R Notebook

1. Load necessary libraries

library(GGally)
library(knitr)
library(ggplot2)
library(dplyr)
library(corrr)
library(MASS)
library(corrgram)

Cluster <- read.csv("clusteringData.csv", 
                   header = T, stringsAsFactors = F)

#get rid of percent sign
Cluster$Positive_Profitability = as.numeric(gsub("\\%", "", Cluster$Positive_Profitability))
Cluster$Profitability = as.numeric(gsub("\\%", "", Cluster$Profitability))
#Verify no percent sign
kable(head(Cluster) %>% arrange(Profitability)) 

Random	Customer_Index	Average_Risk_Grade	Max_of_Cards	Account_Open_Date	Years_on_Books	Gross_Revenue_Amt	Total_Expense_Amt	Net_Profit	Net_Profit_Card	Profitability	Positive_Profitability	Card_Fees_Amt	Purchase_Gallons_Qty	Average_Gallons_Card	Acquisition_Cost	Rebate_Amt	Net_Late_Fee_Count	No_Accounts_by_Customer
0.7806251	Company 31528	6	1	2012-03-21	4	9022.74	573.07	8449.67	8449.67	94	144	24	41383	41383	0	0	10	1
0.1023051	Company 40586	1	1	2008-11-11	7	4143.15	223.47	3919.68	3919.68	95	145	26	21854	21854	0	0	11	1
0.5832711	Company 14002	1	4	2012-08-15	3	62047.75	77.27	61970.48	15492.62	100	150	74	5210	1303	0	0	1	1
0.2187821	Company 50814	3	10	2014-10-24	1	99575.62	280.61	99295.01	9929.50	100	150	0	2150	215	0	0	11	1
0.4913845	Company 52955	1	1	2014-03-10	2	7879.56	NA	7879.56	7879.56	100	150	24	0	0	0	0	4	1
0.9517827	Company 16765	1	1	2000-09-08	15	4272.36	1.04	4271.32	4271.32	100	150	2	50	50	0	0	0	1

#convert profitability and positive profitability to numeric
Cluster$Positive_Profitability <- as.numeric(Cluster$Positive_Profitability)
Cluster$Profitability <- as.numeric(Cluster$Profitability)
#if need to convert them to integer
# Cluster$Profitability <- as.integer(Cluster$Profitability)
# Cluster$Positive_Profitability <- as.integer(Cluster$Positive_Profitability)
Cluster$Account_Open_Date <- as.Date(Cluster$Account_Open_Date , format = "%m/%d/%Y")

summary(Cluster)

     Random          Customer_Index    
 Min.   :0.0000058   Length:55898      
 1st Qu.:0.2480272   Class :character  
 Median :0.4963082   Mode  :character  
 Mean   :0.4985677                     
 3rd Qu.:0.7492804                     
 Max.   :0.9999339                     
                                       
 Average_Risk_Grade  Max_of_Cards  
 Min.   :0.000      Min.   : 1.00  
 1st Qu.:1.000      1st Qu.: 4.00  
 Median :1.000      Median : 8.00  
 Mean   :1.718      Mean   :12.22  
 3rd Qu.:2.000      3rd Qu.:15.00  
 Max.   :7.000      Max.   :79.00  
                                   
 Account_Open_Date    Years_on_Books  
 Min.   :1983-07-01   Min.   : 0.000  
 1st Qu.:2005-03-10   1st Qu.: 3.000  
 Median :2009-02-20   Median : 7.000  
 Mean   :2008-07-17   Mean   : 7.205  
 3rd Qu.:2012-08-30   3rd Qu.:11.000  
 Max.   :2016-02-02   Max.   :32.000  
                                      
 Gross_Revenue_Amt  Total_Expense_Amt   Net_Profit     
 Min.   :    0.95   Min.   :   0.18   Min.   : -378.9  
 1st Qu.:  512.61   1st Qu.:  46.07   1st Qu.:  420.4  
 Median :  935.35   Median : 111.25   Median :  810.6  
 Mean   : 1697.13   Mean   : 205.96   Mean   : 1492.3  
 3rd Qu.: 1944.61   3rd Qu.: 265.72   3rd Qu.: 1704.2  
 Max.   :99575.62   Max.   :6445.75   Max.   :99295.0  
                    NA's   :302                        
 Net_Profit_Card    Profitability   
 Min.   : -229.89   Min.   :-50.00  
 1st Qu.:   67.95   1st Qu.: 85.00  
 Median :  103.44   Median : 89.00  
 Mean   :  136.28   Mean   : 84.77  
 3rd Qu.:  164.34   3rd Qu.: 93.00  
 Max.   :15492.62   Max.   :100.00  
                                    
