**Week 6: Assignment 6 Solutions for Machine Learning Course**

**Description:**

Find all the answers and explanations for Week 6: Assignment 6 of the "Introduction to Machine Learning" course. This article will provide a detailed breakdown of each question, along with the correct answers and the reasoning behind them. Ideal for students looking to understand the concepts better and prepare for their assignments.

**Question 1: Entropy for a 90-10 split between two classes is:**

**a) 0.469****b) 0.165****c) 0.204****d) None of the above**

**Answer:** a) **0.469**

**Reason:**

Entropy is a measure of impurity or disorder in a set. For a 90-10 split, the entropy is calculated using the formula:

$\text{Entropy} = -p \log_2(p) - (1-p) \log_2(1-p)$

Where $p = 0.9$ and $1-p = 0.1$. Plugging in these values gives an entropy of approximately 0.469.

**Question 2: Consider a dataset with only one attribute (categorical). Suppose there are 8 unordered values in this attribute, how many possible combinations are needed to find the best split point for building the decision tree classifier?**

**a) 511****b) 120****c) 512****d) 127**

**Answer:** c) **512**

**Reason:**

For a categorical attribute with 8 unordered values, each value can either be on the left or right side of the split. This leads to $2^8$ combinations, minus the case where all values are on one side, resulting in 512 combinations.

**Question 3: Having built a decision tree, we are using reduced error pruning to reduce the size of the tree. We select a node to collapse. For this particular node with 8 branches, there are remaining data points with the following outputs: 5, 7, 9, 6, and 8 for the left branch. The other remaining data points along the branches of 3, 6, 5, 11, and 7. What are the values for response_left, response_right?**

**a) 6, 9****b) 7, 8, 10, 11, 6****c) 5, 8, 9****d) None of the above**

**Answer:** **Explanation needed to solve this.**