Data

In our example this week, we are going to use the fake data - about real estates in Wroclaw - prices by districts, size of apartments and many more.

apartments$district<-as.factor(apartments$district)
apartments$building_type<-as.factor(apartments$building_type)
apartments$rooms<-factor(apartments$rooms,ordered=TRUE)
attach(apartments)
apartments$price_PLN<-as.numeric(apartments$price_PLN)
apartments$price_EUR<-as.numeric(apartments$price_EUR)

Frequency Tables

In the first step of our analysis, we will group our data into a simple frequency table.

First, let’s look at the distribution of housing prices in our sample and verify tabular validity using the TAI measure:

Ok, it looks quite ugly, so let’s wrap it up using the ‘kable’ package:

##        # classes  Goodness of fit Tabular accuracy 
##       10.0000000        0.9780872        0.8508467

As we can see - the TAI index is quite high. 0.85 means that we can accept the proposed construction of the frequency table.

Basic plots

In this section, we should represent our data using basic (pre-installed in R) graphics. Select the most appropriate graphs depending on the scale of the selected variables. Explore the heterogeneity of the distribution by presenting the data by group (e.g., by neighborhood, building type, etc.). Don’t forget about main titles, labels and legends. Read more about graphical parameters here.

Note that the echo = FALSE parameter has been added to the code snippet to prevent printing the R code that generated the graph.

ggplot2 plots

Now, let’s use the ggplot2 and ggpubr libraries to plot.

Ggplot2 allows you to show the average value for each group using the stat_summary() function. You no longer need to calculate average values before creating a graph!

Univariate Statistics

Before automatically reporting the full summary table of descriptive statistics, this time your goal is to measure the central tendency of the price distribution. Compare the mean, median, and mode along with positional measures - quantiles - by district and building type or number of rooms in the apartment.

    mean(price_PLN)

## [1] 760035

    median(price_PLN)

## [1] 755719.5

    sd(price_PLN) #standard deviation

## [1] 186099.8

    var(price_PLN) #variance

## [1] 34633125960

    coeff_var<-sd(price_PLN)/mean(price_PLN) #coefficient of variability %
    coeff_var

## [1] 0.2448568

    IQR(price_PLN)# difference between quartiles =Q3-Q1 

##      75% 
## 282686.5

    sx<-IQR(price_PLN)/2  #interquartile deviation
    coeff_varx<-sx/median(price_PLN) #IQR coefficient of variability %
    coeff_varx

##       75% 
## 0.1870314

    min(price_PLN)

## [1] 359769

    max(price_PLN)

## [1] 1277691

    quantile(price_PLN,probs=c(0,0.1,0.25,0.5,0.75,0.95,1),na.rm=TRUE)

##        0%       10%       25%       50%       75%       95%      100% 
##  359769.0  518806.8  619073.8  755719.5  901760.2 1054250.8 1277691.0

Ok, we have calculated all of the basic summary statistics above. Let’s wrap them up together now.

apartments %>%
  select(price_PLN,rooms) %>%
  tbl_summary(label= price_PLN ~ "Price",digits=c(price_PLN)~2,by=rooms,type = all_continuous() ~ "continuous2", statistic = all_continuous() ~ c("{N_nonmiss}", "{median} ({p25}, {p75})", "{min}, {max}"),missing = "no")

dfSummary(apartments,
          plain.ascii  = FALSE, 
          style        = "grid", 
          graph.magnif = 0.75, 
          valid.col    = FALSE,
          tmp.img.dir  = "/tmp")

## temporary images written to 'C:\tmp'

Data Frame Summary

apartments

Dimensions: 200 x 6
Duplicates: 0

No	Variable	Stats / Values	Freqs (% of Valid)	Graph	Missing
1	price_PLN [numeric]	Mean (sd) : 760035 (186099.8) min < med < max: 359769 < 755719.5 < 1277691 IQR (CV) : 282686.5 (0.2)	200 distinct values		0 (0.0%)
2	price_EUR [numeric]	Mean (sd) : 175934 (43078.6) min < med < max: 83280 < 174935 < 295762 IQR (CV) : 65436.2 (0.2)	200 distinct values		0 (0.0%)
3	rooms [ordered, factor]	1. 1 2. 2 3. 3 4. 4	44 (22.0%) 50 (25.0%) 58 (29.0%) 48 (24.0%)		0 (0.0%)
4	size [numeric]	Mean (sd) : 46.2 (20.1) min < med < max: 17 < 43.7 < 87.7 IQR (CV) : 30.2 (0.4)	162 distinct values		0 (0.0%)
5	district [factor]	1. Biskupin 2. Krzyki 3. Srodmiescie	65 (32.5%) 79 (39.5%) 56 (28.0%)		0 (0.0%)
6	building_type [factor]	1. kamienica 2. niski blok 3. wiezowiec	61 (30.5%) 63 (31.5%) 76 (38.0%)		0 (0.0%)