 Positive_Profitability Card_Fees_Amt   
 Min.   :  0.0          Min.   :-626.0  
 1st Qu.:135.0          1st Qu.:  74.0  
 Median :139.0          Median : 150.0  
 Mean   :134.8          Mean   : 242.5  
 3rd Qu.:143.0          3rd Qu.: 300.0  
 Max.   :150.0          Max.   :1912.0  
                                        
 Purchase_Gallons_Qty Average_Gallons_Card
 Min.   :      0      Min.   :     0      
 1st Qu.:   3210      1st Qu.:   591      
 Median :   7702      Median :   986      
 Mean   :  15650      Mean   :  1297      
 3rd Qu.:  17751      3rd Qu.:  1524      
 Max.   :1850413      Max.   :108848      
                                          
 Acquisition_Cost    Rebate_Amt      
 Min.   :  0.000   Min.   :-960.000  
 1st Qu.:  0.000   1st Qu.:   0.000  
 Median :  0.000   Median :   0.000  
 Mean   :  5.666   Mean   :  -1.893  
 3rd Qu.:  0.000   3rd Qu.:   0.000  
 Max.   :475.000   Max.   :   0.000  
                                     
 Net_Late_Fee_Count No_Accounts_by_Customer
 Min.   :-2.000     Min.   :1              
 1st Qu.: 0.000     1st Qu.:1              
 Median : 2.000     Median :1              
 Mean   : 2.915     Mean   :1              
 3rd Qu.: 5.000     3rd Qu.:1              
 Max.   :12.000     Max.   :1              
                                           

set.seed(121)
sampleSet <- sample_n(Cluster, 30)
ggplot(sampleSet, aes(x = Profitability, y = Card_Fees_Amt)) + geom_point(alpha = 0.1, color = "blue")+ geom_smooth(method = "lm")

ggplot(sampleSet, aes(x = Profitability, y = Card_Fees_Amt)) + geom_point() + scale_x_log10() + scale_y_log10() + geom_smooth(method = "lm")

ggplot(sampleSet, aes(x = Positive_Profitability, y = Card_Fees_Amt, color = factor(Average_Risk_Grade))) + geom_point(alpha = 0.3)

ggplot(sampleSet, aes(x = Positive_Profitability, y = Card_Fees_Amt, color = factor(Average_Risk_Grade))) + geom_point(alpha = 0.3) + facet_wrap(~ Average_Risk_Grade)

newdata = sampleSet[,c(3:4, 5:18)]
plot(newdata, pch=16, col="blue", main="Matrix Scatterplot of ...")

mod1 = lm(Positive_Profitability ~ Average_Gallons_Card + Net_Late_Fee_Count +Net_Profit_Card + Years_on_Books + Card_Fees_Amt +No_Accounts_by_Customer + Rebate_Amt + Average_Risk_Grade + Gross_Revenue_Amt+ Purchase_Gallons_Qty, data=sampleSet)
summary(mod1)

Call:
lm(formula = Positive_Profitability ~ Average_Gallons_Card + 
    Net_Late_Fee_Count + Net_Profit_Card + Years_on_Books + Card_Fees_Amt + 
    No_Accounts_by_Customer + Rebate_Amt + Average_Risk_Grade + 
    Gross_Revenue_Amt + Purchase_Gallons_Qty, data = sampleSet)

Residuals:
    Min      1Q  Median      3Q     Max 
-32.587  -4.390   1.088   8.801  20.728 

Coefficients: (1 not defined because of singularities)
                          Estimate Std. Error t value Pr(>|t|)    
(Intercept)              1.343e+02  1.102e+01  12.189 1.03e-10 ***
Average_Gallons_Card    -2.557e-02  8.107e-03  -3.154  0.00500 ** 
Net_Late_Fee_Count      -1.235e+00  1.675e+00  -0.738  0.46937    
Net_Profit_Card          1.706e-01  5.549e-02   3.075  0.00597 ** 
Years_on_Books           9.266e-01  6.299e-01   1.471  0.15686    
Card_Fees_Amt            3.038e-02  3.518e-02   0.863  0.39817    
No_Accounts_by_Customer         NA         NA      NA       NA    
Rebate_Amt               2.088e+02  2.318e+02   0.901  0.37841    
Average_Risk_Grade      -1.431e+00  2.722e+00  -0.526  0.60491    
Gross_Revenue_Amt       -5.873e-03  1.290e-02  -0.455  0.65372    
Purchase_Gallons_Qty     8.866e-04  9.550e-04   0.928  0.36428    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 15.07 on 20 degrees of freedom
Multiple R-squared:  0.6004,    Adjusted R-squared:  0.4205 
F-statistic: 3.338 on 9 and 20 DF,  p-value: 0.01185

mod2 = lm(Positive_Profitability ~ Average_Gallons_Card + Max_of_Cards + Net_Late_Fee_Count + Total_Expense_Amt + Net_Profit + Net_Profit_Card + Years_on_Books + Card_Fees_Amt + No_Accounts_by_Customer + Rebate_Amt + Average_Risk_Grade + Gross_Revenue_Amt+ Purchase_Gallons_Qty + Acquisition_Cost, data=sampleSet)
summary(mod2)

