A training set has 10 examples, 6+ and 4-. You are considering two possible splits when generating the next level in your decision tree.
Split 1: If you split on the binary feature sex, the branch on the value "male" will have 2+ and 0- and the branch on the value "female" will have the 4+ and 4-.
Split 2: If you split on the binary feature college-grad, the branch on the value "yes" will have 4+ and 2- and the branch on the value "no" will have 2+ and 2-.
You must show your work when answering the question below or you may not receive any credit. You don’t have to show every minor calculation, but you need to show all of the major formulas and the key calculations. Please simplify your answer for the parts that easily simplify; otherwise feel free to leave your answer unsimplified, but please write your equations clearly.
a) The Gini for Split 1 is: _____________________________________ (Show work below!)
b) The Gini for Split 2 is: _____________________________________ (Show work below!)
jtjptGINI2)]|([1)(
Page 6 of 6
Long Answer Question #1b (8 points)
This is the same question as 1a but with error rate instead of Gini. I copied the preamble to the problem below so that you do not need to flip back and forth.
A training set has 10 examples, 6+ and 4-. You are considering two possible splits when generating the next level in your decision tree.
Split 1: If you split on the binary feature sex, the branch on the value "male" will have 2+ and 0- and the branch on the value "female" will have the 4+ and 4-.
Split 2: If you split on the binary feature college-grad, the branch on the value "yes" will have 4+ and 2- and the branch on the value "no" will have 2+ and 2-.
This problem is worth fewer points than part 1a. While you need to justify your answers, you may do so with just a couple of sentences if you do this problem in the easiest possible way.
a) Error rate associated with Split 1: __________________________________
b) Error rate associated with Split 2: ___________________________________
c) Will either of these splits improve the error rate from the original training set before the split? Circle one: Yes No
Now briefly justify your answer below:
