Answer the following question using the table given. 1. How does decision tree algorithm work? Define in your own words. What is the goal at each split? How can you define impurity? 2. What is the formulae for entropy and gini index? 3. What is the gini index at the initial state? 4. What is the entropy at the initial state? 5. What is the information gain splitting on temperature as your first split using gini index? Split into each group separately (split into warm, cold, and hot) 6. What is the information gain splitting on weather as your first split using gini index? Split into each group separately. 7. Based on questions 5 and 6, which variable would be chosen for the first split using gini index, weather or temperature? 8. What is the information gain splitting on temperature as your first split using entropy measure? Split into each group separately (split into warm, cold, and hot) 9. What is the information gain splitting on weather as your first split using entropy measure? Split into each group separately. 10. Based on questions 8 and 9, which variable would be chosen for the first split using entropy measure, weather or temperature? weather temperature jogging sunny warm yes sunny warm yes rainy cold no rainy warm yes rainy cold no rainy cold no sunny hot rainy warm rainy hot 222 no no no sunny cold no sunny cold no sunny cold yes sunny warm yes sunny hot no sunny hot yes rainy hot yes rainy hot no rainy cold yes sunny cold yes sunny cold no sunny hot yes sunny warm no sunny warm no sunny warm yes sunny hot yes