Call:
lm(formula = Positive_Profitability ~ Average_Gallons_Card + 
    Max_of_Cards + Net_Late_Fee_Count + Total_Expense_Amt + Net_Profit + 
    Net_Profit_Card + Years_on_Books + Card_Fees_Amt + No_Accounts_by_Customer + 
    Rebate_Amt + Average_Risk_Grade + Gross_Revenue_Amt + Purchase_Gallons_Qty + 
    Acquisition_Cost, data = sampleSet)

Residuals:
     Min       1Q   Median       3Q      Max 
-10.2186  -3.5368   0.3706   3.7782  13.9619 

Coefficients: (3 not defined because of singularities)
                          Estimate Std. Error t value Pr(>|t|)    
(Intercept)              1.275e+02  5.833e+00  21.852 2.08e-14 ***
Average_Gallons_Card    -2.718e-03  4.973e-03  -0.547  0.59136    
Max_of_Cards             2.013e+00  6.051e-01   3.327  0.00375 ** 
Net_Late_Fee_Count      -1.510e+00  8.435e-01  -1.790  0.09023 .  
Total_Expense_Amt       -1.045e-01  1.512e-02  -6.914 1.83e-06 ***
Net_Profit              -1.607e-03  6.417e-03  -0.250  0.80505    
Net_Profit_Card          1.015e-01  3.083e-02   3.292  0.00405 ** 
Years_on_Books           2.313e-01  3.378e-01   0.685  0.50223    
Card_Fees_Amt            1.715e-02  2.924e-02   0.587  0.56473    
No_Accounts_by_Customer         NA         NA      NA       NA    
Rebate_Amt               4.079e+02  1.182e+02   3.452  0.00284 ** 
Average_Risk_Grade       4.954e-01  1.372e+00   0.361  0.72220    
Gross_Revenue_Amt               NA         NA      NA       NA    
Purchase_Gallons_Qty     1.428e-04  4.835e-04   0.295  0.77111    
Acquisition_Cost                NA         NA      NA       NA    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 7.471 on 18 degrees of freedom
Multiple R-squared:  0.9116,    Adjusted R-squared:  0.8575 
F-statistic: 16.87 on 11 and 18 DF,  p-value: 2.77e-07

mod3 <- lm(Positive_Profitability ~ Average_Gallons_Card + Max_of_Cards + Total_Expense_Amt + Net_Profit_Card + Years_on_Books + Purchase_Gallons_Qty + Acquisition_Cost, data = sampleSet)
summary(mod3)

Call:
lm(formula = Positive_Profitability ~ Average_Gallons_Card + 
    Max_of_Cards + Total_Expense_Amt + Net_Profit_Card + Years_on_Books + 
    Purchase_Gallons_Qty + Acquisition_Cost, data = sampleSet)

Residuals:
     Min       1Q   Median       3Q      Max 
-22.5467  -3.3218  -0.1206   3.7106  21.7142 

Coefficients: (1 not defined because of singularities)
                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)           1.260e+02  6.744e+00  18.685 2.12e-15 ***
Average_Gallons_Card  4.329e-03  5.793e-03   0.747 0.462511    
Max_of_Cards          1.415e+00  3.498e-01   4.046 0.000502 ***
Total_Expense_Amt    -1.049e-01  1.670e-02  -6.284 2.07e-06 ***
Net_Profit_Card       5.439e-02  3.105e-02   1.752 0.093136 .  
Years_on_Books        4.045e-01  4.117e-01   0.983 0.336034    
Purchase_Gallons_Qty  6.039e-05  1.961e-04   0.308 0.760868    
Acquisition_Cost             NA         NA      NA       NA    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9.701 on 23 degrees of freedom
Multiple R-squared:  0.8095,    Adjusted R-squared:  0.7598 
F-statistic: 16.29 on 6 and 23 DF,  p-value: 3.006e-07

sampleSet <- sampleSet[, -c(1:3, 5, 7, 9, 11:13, 17:19 )]
Cluster1 <- Cluster %>% dplyr::select(Positive_Profitability, Average_Risk_Grade, Average_Gallons_Card, Max_of_Cards, Total_Expense_Amt, Net_Profit_Card, Years_on_Books, Purchase_Gallons_Qty, Acquisition_Cost)
#Sig Variables 56%
c1 <- lm(Positive_Profitability ~  Average_Gallons_Card+ Max_of_Cards + Total_Expense_Amt + Net_Profit_Card + Years_on_Books + Purchase_Gallons_Qty + Acquisition_Cost, data = Cluster1)