To produce optimal results, summarytools has its own version of the base by() function. It’s called stby(), and we use it exactly as we would by():

(stats_by_rooms <- stby(data      = apartments, INDICES   = apartments$rooms, FUN       = descr, stats     = "common", transpose = TRUE))

## Non-numerical variable(s) ignored: rooms, district, building_type

Descriptive Statistics
apartments
Group: rooms = 1
N: 44

	Mean	Std.Dev	Min	Median	Max	N.Valid	Pct.Valid
price_EUR	119332.95	15497.90	83280.00	120488.00	152117.00	44.00	100.00
price_PLN	515518.05	66951.03	359769.00	520507.00	657146.00	44.00	100.00
size	19.28	1.46	17.00	19.10	21.90	44.00	100.00

Group: rooms = 2
N: 50

	Mean	Std.Dev	Min	Median	Max	N.Valid	Pct.Valid
price_EUR	158233.22	15063.13	136640.00	156773.00	205702.00	50.00	100.00
price_PLN	683567.70	65072.66	590286.00	677260.00	888634.00	50.00	100.00
size	36.80	4.46	29.60	35.95	43.70	50.00	100.00

Group: rooms = 3
N: 58

	Mean	Std.Dev	Min	Median	Max	N.Valid	Pct.Valid
price_EUR	192987.55	20125.88	146475.00	195904.00	223572.00	58.00	100.00
price_PLN	833706.02	86943.90	632770.00	846303.50	965829.00	58.00	100.00
size	53.33	7.21	41.20	53.45	65.20	58.00	100.00

Group: rooms = 4
N: 48

	Mean	Std.Dev	Min	Median	Max	N.Valid	Pct.Valid
price_EUR	225650.42	26347.03	170525.00	223226.50	295762.00	48.00	100.00
price_PLN	974809.96	113819.21	736669.00	964338.50	1277691.00	48.00	100.00
size	72.05	10.18	53.30	70.85	87.70	48.00	100.00

apartments %>%
  descr(stats = "common") %>%
  tb()

## # A tibble: 3 × 8
##   variable      mean       sd    min      med       max n.valid pct.valid
##   <chr>        <dbl>    <dbl>  <dbl>    <dbl>     <dbl>   <dbl>     <dbl>
## 1 price_EUR 175934.   43079.   83280 174935    295762       200       100
## 2 price_PLN 760035.  186100.  359769 755720.  1277691       200       100
## 3 size          46.2     20.1     17     43.7      87.7     200       100

grouped_descr <- stby(data    = apartments,INDICES = apartments$rooms, FUN     = descr, stats   = "common")

grouped_descr %>% tb()

## # A tibble: 12 × 9
##    rooms variable      mean        sd      min      med    max n.valid pct.valid
##    <fct> <chr>        <dbl>     <dbl>    <dbl>    <dbl>  <dbl>   <dbl>     <dbl>
##  1 1     price_EUR 119333.   15498.    83280   120488   1.52e5      44       100
##  2 1     price_PLN 515518.   66951.   359769   520507   6.57e5      44       100
##  3 1     size          19.3      1.46     17       19.1 2.19e1      44       100
##  4 2     price_EUR 158233.   15063.   136640   156773   2.06e5      50       100
##  5 2     price_PLN 683568.   65073.   590286   677260   8.89e5      50       100
##  6 2     size          36.8      4.46     29.6     36.0 4.37e1      50       100
##  7 3     price_EUR 192988.   20126.   146475   195904   2.24e5      58       100
##  8 3     price_PLN 833706.   86944.   632770   846304.  9.66e5      58       100
##  9 3     size          53.3      7.21     41.2     53.4 6.52e1      58       100
## 10 4     price_EUR 225650.   26347.   170525   223226.  2.96e5      48       100
## 11 4     price_PLN 974810.  113819.   736669   964338.  1.28e6      48       100
## 12 4     size          72.0     10.2      53.3     70.8 8.77e1      48       100

stby(data    = apartments, 
     INDICES = apartments$rooms, 
     FUN     = descr, 
     stats   = "fivenum") %>%
  tb(order = 3) %>%
  kable(format = "html", digits = 2) %>%
  collapse_rows(columns = 1, valign = "top")

Your turn!

