Question

solve using gini index and give the decision tree

cid marital housingHas_loarApproveloan job age young married yes divorced no married single divorced no married married single married divorce yes Jabeuew married yes manager es no Senior retired middle age technician bunon manager no es 3 no no yes 4 no no no middle agemanager middle agmanager Senior 5 no no 6 no no no manager 7 no no no young manager middle_agemanager middle agemanager young young 8 es no yes 9 no yes no 10 no no 11 no yes 12 single single single manager yes no yes young manager 13 no no no young manager middle_agemanager Senior 14 es married married single no yes 15 no yes no retired technioian 16 no no no young Senior 17 yes married yes marriedyes divorced no married yes married married marriedyes single yes no retired middle agdretired Senior 18 no no 19 no no retired middle_age technician young 20 no yes 21 no no technician middle_age technician technician 22 no no no 23 no no no young 24 no yes yes technician bunon 25 yes married single no 26 Senior retired no no no young technician 27 no no no

Answer 1

THERE ARE TWO METHODS FOR DECISION TREE :-

1. INFORMATION GAIN

2. GINI INDEX

IN THIS QUESTION, WE HAVE TO FIND DECISION TREE BY GINI INDEX METHOD.

THE FORMULA USED IN GINI INDEX IS

GiniInde 1 -p

AND TO FIND GINI INDEX FOR ATTRIBUTES WE HAVE TO ADD WEIGHT AND SUM OF EACH GINI INDICES IN THE ATTRIBUTE.

THE GINI INDICES FOR DIFFERENT VARIABLES IS AS FOLLOWS :-

TOTAL CID = 27 attribute age young 12 yes = 6 no = 6 gini index for age = young is 0.5 probality of age probality of age probality of age young is 12/27 young and Approve_loan = yes is 6/12 young and Approve_loan = no is 6/12 middle_age 6 probality of age yes = 1 middle_age is 6/27 probality of age = middle_age and Approve_loan = yes is 1/6 probality of age middle_age and Approve_loan = no is 5/6 no =5 gini index for age = middle_age is 0.27778 probality of age probality of age = senior and Approve_loan = yes is 2/9 probality of age = senior and Approve_loan = no is 7/9 senior is 9/27 senior 9 yes = 2 no 7 gini index for age = senior is 0.34567 gini index for age is 0.39917

attribute job probality of job probality of job = manager and Approve_loan probality of job = manager and Approve_loan = no is 9/13 manager 13 manager is 13/27 yes is 4/13 yes no 9 gini index for job = manager is 0.42603 probality of job probality of job = retired and Approve_loan = yes is 2/6 probality of job = retired and Approve_loan = no is 4/6 retired is 6/27 retired 6 2 yes no =4 gini index for job = retired is 0.44444 technician 8 probality of job technician is 8/27 probality of job = technician and Approve_loan = yes is 3/8 probality of job = technician and Approve_loan = no is 5/8 yes 3 no 5 gini index for job = technician is 0.46375 gini index for job is 0.44277

attribute marital probality of marital = married is 15/27 probality of marital = married and Approve_loan = yes is 3/15 probality of marital = married and Approve_loan = no is 12/15 married 15 yes= 3 no 12 gini index for marital = married is 0.32 probality of marital probality of marital = divorced and Approve_loan = yes is 2/4 probality of marital = divorced and Approve_loan = no is 2/4 divorced 4 divorced is 4/27 yes = 2 2 no = gini index for marital divorced is 0.5 probality of marital = single is 8/27 probality of marital = single and Approve_loan = yes is 4/8 probality of marital = single and Approve_loan = no is 4/8 single 8 yes = 4 4 no gini index for marital = single is 0.5 gini index for marital is 0.4

attribute housing probality of housing probality of housing = yes and Approve_loan = yes is 6/12 probality of housing yes and Approve_loan = no is 6/12 yes is 12/27 yes 12 yes = 6 no = 6 gini index for housing = yes is 0.5 probality of housing = no is 15/27 probality of housing = no and Approve_loan = yes is 3/15 probality of housing = no and Approve_loan = no is 12/15 no 15 yes = 3 12 no = gini index for housing = no is 0.32 gini index for housing is e.4 attribute Has_loan

attribute Has_loan yes is 4/27 yes and Approve_loan yes 4 yes probality of Has_loan probality of Has_loan probality of Has_loan = yes and Approve_loan = no is 1 yes is e 4 gini index for Has_loan = yes is 0 probality of Has_loan = no is 23/27 probality of Has_loan = no and Approve_1loan probality of Has_loan = no and Approve_loan = no is 14/23 : 23 no yes is 9/23 yes 14 no = gini index for Has_loan = no is 0.47637 gini index for Has_loan is 0.40579

ATTRIBUTE GINI INDEX 0.42603 age job 0.44277 marital 0.4 housing 0.4 Has_loan 0.40579

THE DECISION TREE FROM GINI INDEX METHOD IS DRAWN BY TAKING THE MINIMUM GINI INDEX VALUE FIRST AND SO ON.

THE DECISION TREE FOR THE GIVEN QUESTION IS AS FOLLOWS :-

HOUSING? .YES NO. MARITAL? MARITAL? SINGLE DIVORCED MARRIED DIVORCED MARRIED SINGLE HAS LOAN? HAS_LOAN? HAS LOAN? HAS LOAN? HAS LOAN? HAS LOAN? YES NO YES YES NO YES YES NC NO NO YES NC NO NO NO NO NO NO AGE? AGE? AGE? AGE? AGE? AGE? YOUNG YOUNG SENIOR YOUNG SENICR YOUNG SENIOR YOUNG ENIOR YOUNG SENOR SENIOR MDDLE AGE MODLEAGE MODLE AGE MDOLE AGE MODLE AGE MODLE AGE JоB? JOB JоB? JOB? JоB? JOB? JоB? JоB? JOB? Jов? JOB? JOB? JOB? JOB? JOB? JOB? JOB? JOB? YES) (NO ES) (NO YES (NO YES) (NO YES) (NO YES (NO YES YES) (NO YES) (NO Activate Windows YES) (NO NO YES (NO