Dropping 302 rows with missing values

summary(c1)

Call:
lm(formula = Positive_Profitability ~ Average_Gallons_Card + 
    Max_of_Cards + Total_Expense_Amt + Net_Profit_Card + Years_on_Books + 
    Purchase_Gallons_Qty + Acquisition_Cost, data = Cluster1)

Residuals:
    Min      1Q  Median      3Q     Max 
-505.88   -1.81    1.87    4.94  154.88 

Coefficients:
                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)           1.307e+02  1.356e-01  963.66   <2e-16 ***
Average_Gallons_Card -1.764e-03  5.666e-05  -31.14   <2e-16 ***
Max_of_Cards          3.489e-01  7.134e-03   48.90   <2e-16 ***
Total_Expense_Amt    -4.596e-02  3.845e-04 -119.54   <2e-16 ***
Net_Profit_Card       3.400e-02  4.330e-04   78.52   <2e-16 ***
Years_on_Books        5.453e-01  1.208e-02   45.12   <2e-16 ***
Purchase_Gallons_Qty  2.529e-04  4.193e-06   60.31   <2e-16 ***
Acquisition_Cost     -1.852e-01  1.866e-03  -99.27   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 13.01 on 55588 degrees of freedom
  (302 observations deleted due to missingness)
Multiple R-squared:  0.566, Adjusted R-squared:  0.5659 
F-statistic: 1.036e+04 on 7 and 55588 DF,  p-value: < 2.2e-16

#Removed acquisition 49%
c2 <- lm(Positive_Profitability ~ Average_Gallons_Card+ Max_of_Cards + Total_Expense_Amt + Net_Profit_Card + Years_on_Books + Purchase_Gallons_Qty, data = Cluster1)

Dropping 302 rows with missing values

summary(c2)

Call:
lm(formula = Positive_Profitability ~ Average_Gallons_Card + 
    Max_of_Cards + Total_Expense_Amt + Net_Profit_Card + Years_on_Books + 
    Purchase_Gallons_Qty, data = Cluster1)

Residuals:
    Min      1Q  Median      3Q     Max 
-589.13   -1.94    2.20    5.60  223.04 

Coefficients:
                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)           1.293e+02  1.464e-01  883.43   <2e-16 ***
Average_Gallons_Card -2.132e-03  6.134e-05  -34.75   <2e-16 ***
Max_of_Cards          4.666e-01  7.633e-03   61.12   <2e-16 ***
Total_Expense_Amt    -6.493e-02  3.620e-04 -179.36   <2e-16 ***
Net_Profit_Card       3.950e-02  4.659e-04   84.77   <2e-16 ***
Years_on_Books        6.673e-01  1.304e-02   51.16   <2e-16 ***
Purchase_Gallons_Qty  3.576e-04  4.402e-06   81.23   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 14.12 on 55589 degrees of freedom
  (302 observations deleted due to missingness)
Multiple R-squared:  0.489, Adjusted R-squared:  0.489 
F-statistic:  8868 on 6 and 55589 DF,  p-value: < 2.2e-16

#removed acquisition and Purchase gallons 43%
c3 <- lm(Positive_Profitability ~ Average_Gallons_Card+ Max_of_Cards + Total_Expense_Amt + Net_Profit_Card + Years_on_Books, data = Cluster1)

Dropping 302 rows with missing values

summary(c3)

Call:
lm(formula = Positive_Profitability ~ Average_Gallons_Card + 
    Max_of_Cards + Total_Expense_Amt + Net_Profit_Card + Years_on_Books, 
    data = Cluster1)

Residuals:
    Min      1Q  Median      3Q     Max 
-566.62   -2.48    2.36    6.37  286.67 

Coefficients:
                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)           1.246e+02  1.424e-01  875.45   <2e-16 ***
Average_Gallons_Card  6.815e-04  5.355e-05   12.73   <2e-16 ***
Max_of_Cards          7.784e-01  6.978e-03  111.54   <2e-16 ***
Total_Expense_Amt    -5.411e-02  3.560e-04 -151.98   <2e-16 ***
Net_Profit_Card       3.807e-02  4.924e-04   77.32   <2e-16 ***
Years_on_Books        7.743e-01  1.373e-02   56.41   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 14.93 on 55590 degrees of freedom
  (302 observations deleted due to missingness)
Multiple R-squared:  0.4284,    Adjusted R-squared:  0.4283 
F-statistic:  8333 on 5 and 55590 DF,  p-value: < 2.2e-16