Your task this week is to: prepare your own descriptive analysis for the “CreditCard” dataset (AER package). It is a cross-sectional dataframe on the credit history for a sample of applicants for a type of credit card.

Are the yearly incomes (in USD 10,000), credit card expenditures, age, ratio of monthly credit card expenditure to yearly income - significantly different for applicants for customers with different credit risk (“card” variable - factor)?

Prepare a professional data visualizations, descriptive statistics’ tables and interpret them.

data(CreditCard)
#there are some applicants that are younger that one year old, so we assume some mistake in that matter:
CreditCard<- CreditCard[CreditCard$age > 18, ]

Accepted <- CreditCard[CreditCard$card == 'yes', ]
NotAccepted <- CreditCard[CreditCard$card == 'no', ]
nrow(Accepted)

## [1] 1017

nrow(NotAccepted)

## [1] 295

nrow(Accepted)/nrow(CreditCard)

## [1] 0.7751524

We can see that >77% of Applications got accepted.

Now lets look at some basic graphs showing relation of other variables and applications for credit card being accepted.

CreditCard %>% 
  filter(card %in% c('no','yes')) %>% 
  ggplot(aes(x = factor(card), y = age, fill = factor(card))) +
  
  stat_halfeye(
    adjust = 0.5,
    justification = -0.2,
    .width = 0,
    point_colour = NA
  ) +
  geom_boxplot(
    width = 0.12,
    outlier.color = NA,
    alpha = 0.5
  ) +
  stat_dots(
    side = "left",
    justification = 1.1,
    binwidth = 0.05
  ) +

  labs(
    title = "Age in regards to credit card application acceptance",
    x = "accepted",
    y = "Age",
    fill = "Got accepted fo credit card"
  ) +
  coord_flip()

Age is visibly positive-skewed for both groups and range of age of accepted applicants is bigger. There is no visible significant dominance of acceptance of applications in any age group, accepted applicators could tend to be slightly older, which we will look into later.

CreditCard$income<- CreditCard$income
CreditCard %>% 
  filter(card %in% c('no','yes')) %>% 
  ggplot(aes(x = factor(card), y = income, fill = factor(card))) +
  
  stat_halfeye(
    adjust = 0.5,
    justification = -0.2,
    .width = 0,
    point_colour = NA
  ) +
  geom_boxplot(
    width = 0.15,
    outlier.color = NA,
    alpha = 0.5
  ) +
  stat_dots(
    side = "left",
    justification = 1.1,
    binwidth = 0.0025
  ) +

  labs(
    title = "Income in regards to credit card application acceptance",
    x = "accepted",
    y = "Income [in 10.000 USD]",
    fill = "Got accepted fo credit card"
  ) +
  coord_flip()

We can notice income being positive-skewed and leptokurtic for both groups. Range is bigger for accepted applicants. Income seems to be lower for not accepted applicants and will be analysed further later.

library(ggplot2)
hist(NotAccepted$reports, col=rgb(0,0,1,0.3), xlim=c(0, max(NotAccepted$reports)),
     xlab='reports', ylab='declined applications', main='Major derogatory reports for not accepted Applicants')

hist(Accepted$reports, col=rgb(1,0,1,0.3), xlim=c(0, max(Accepted$reports)),
     xlab='reports', ylab='accepted applications', main='Major derogatory reports for accepted Applicants')

No applicant with more than 4 reports got accepted, overall not accepted applicants tend to have more derogatory reports. With bigger number of reports percentile of rejected applications also rises and we can see that having reports significantly affects and decreases chances of being accepted, although having reports is not the case with majority of applicants.

cor(CreditCard$reports, CreditCard$income)

## [1] 0.01054498

hist(Accepted$active, col=rgb(1,1,0.5,1), xlim=c(0, max(NotAccepted$active)),
     xlab='active credit accounts', ylab='applications', main='Number of active credit accounts for applicants')
hist(NotAccepted$active, col=rgb(0,1,0,1), xlim=c(0, max(NotAccepted$active)), add = TRUE)
legend('topright', c('accepted', 'not accepted'),
       fill=c(rgb(1,1,0.5,1), rgb(0,1,0,1)))

We can see, that with bigger number of credit accounts comes bigger share of accepted applications. It is probably due to the fact that opening credit accounts have somewhat similar requirements - applicants with many accounts could be able to meet those requirements easier.

