Please answer all questions below. Thank you very much.

d. A financial services company offers a home equity line of credit to its clients. The company has extended several thousand lines of credit in the past, and some of these accepted applicants have defaulted. The following decision tree model was built to classify a defaulter (Default = 1, Not default = 0) based on a sample of 2000 past applicants. = 1 50.0% 1000 0 50.0% 1000 Total 100.0% 2000 Debito income to 1 21.9% 250 o 78.1% 901 Total 100.0% 1154 88.3% 0 11.7% Total 100.0% 747 99 846 Number of deinguery wade Ines (2] >-31 59 18.5% 1941 0 81.5% 855 Total 100.0% 1049 56.2% 0 43.8% Total 100.0% 46 105 Age of oldest trade ine in months 1831 182 25.8% 0 74.2% Total 100.0% 15711 8.4% 452110 91.6% 609 Total 100.0% 37 405 440 (i) List all of the rules derived from the above decision tree. [4 marks] (ii) Construct a confusion matrix showing the frequency of all events for the above decision tree at a cut-off value of 0.5. [3 marks] (iii) Suppose the company received two applications with the details in the following table. What is the predicted score of default for each applicant? Application 1 Application 2 40 39 Variables Debt to income ratio (%) Number of delinquent trade lines Age of oldest trade line in months 1 4 250 200 [2 marks] d. A financial services company offers a home equity line of credit to its clients. The company has extended several thousand lines of credit in the past, and some of these accepted applicants have defaulted. The following decision tree model was built to classify a defaulter (Default = 1, Not default = 0) based on a sample of 2000 past applicants. = 1 50.0% 1000 0 50.0% 1000 Total 100.0% 2000 Debito income to 1 21.9% 250 o 78.1% 901 Total 100.0% 1154 88.3% 0 11.7% Total 100.0% 747 99 846 Number of deinguery wade Ines (2] >-31 59 18.5% 1941 0 81.5% 855 Total 100.0% 1049 56.2% 0 43.8% Total 100.0% 46 105 Age of oldest trade ine in months 1831 182 25.8% 0 74.2% Total 100.0% 15711 8.4% 452110 91.6% 609 Total 100.0% 37 405 440 (i) List all of the rules derived from the above decision tree. [4 marks] (ii) Construct a confusion matrix showing the frequency of all events for the above decision tree at a cut-off value of 0.5. [3 marks] (iii) Suppose the company received two applications with the details in the following table. What is the predicted score of default for each applicant? Application 1 Application 2 40 39 Variables Debt to income ratio (%) Number of delinquent trade lines Age of oldest trade line in months 1 4 250 200 [2 marks]