#removed acquisition and Purchase gallons, Years_on_Books 40%
c4<- lm(Positive_Profitability ~ Average_Gallons_Card+ Max_of_Cards + Total_Expense_Amt + Net_Profit_Card, data = Cluster1)

Dropping 302 rows with missing values

summary(c4)

Call:
lm(formula = Positive_Profitability ~ Average_Gallons_Card + 
    Max_of_Cards + Total_Expense_Amt + Net_Profit_Card, data = Cluster1)

Residuals:
    Min      1Q  Median      3Q     Max 
-574.24   -0.82    2.83    5.36  311.75 

Coefficients:
                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)           1.296e+02  1.144e-01 1132.91   <2e-16 ***
Average_Gallons_Card  8.107e-04  5.501e-05   14.74   <2e-16 ***
Max_of_Cards          8.975e-01  6.839e-03  131.23   <2e-16 ***
Total_Expense_Amt    -5.942e-02  3.530e-04 -168.32   <2e-16 ***
Net_Profit_Card       3.838e-02  5.063e-04   75.80   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 15.36 on 55591 degrees of freedom
  (302 observations deleted due to missingness)
Multiple R-squared:  0.3957,    Adjusted R-squared:  0.3956 
F-statistic:  9100 on 4 and 55591 DF,  p-value: < 2.2e-16

#removed acquisition and Purchase gallons, Years_on_Books, NetProfit_Card 33%
c4<- lm(Positive_Profitability ~ Average_Gallons_Card+ Max_of_Cards + Total_Expense_Amt,  data = Cluster1)

Dropping 302 rows with missing values

summary(c4)

Call:
lm(formula = Positive_Profitability ~ Average_Gallons_Card + 
    Max_of_Cards + Total_Expense_Amt, data = Cluster1)

Residuals:
    Min      1Q  Median      3Q     Max 
-303.92   -1.87    2.49    6.69  319.49 

Coefficients:
                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)           1.326e+02  1.129e-01 1174.63   <2e-16 ***
Average_Gallons_Card  2.958e-03  4.953e-05   59.71   <2e-16 ***
Max_of_Cards          8.857e-01  7.182e-03  123.33   <2e-16 ***
Total_Expense_Amt    -6.134e-02  3.698e-04 -165.87   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 16.13 on 55592 degrees of freedom
  (302 observations deleted due to missingness)
Multiple R-squared:  0.3332,    Adjusted R-squared:  0.3332 
F-statistic:  9261 on 3 and 55592 DF,  p-value: < 2.2e-16

#removed acquisition and Purchase gallons, Years_on_Books, NetProfit_Card .02%
c4<- lm(Positive_Profitability ~ Average_Gallons_Card+ Max_of_Cards,  data = Cluster1)
summary(c4)

Call:
lm(formula = Positive_Profitability ~ Average_Gallons_Card + 
    Max_of_Cards, data = Cluster1)

Residuals:
     Min       1Q   Median       3Q      Max 
-134.665   -0.067    4.665    8.655   16.368 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)          1.336e+02  1.370e-01 974.613  < 2e-16 ***
Average_Gallons_Card 1.931e-04  5.700e-05   3.388 0.000705 ***
Max_of_Cards         7.931e-02  6.470e-03  12.259  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 19.7 on 55895 degrees of freedom
Multiple R-squared:  0.002871,  Adjusted R-squared:  0.002835 
F-statistic: 80.46 on 2 and 55895 DF,  p-value: < 2.2e-16

#Net Profit Card 
c4<- lm(Positive_Profitability ~  Net_Profit_Card,  data = Cluster1)
summary(c4)

Call:
lm(formula = Positive_Profitability ~ Net_Profit_Card, data = Cluster1)

Residuals:
    Min      1Q  Median      3Q     Max 
-460.15    0.47    4.55    7.81   19.41 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)     1.306e+02  1.076e-01 1213.00   <2e-16 ***
Net_Profit_Card 3.096e-02  5.206e-04   59.46   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 19.13 on 55896 degrees of freedom
Multiple R-squared:  0.05949,   Adjusted R-squared:  0.05947 
F-statistic:  3536 on 1 and 55896 DF,  p-value: < 2.2e-16

#Net Profit Card 
c4<- lm(Positive_Profitability ~  Average_Gallons_Card ,  data = Cluster1)
summary(c4)

Call:
lm(formula = Positive_Profitability ~ Average_Gallons_Card, data = Cluster1)

