets?

f. Use the k-nearest neighbor technique to create a classifier for this data (with normalized inputs). What value of k seems to work best? How accurate is this procedure on the training and validation data sets?

g. Use a classification tree to create a classifier for this data (with normalized inputs and at least 4 observations per terminal node). Write pseudo-code summarizing the classification rules for the optimal tree. How accurate is this procedure on the training and validation data sets?

h. Use a neural network to create a classifier for this data (use normalized inputs and a single hidden layer with 3 nodes). How accurate is this procedure on the training and validation data sets?

i. Return to the Data sheet and use the Transform, Bin Continuous Data command to create binned variables for Calavarite, Sylvanite, and Petzite. Use XLMiner’s standard data partition command to partition the data into a training set (with 60% of the observations) and validation set (with 40% of the observations) using the default seed of 12345. Now use the Naïve Bayes technique to create a classifier for the data using the new binned variables for Calavarite, Sylvanite, and Petzite. How accurate is this procedure on the training and validation data sets?

j. Which of the classification techniques would you recommend the company actually use?

k. Suppose the company analyzes five sites on Milos that produce the following average levels of calavarite, sylvanite, and petzite. According to your recommended classifier, which of these sites, if any, should be considered for further analysis?

Site	Calavarite	Sylvanite	Petzite
1	0.058	0.041	0.037
2	0.045	0.023	0.039
3	0.052	0.023	0.044
4	0.043	0.042	0.056
5	0.050	0.032	0.038