CreditCard %>% 
  filter(card %in% c('no','yes')) %>% 
  ggplot(aes(x = factor(card), y = months, fill = factor(card))) +
  
  stat_halfeye(
    adjust = 0.5,
    justification = -0.3,
    .width = 0,
    point_colour = NA
  ) +
  geom_boxplot(
    width = 0.15,
    outlier.color = NA,
    alpha = 0.5
  ) +
  stat_dots(
    side = "left",
    justification = 1.1,
    binwidth = 0.1
  ) +

  labs(
    title = "Months lived at current address in regards to application acceptance",
    x = "accepted",
    y = "months",
    fill = "Got accepted fo credit card"
  ) +
  coord_flip()

hist(Accepted$months, col=rgb(1,0,0,0.8), xlim=c(0, 300),
     xlab='months', ylab='applications', main="Months lived at current address in regards to application acceptance")
hist(NotAccepted$months, col=rgb(0,0,1,0.8), xlim=c(0, 300), add = TRUE)
legend('topright', c('accepted', 'not accepted'),
       fill=c(rgb(1,0,0,0.8), rgb(0,0,1,0.8)))

Although people who lived at current address for long time, meaning more than 8 years, tend to be accepted for credit card application, the biggest group of applicants have not been living under their current address for longer time than 4-5 years. For this group months living at current address do not seem to affect decision about application too much, as applicants from this group were not more or less accepted than applicants overall, not regarding how long they lived at their current address. With smaller group mentioned, accepted applicants tend to have lived longer at their address.

hist(Accepted$dependents, col=rgb(1,0,0.5,1), xlim=c(0, max(Accepted$dependents)),
     xlab='number of dependants', ylab='applications', main='Number of dependants for applicants')
hist(NotAccepted$dependents, col=rgb(0.7,1,0,1), xlim=c(0, max(Accepted$dependents)), add = TRUE)
legend('topright', c('accepted', 'not accepted'),
       fill=c(rgb(1,0,0.5,1), rgb(0.7,1,0,1)))

We can see, that share of declined applications tends to be bigger with bigger number of dependants.

nrow(Accepted[Accepted$owner == 'no',])

## [1] 528

nrow(Accepted[Accepted$owner == 'yes',])

## [1] 489

nrow(NotAccepted[NotAccepted$owner == 'no',])

## [1] 205

nrow(NotAccepted[NotAccepted$owner == 'yes',])

## [1] 90

Share of applicants that do not own their home is significantly bigger in group of applicants that were not accepted.

Just to check if no applicant has more than one major card:

max(CreditCard$majorcards)

## [1] 1

nrow(Accepted[Accepted$majorcards == 1,])

## [1] 854

nrow(Accepted[Accepted$majorcards == 0,])

## [1] 163

nrow(NotAccepted[NotAccepted$majorcards == 1,])

## [1] 219

nrow(NotAccepted[NotAccepted$majorcards == 0,])

## [1] 76

Share of applicants that do own major credit card is bigger in group of applicants that were accepted.

nrow(Accepted[Accepted$selfemp == 'no',])

## [1] 954

nrow(Accepted[Accepted$selfemp == 'yes',])

## [1] 63

nrow(NotAccepted[NotAccepted$selfemp == 'no',])

## [1] 267

nrow(NotAccepted[NotAccepted$selfemp == 'yes',])

## [1] 28

Share of applicants that are self-employed is bigger in group of applicants that were not accepted.

    mean(Accepted$share)

## [1] 0.08840693

    mean(NotAccepted$share)

## [1] 0.0004770558

    median(Accepted$share)

## [1] 0.0598016

    median(NotAccepted$share)

## [1] 0.0004651163

We can predict and see above, that share is significantly lower for not accepted applicants, as it depends strongly on being accepted. the same comes for expenditure, that is just equal to zero for all rejected applicants:

  max(NotAccepted$expenditure)

## [1] 0

  mean(Accepted$expenditure)

## [1] 238.6245

Now, let’s take a look on univariate statistics for whole group of applicants, accepted ones and those who weren’t accepted:

Arithmetic mean:

    mean(CreditCard$income)

## [1] 3.367257

    mean(Accepted$income)

## [1] 3.453847

    mean(NotAccepted$income)

## [1] 3.068741

Average income is visibly lower for not accepted applicants, which could suggest that income could affect decision of acceptance, if it is not affected by outliners in misguiding way.