Residuals:
     Min       1Q   Median       3Q      Max 
-134.997    0.256    4.429    8.358   15.469 

Coefficients:
                      Estimate Std. Error  t value Pr(>|t|)    
(Intercept)          1.345e+02  1.115e-01 1206.067  < 2e-16 ***
Average_Gallons_Card 1.858e-04  5.707e-05    3.257  0.00113 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 19.73 on 55896 degrees of freedom
Multiple R-squared:  0.0001897, Adjusted R-squared:  0.0001718 
F-statistic: 10.61 on 1 and 55896 DF,  p-value: 0.001128

#Max_Cards 
c4<- lm(Positive_Profitability ~  Max_of_Cards,  data = Cluster1)
summary(c4)

Call:
lm(formula = Positive_Profitability ~ Max_of_Cards, data = Cluster1)

Residuals:
     Min       1Q   Median       3Q      Max 
-134.834   -0.043    4.641    8.720   16.115 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  133.80564    0.11486 1164.93   <2e-16 ***
Max_of_Cards   0.07908    0.00647   12.22   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 19.7 on 55896 degrees of freedom
Multiple R-squared:  0.002666,  Adjusted R-squared:  0.002648 
F-statistic: 149.4 on 1 and 55896 DF,  p-value: < 2.2e-16

#Max_Cards 
c4<- lm(Positive_Profitability ~  Years_on_Books,  data = Cluster1)
summary(c4)

Call:
lm(formula = Positive_Profitability ~ Years_on_Books, data = Cluster1)

Residuals:
     Min       1Q   Median       3Q      Max 
-133.945   -3.428    3.572    9.572   23.572 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    125.08276    0.14087  887.92   <2e-16 ***
Years_on_Books   1.34481    0.01621   82.95   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 18.62 on 55896 degrees of freedom
Multiple R-squared:  0.1096,    Adjusted R-squared:  0.1096 
F-statistic:  6881 on 1 and 55896 DF,  p-value: < 2.2e-16

#Purchase_Gallons_Qty 
c4<- lm(Positive_Profitability ~ Purchase_Gallons_Qty,  data = Cluster1)
summary(c4)

Call:
lm(formula = Positive_Profitability ~ Purchase_Gallons_Qty, data = Cluster1)

Residuals:
     Min       1Q   Median       3Q      Max 
-134.378   -0.104    4.668    8.677   15.940 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)          1.341e+02  9.764e-02 1373.06   <2e-16 ***
Purchase_Gallons_Qty 4.550e-05  3.253e-06   13.98   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 19.7 on 55896 degrees of freedom
Multiple R-squared:  0.003487,  Adjusted R-squared:  0.003469 
F-statistic: 195.6 on 1 and 55896 DF,  p-value: < 2.2e-16

#Acquisition_Cost 
c4<- lm(Positive_Profitability ~ Acquisition_Cost,  data = Cluster1)
summary(c4)

Call:
lm(formula = Positive_Profitability ~ Acquisition_Cost, data = Cluster1)

Residuals:
     Min       1Q   Median       3Q      Max 
-136.695   -1.695    3.305    6.305  154.555 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)      136.695248   0.067131  2036.3   <2e-16 ***
Acquisition_Cost  -0.339475   0.001877  -180.9   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 15.67 on 55896 degrees of freedom
Multiple R-squared:  0.3692,    Adjusted R-squared:  0.3692 
F-statistic: 3.271e+04 on 1 and 55896 DF,  p-value: < 2.2e-16

set.seed(201)
cluster1Smple <- sample_n(Cluster1, 40) %>% na.omit()
summary(cluster1Smple)

 Positive_Profitability Average_Risk_Grade Average_Gallons_Card  Max_of_Cards   Total_Expense_Amt
 Min.   :124.0          Min.   :1.000      Min.   : 224.0       Min.   : 1.00   Min.   :  23.09  
 1st Qu.:134.5          1st Qu.:1.000      1st Qu.: 864.5       1st Qu.: 5.50   1st Qu.:  57.66  
 Median :138.0          Median :1.000      Median :1272.0       Median : 8.00   Median : 130.60  
 Mean   :137.9          Mean   :1.385      Mean   :1594.8       Mean   :12.95   Mean   : 232.18  
 3rd Qu.:142.5          3rd Qu.:1.000      3rd Qu.:1567.5       3rd Qu.:20.00   3rd Qu.: 317.71  
 Max.   :146.0          Max.   :5.000      Max.   :6440.0       Max.   :41.00   Max.   :1039.41  
 Net_Profit_Card  Years_on_Books   Purchase_Gallons_Qty Acquisition_Cost
 Min.   : 53.79   Min.   : 1.000   Min.   : 1344        Min.   :0       
 1st Qu.: 86.75   1st Qu.: 4.000   1st Qu.: 4696        1st Qu.:0       
 Median :105.64   Median : 7.000   Median :10952        Median :0       
 Mean   :144.00   Mean   : 7.538   Mean   :19737        Mean   :0       
 3rd Qu.:155.69   3rd Qu.:11.000   3rd Qu.:31535        3rd Qu.:0       
 Max.   :598.36   Max.   :17.000   Max.   :62123        Max.   :0       

