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myrzilka [38]
2 years ago
6

Data analysts at Universal bank is building a classification tree to classify its customers into two classes: nonacceptors (clas

s 0) and acceptors (class 1) of personal loan offer. Each customer can be described by a set of attributes, such as age, experience, income, family size, education, average spending on credit cards per month, etc. The data analysts are in the process of identifying the most powerful predictor to split a set of training records (denoted by A). After splitting A with customer's family size, two subsets of records are generated, denoted by A1 and A2 respectively. The number of nonacceptors and acceptors in A, A1, and A2 are given below.
A A1 A2
Number of Nonacceptors 352 340 12
Number of Acceptors 223 36 187

Round your answers to 3 digits after the decimal point.

The Gini index of A is __________.
The Gini index of A1 is __________.
The Gini index of A2 is ___________.
Business
1 answer:
tresset_1 [31]2 years ago
4 0

Answer:

Check the explanation

Explanation:

Number of        Number of         The proportion of     The proportion of

Non Acceptors    Acceptors      Non-acceptors (p0)    Acceptors (p1)

A        352                 223                             100%                   100%

A1       348                  36                               99%                  16%

A2        4                     187                              1%                      84%

                                 Gini Index 1-(0.99)^2-(0.01)^2 1-(0.16)^2-(0.84)^2

                                                                            0.0198      0.2688

Combined Gini Index for A1 and A2:

                   Number of Non Acceptors Number of Acceptors Total

A                                352                                           223               575

A1                                348                                            36               384

A2                                    4                                             187             191

                                 Combined   Gini Index 1-(352/575)^2-(223/575)^2

                                                                                                         0.4748

Gini index if training records are split by customer's family size:

                      Number of Non Acceptors Number of Acceptors Total

A                                         352                                     223           575

A1                                          348                                    36             384

A2                                            4                                        187            191  

                                 Gini Index for this node 1-(352/575)^2-(223/575)^2

                                                                                                           0.4748

                                                          Gini (A1) 1-(348/384)^2-(36/384)^2

                                                                                                           0.1699

                                                          Gini (A2) 1-(4/191)^2-(187/191)^2

                                                                                                          0.0410

                             Gini (A1,A2) 0.4748-(384/575)^0.1699-(191/575)^0.0410

                                                                                                              -1.4147

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