Median

    median(CreditCard$income)

## [1] 2.9

    median(Accepted$income)

## [1] 3

    median(NotAccepted$income)

## [1] 2.58

Median, not being affected by extreme values as mean, also puts central tendency of income for group of accepted applicants higher then for group of not accepted applicants. For every group mean is remarkably bigger than median, so, as noticed earlier, shape of distribution for income of each group of applicants is right-skewed.

Standard deviation

     sd(CreditCard$income)

## [1] 1.697377

     sd(Accepted$income)

## [1] 1.710739

     sd(NotAccepted$income)

## [1] 1.618076

Standard deviation do not differ much between groups. Being relatively high, it suggests data being more widely scattered around the mean.

Variance

    var(CreditCard$income)

## [1] 2.881089

    var(Accepted$income)

## [1] 2.926627

    var(NotAccepted$income)

## [1] 2.618171

Analogically, we can conclude the same as from standard deviation. We can see more clearly than above that variance is bigger for accepted applicants.

Coefficient of variation in %

    coeff_var<- 100 * sd(CreditCard$income)/mean(CreditCard$income)
    coeff_var

## [1] 50.40831

    coeff_varA<- 100 * sd(Accepted$income)/mean(Accepted$income)
    coeff_varA

## [1] 49.5314

    coeff_varNA<- 100 * sd(NotAccepted$income)/mean(NotAccepted$income)
    coeff_varNA

## [1] 52.72769

group of not accepted applicants is slightly more variable relative to their income than accepted applicants, but it is not a markable difference.

Quantiles

    quantile(CreditCard$income,probs=c(0,0.1,0.25,0.5,0.75,0.95,1),na.rm=TRUE)

##        0%       10%       25%       50%       75%       95%      100% 
##  0.210000  1.800000  2.237125  2.900000  4.000000  6.900000 13.500000

    quantile(Accepted$income,probs=c(0,0.1,0.25,0.5,0.75,0.95,1),na.rm=TRUE)

##    0%   10%   25%   50%   75%   95%  100% 
##  0.21  1.90  2.35  3.00  4.00  7.00 13.50

    quantile(NotAccepted$income,probs=c(0,0.1,0.25,0.5,0.75,0.95,1),na.rm=TRUE)

##      0%     10%     25%     50%     75%     95%    100% 
##  0.4900  1.6752  2.0000  2.5800  3.6500  6.1500 11.0000

Difference between quartiles = Q3-Q1

    IQR(CreditCard$income)

##      75% 
## 1.762875

    IQR(Accepted$income)

##  75% 
## 1.65

     IQR(NotAccepted$income)

##  75% 
## 1.65

Difference between quartiles is the same for both groups of accepted and not accepted applicants.

IQR coefficient of variation in %

     #interquartile deviation
    sx<-IQR(CreditCard$income)/2
    sxA<-IQR(Accepted$income)/2
    sxNA<-IQR(NotAccepted$income)/2
    
    coeff_varx<- 100 * sx/median(CreditCard$income)
    coeff_varx

##     75% 
## 30.3944

    coeff_varxA<- 100 * sxA/median(Accepted$income)
    coeff_varxA

##  75% 
## 27.5

    coeff_varxNA<- 100 * sxNA/median(NotAccepted$income)
    coeff_varxNA

##      75% 
## 31.97674

Interquartile coefficient of variation is, similarly to coefficient of variation counted in regards to whole group, bigger for not accepted applicants, with bigger difference between coefficient for accepted and not accepted group. The level of dispersion around the mean in interquartile would be higher for not accepted applicants.

