Would Taiwanese Customers Default on Their Loan Repayments - Report Example

Report on Whether Taiwanese Customers will Default on their Loan Repayments Name: Year: Table of Contents Introduction 3 1A. Initial Data Exploration 3 Attribute type 3 Nominal 3 Ordinal 4 Interval 4 Ratio 4 2. Summarizing Properties 5 Means 5 Median 5 Range 6 Frequencies/Mode 7 Distributions 7 Measures of spread (Variance and standard deviation) 8 Percentiles and Inter-quartile range 8 1B Preprocessing 9 a. Binning 9 Equi-width binning 9 Equi-depth binning 10 b. Normalization 10 Min-max normalization 10 Z-score normalization 11 c. Discretization 11 d. Education Binarization 12 Summary 14 References 15 Introduction This report presents data analytical results that seek to help in determining whether or not, the Taiwanese customers would repay their loans. The determination of whether they will pay or not depends on the reliability of the data in making such a decision. The reliability measures is based on the distribution characteristics of the attributes of data (Shevlyakov and Vilʹchevskiĭ, 2002). The conclusion on the matter is based on the analytical results of the current records. The analytical results of the given data is as follows. Note: The year of reference in this report is 2005 1A. Initial Data Exploration Attribute type For this dataset, the data attributes are identified as either nominal, ordinal, interval or ratio. The loan information contained in dataset included the customer id, loan limit balance, gender, education, marital status, age, past monthly payment records, bill statement, and defaulting information. Nominal According to Stephens (2009), nominal data/scale can simply be described as a name or better put, label. In this sample data, the nominal data includes the customer Id, marital status (dichotomous), sex (dichotomous) and default status (dichotomous). Ordinal An ordinal data set/scale is one which has hierarchical dimensions. I.e, order matters. In this particular case, the data that order matters include education, repayment delay status (Stephens , 2009). Interval Interval scales can be described as the numeric scales in which not only the order, but also the exact differences between the values. The given classic example would be temperature. There is no such thing as ‘no temperature’ and 40 and 50 degrees celcius is the difference between 90 and 100 degrees Celcius is the same 10 degrees. Interval scales can give an easier realm of statistical analysis on the data sets. In this particular case, data attribute with such characteristics is the age, limit balance, monthly amount paid, monthly bill statement. Ratio Stephens (2009) describes ratio scales as data which can have an absolute zero-which allows for a wide range of descriptive and inferential statistics. Ratio scales are those which can be easily have their ratios computed (subtraction, multiplication, addition) and have measures of central tendency easily determined eg the mean, median and measures of dispersion such as the standard deviation, coefficient of variation. In this data set, the first data set that meets this description is the age, limit balance, monthly bills and the monthly payment amount. Simply put, in this particular case, all the interval data attributes up there are ratio data attributes as well. In fact, when it comes to the monthly computations, they are mainly ratio data. 2. Summarizing Properties Means Except for the case of high influence of the outliers, the mean is used to give a generalized representation of the data (Bowman and Robinson, 2007). In this case, the mean would be used to represent the average amount given to the customers, the average age of the customers, the average payments for each month (so as to compare the month statistics) and the average monthly repayments. For this dataset, the mean amount given out to the customers is 167065 NT Dollar, with an average borrowing age of 35-36 (35.7 years average) years. The average bill amounts for the months from September backwards to April are approximately: 51628, 49326, 47153, 44021, 41599, And 40130 NT Dollars respectively. From this it can be seen that towards September from April, the average Bill amounts were increasing with highest average in September. The average amounts paid by the customers for the months of September backwards to April are approximately 5732, 6248, 5964, 5054, 4553 and 5623 NT Dollars respectively. On average, the month of August recorded the highest amount of repayment by the customers. Median The median is much more like the middle of the data set about which values lie above and below and may give a more robust representation of the customer behavior compared to the mean computed above. It can also be said to be a more representative of the population than the mean (Bowman and Robinson, 2007). The median amount given out to customers is 140000 NT Dollars The median age of customers is 34 years. The median bills for September backwards to April are 20633, 20072, 19155, 18808, 17875 and 16477 NT Dollars respectively. September records the highest representative bills of the months given. The median monthly repayments from September backwards to April are 2101 2055 1842 1526.5 1500 1500 NT Dollars respectively. The median shows September as the month with the highest repayments and with the repayments increasing from April to September. In this case, The median may be viewed as more representative of the customers as opposed to the mean which is highly affected by the outliers (Bowman and Robinson, 2007). The median for defaulting status is 0 indicating no defaulting. Range The range is used to determine the difference between the smallest and the highest recording of the data. The difference between the highest and the smallest amount borrowed is 990000 NT Dollars. The difference between the youngest and the oldest borrowers is 52 years. The range for the Bills from September backwards to April is 979819, 1017281, 553215, 907174, 988543, 986584, NT Dollars respectively. August has the highest difference between the smallest and the largest Bill and July has the smallest difference. The repayment range is 260416 358689 896040 281225 207019 528666 NT Dollars for September to backwards to April respectively. July has the smallest difference between the highest and lowest repayment. Frequencies/Mode This measure is used to determine the mostly occurring entry.. It is very helpful in determining which group of a given attribute has the highest score/occurrence. In this case, 50000 NT Dollars is the amount that was most given out to the customers. There were more females borrowing compared to males. Most of the customers are University students. In terms of marriage, most of the customers are single. The largest borrowing age is 27 years. The payment status show that people mostly repaid earlier than due date for all the months. Both bills and the repayment amounts do not show one particular entry that mostly occurred. Defaulting for next month shows that most of the customers did not default payment for the next month the default status of highest frequency is 0 meaning more of the customers did not default on payment. Distributions With respect to this case, the most appropriate data attribute distribution analysis is the age. In this particular case, the age distribution analysis was as shown below ranges Age bands Age Distribution 59 26 Equi-depth binning Equi-depth binning is also known as equal-frequency binning. It is carried by classifying the data into classes of equal frequency. According to Han et al (2012), equi-depth binning divides data into N groups with each group having approximately same number of values. Using excel, the desired frequency for the age was determined to be 10 and then the equi-depth binning carried out using the function below. b. Normalization Min-max normalization The min-max normalization involves dividing the difference between a particular value and the minimum value of the dataset by the range of the dataset. A min-max score is an index of how much the value is far from the minimum value of the dataset. The min-max normalization may not give a true smoothing of the given data since the maximum value and the minimum values may be outliers (Brackett, 2012). A plot of the min-max is as shown below Figure1: The min-max distribution. The score is always positive Z-score normalization The Z-score was carried out by dividing the difference between the value and the mean by the standard deviation. The Z-normaization can be a better smoothing criterion compared to min-max normalization (Brackett, 2012). The Z-score helps us determine the probability of a score occurring within within our normal distribution. The scores closer to the mean have the highest probability of occuring. Below is a plot of the Z-normalization. c. Discretization In order to carry out data discretization, Excel If function was applied to filter and assign the discretization values that describe the age bracket into which a particular age falls. To carry out the process, age was determined to be of the groups in the teenage, young, mid-age, mature and old age ranges 66 respectively. This classification was in accordance with Grasso and Burkins’ (2010) categorisation criterion. The excel if function entered was as shown below A2=IF(A2=66,"Old",IF(A2 Read More