Consider a scenario where a dataset (D) has 10 instances. Each of these instances is represented by 4 descriptive feature (F1, F2, F3 and F4) and has 1 target feature that takes binary values. Because the target feature is binary, only 1 bit is required to store the target value of each instance. Features F1, F2, F3 and F4 are all categorical, with 5, 4, 3, and 2 possible discrete values, respectively. The decision trees to be trained on D will be deployed and utilized to classify previously unseen instances on a high-performance computer, hence algorithm efficiency is not a concern. Given this context, which measure is the most appropriate for the ID3 algorithm to induce a decision tree using D?

What is the cost of the product associated with the transaction with an ID of 6000 in the given dataset?

What is the entropy of the last 10 instances of the given dataset?

Use rpart to build a decision tree based on the dataframe created from the given dataset. Train the model on only the descriptive features, but excluding ID. Set the parameters as follows: complexity parameter should be 0.001, the minimum split size should be 10, the minimum leaf size should be 5, and the maximum tree depth should be 3. How many instances are represented in the right most leaf node in the lowest level of the resulting decision tree?

Use rpart to build a decision tree based on the dataframe created from the given dataset. Train the model on only the descriptive features, but excluding ID. Set the parameters as follows: complexity parameter should be 0.001, the minimum split size should be 10, the minimum leaf size should be 5, and the maximum tree depth should be 2. How many instances are represented in the left most leaf node in the lowest level of the resulting decision tree?

Use rpart to build a decision tree based on the last 1000 instances from the given dataset. Train the model on only the descriptive features, but excluding ID. Set the parameters as follows: complexity parameter should be 0.01, the minimum split size should be 2, the minimum leaf size should be 1, and the maximum tree depth should be 5. Use this tree to make a prediction on the instance represented by the following vector (only the target feature is excluded from this vector): (10001,B,Flight,3,4,2412,3,high,F,6,5.68).

What is the gini index information gain of the instances with IDs in the range of [6000, 6020] when they are split on Product_importance? Note the range is inclusive of the boundary values.

What is the gini index of the instances with IDs in the range of [6000, 6020]? Note the range is inclusive of the boundary values.

What is the entropy information gain of the instances with IDs in the range of [6000, 6020] when they are split on Gender? Note the range is inclusive of the boundary values.