kc <- kmeans(cluster1Smple[, 3:9], 4, nstart = 20)
kc$centers

  Average_Gallons_Card Max_of_Cards Total_Expense_Amt Net_Profit_Card Years_on_Books
1             3233.800    20.400000         577.02400        163.8960       6.200000
2             1277.333    32.000000         581.15000        135.8300      10.666667
3             1272.750     6.583333          96.52958        135.5987       7.375000
4             1664.143    21.285714         301.37571        162.0914       7.714286
  Purchase_Gallons_Qty Acquisition_Cost
1            58223.400                0
2            40548.667                0
3             6727.458                0
4            27929.857                0

kc$size

[1]  5  3 24  7

table(kc$cluster, cluster1Smple$Average_Risk_Grade)

   
     1  2  3  4  5
  1  3  1  1  0  0
  2  3  0  0  0  0
  3 19  2  1  1  1
  4  6  1  0  0  0

kc$cluster <- as.factor(kc$cluster)
ggplot(cluster1Smple, aes(Total_Expense_Amt, Years_on_Books, color = kc$cluster, alpha = 0.1)) + geom_point()

ggplot(cluster1Smple, aes(Max_of_Cards, Total_Expense_Amt, color = kc$cluster, alpha = 0.5)) + geom_point()

head(cluster1Smple)

library(dendextend)
library(circlize)
irisCluster <- kmeans(cluster1Smple[, 3:9], 3, nstart = 20)
irisCluster$centers

  Average_Gallons_Card Max_of_Cards Total_Expense_Amt Net_Profit_Card Years_on_Books
1              1272.75     6.583333          96.52958        135.5987          7.375
2              1548.10    24.500000         385.30800        154.2130          8.600
3              3233.80    20.400000         577.02400        163.8960          6.200
  Purchase_Gallons_Qty Acquisition_Cost
1             6727.458                0
2            31715.500                0
3            58223.400                0

# create a dendrogram
hc <- hclust(dist(cluster1Smple[, 3:9]))
dend <- as.dendrogram(hc)
# modify the dendrogram to have some colors in the branches and labels
dend <- dend %>% 
   color_branches(k=3) %>% 
   color_labels
# plot the radial plot
par(mar = rep(0,4))
# circlize_dendrogram(dend, dend_track_height = 0.8) 
circlize_dendrogram(dend, labels_track_height = NA, dend_track_height = .3) 

# Create the dend:
hc <- hclust(dist(cluster1Smple), "ave")
d <- as.dendrogram(hc)
library(dendextend)
d <- d %>% color_branches(k=3) %>% color_labels
# horiz normal version
par(mar = c(3,1,1,7))
plot(d, horiz  = TRUE)

plot(d, type = "triangle", ylab = "Height")

# Define nodePar
nodePar <- list(lab.cex = 0.6, pch = c(NA, 19), 
                cex = 0.7, col = "blue")
# Customized plot; remove labels
plot(d, ylab = "Height", nodePar = nodePar, leaflab = "none", horiz = T)

library(ape)
dd <- as.phylo(d)
plot(as.phylo(d), type = "unrooted", cex = 0.6,
     no.margin = TRUE)

colors = c("red", "blue", "green", "black")
clus4 = cutree(d, 4)
plot(as.phylo(d), type = "fan", tip.color = colors[clus4],
     label.offset = 1, cex = 0.7)

Principle Component Analysis

cluster1Smple <-  cluster1Smple[, c(1:3, 6:7, 9)]
head(cluster1Smple)

dim(cluster1Smple)

[1] 39  6

library("factoextra")
library("FactoMineR")
res.pca <- PCA(cluster1Smple, graph = FALSE)
res.pca