Minimum and maximum

    min(Accepted$income)

## [1] 0.21

    min(NotAccepted$income)

## [1] 0.49

    max(Accepted$income)

## [1] 13.5

    max(NotAccepted$income)

## [1] 11

Let’s also see income of accepted and not accepted applicants on graphs:

list <- split(CreditCard$income, CreditCard$card)
inline_plot <- data.frame(card = c('no', 'yes'), boxplot = "", histogram = "",
                          line1 = "", line2 = "", points1 = "")
inline_plot %>%
  kbl(booktabs = TRUE) %>%
  kable_paper(full_width = FALSE) %>%
  column_spec(2, image = spec_boxplot(list)) %>%
  column_spec(3, image = spec_hist(list)) %>%
  column_spec(4, image = spec_plot(list, same_lim = TRUE)) %>%
  column_spec(5, image = spec_plot(list, same_lim = FALSE)) %>%
  column_spec(6, image = spec_plot(list, type = "p"))

To summarize above statistics regarding income, we can see that level of income significantly differs between groups of accepted and not accepted applicants, as it tends to be lower for applicants that were not accepted for credit card.

CreditCard$income<- CreditCard$income * 10000
summaryIncome <-list("yearly income" =
       list("Min"= ~ min(income),
            "Max"= ~ max(income),
            "Q1"= ~ quantile(income,0.25),
            "Median"= ~ round(median(income),2),
            "Q3"= ~ quantile(income,0.75),
            "Mean"= ~ round(mean(income),2),
            "Sd"= ~ round(sd(income),2),
             "IQR"= ~ round(iqr(income),2),
            "Var %"= ~ round((100 * sd(income)/mean(income)),2),
            "IQR Var %"= ~ round((100 * 0.5 * iqr(income)/median(income)),2),
            "Skewness"= ~  round(skew(income),2),
             "Kurtosis"= ~  round(kurtosi(income),2)
            ))
summaryIncome<-summary_table(CreditCard, summaries = summaryIncome, by = c("card"))
kbl(summaryIncome, digits=1, caption="Table 1. Yearly Income [in USD] in regards to credit card application acceptance",  col.names = c('application', 'not Accepted', 'Accepted')) %>% kable_classic(full_width = F, html_font = "Cambria") %>% kable_styling(bootstrap_options = c("striped", "hover"))

CreditCard$income<- CreditCard$income / 10000

Below you can see summary table of age in regards to application acceptance as continuation of its analysis. The level of dispersion around the mean is bigger for accepted applicants. We can confirm positive skewness that was noticed on graph as well as range being bigger for accepted applicants. Group of applicants that were accepted for credit card tends to be slightly older than not accepted group, but that is not an explicit difference, so it could not be that significant.

summaryAge <-list("Age" =
       list("Min"= ~ min(age),
            "Max"= ~ max(age),
            "Q1"= ~ quantile(age,0.25),
            "Median"= ~ round(median(age),2),
            "Q3"= ~ quantile(age,0.75),
            "Mean"= ~ round(mean(age),2),
            "Sd"= ~ round(sd(age),2),
             "IQR"= ~ round(iqr(age),2),
            "Sx"= ~ round(iqr(age)/2,2),
            "Var %"= ~ round((100 * sd(age)/mean(age)),2),
            "IQR Var %"= ~ round((100 * 0.5 * iqr(age)/median(age)),2),
            "Skewness"= ~  round(skew(age),2),
             "Kurtosis"= ~  round(kurtosi(age),2)
            ))
summaryAge<-summary_table(CreditCard, summaries = summaryAge, by = c("card"))
kbl(summaryAge, digits=1, caption="Table 2. Age in regards to credit card application acceptance",  col.names = c('application', 'not Accepted', 'Accepted')) %>% kable_classic(full_width = F, html_font = "Cambria") %>% kable_styling(bootstrap_options = c("striped", "hover"))

To answer the question and summarize report, as far as ratio of monthly credit card expenditure to yearly income and average monthly credit card expenditure are concerned, they depend strongly on being accepted for credit card application, therefore differ in between accepted and not accepted group. Applicants accepted for credit card tend to have bigger income then those not accepted. Share of people that do not own their own home is bigger within applicants that were not accepted, as well as share of people that are self-employed. Age of accepted and not accepted applicants does not differ significantly. Accepted group consists of less applicants with major derogatory reports and no applicants with bigger number of such reports. Accepted applicants more often have major credit card. Share of declined applications tends to be bigger with bigger number of dependants. When it comes to months living at current address, only with smaller group that have been living at current address for long time we can see some markable difference - they tend to be more frequently in accepted group of applicants.