**Results for the Principal Component Analysis (PCA)**
The analysis was performed on 39 individuals, described by 6 variables
*The results are available in the following objects:

   name               description                          
1  "$eig"             "eigenvalues"                        
2  "$var"             "results for the variables"          
3  "$var$coord"       "coord. for the variables"           
4  "$var$cor"         "correlations variables - dimensions"
5  "$var$cos2"        "cos2 for the variables"             
6  "$var$contrib"     "contributions of the variables"     
7  "$ind"             "results for the individuals"        
8  "$ind$coord"       "coord. for the individuals"         
9  "$ind$cos2"        "cos2 for the individuals"           
10 "$ind$contrib"     "contributions of the individuals"   
11 "$call"            "summary statistics"                 
12 "$call$centre"     "mean of the variables"              
13 "$call$ecart.type" "standard error of the variables"    
14 "$call$row.w"      "weights for the individuals"        
15 "$call$col.w"      "weights for the variables"          

Eigenvalues: The amount of variation retained by each principle component. The first PC corresponds to the direction with the maximum amount of variation in the data set.

eigenvalues <- res.pca$eig
eigenvalues[, 1:3]

fviz_screeplot(res.pca, ncp = 10)

Correlation circle can help to visualize the most correlated variables (i.e, variables that group together).

head(res.pca$var$coord)

                            Dim.1       Dim.2       Dim.3       Dim.4        Dim.5
Positive_Profitability  0.2703974  0.79072304 -0.50243193  0.11335299  0.190671397
Average_Risk_Grade      0.5188911 -0.57893025 -0.12256363  0.61206188  0.077137696
Average_Gallons_Card    0.8164903  0.08213607  0.46206813 -0.19226484  0.275906629
Net_Profit_Card         0.8594656  0.34597993  0.05814373  0.04069142 -0.369567737
Years_on_Books         -0.4857148  0.57199989  0.46898556  0.46577594 -0.001590538
Acquisition_Cost        0.0000000  0.00000000  0.00000000  0.00000000  0.000000000

fviz_pca_var(res.pca)

head(res.pca$var$cos2)

                            Dim.1       Dim.2       Dim.3       Dim.4        Dim.5
Positive_Profitability 0.07311474 0.625242930 0.252437849 0.012848899 3.635558e-02
Average_Risk_Grade     0.26924795 0.335160240 0.015021843 0.374619742 5.950224e-03
Average_Gallons_Card   0.66665647 0.006746334 0.213506960 0.036965770 7.612447e-02
Net_Profit_Card        0.73868109 0.119702112 0.003380693 0.001655792 1.365803e-01
Years_on_Books         0.23591891 0.327183874 0.219947460 0.216947223 2.529810e-06
Acquisition_Cost              NaN         NaN         NaN         NaN          NaN

fviz_pca_var(res.pca, col.var="cos2") +
scale_color_gradient2(low="white", mid="blue", 
                    high="red", midpoint=0.5) + theme_minimal()

head(res.pca$var$contrib)

                           Dim.1      Dim.2      Dim.3      Dim.4        Dim.5
Positive_Profitability  3.685926 44.2169192 35.8426396  1.9981573 1.425636e+01
Average_Risk_Grade     13.573571 23.7023924  2.1328914 58.2578443 2.333301e+00
Average_Gallons_Card   33.608088  0.4770979 30.3149986  5.7486187 2.985120e+01
Net_Profit_Card        37.239058  8.4652834  0.4800111  0.2574954 5.355815e+01
Years_on_Books         11.893357 23.1383071 31.2294593 33.7378843 9.920312e-04
Acquisition_Cost        0.000000  0.0000000  0.0000000  0.0000000 0.000000e+00

fviz_pca_contrib(res.pca, choice = "var", axes = 1)

The function fviz_pca_contrib() is deprecated. Please use the function fviz_contrib() which can handle outputs  of PCA, CA and MCA functions.

# Contributions of variables on PC2
fviz_pca_contrib(res.pca, choice = "var", axes = 2)

The function fviz_pca_contrib() is deprecated. Please use the function fviz_contrib() which can handle outputs  of PCA, CA and MCA functions.

# Total contribution on PC1 and PC2
fviz_pca_contrib(res.pca, choice = "var", axes = 1:2)

The function fviz_pca_contrib() is deprecated. Please use the function fviz_contrib() which can handle outputs  of PCA, CA and MCA functions.

# Control variable colors using their contributions
fviz_pca_var(res.pca, col.var="contrib")

res.desc <- dimdesc(res.pca, axes = c(1,2))
# Description of dimension 1
res.desc$Dim.1

$quanti
                     correlation      p.value
<NA>                          NA           NA
Net_Profit_Card        0.8594656 2.480154e-12
Average_Gallons_Card   0.8164903 2.349891e-10
Average_Risk_Grade     0.5188911 7.132008e-04
Years_on_Books        -0.4857148 1.721179e-03

# Description of dimension 2
res.desc$Dim.2

$quanti
                       correlation      p.value
<NA>                            NA           NA
Positive_Profitability   0.7907230 2.112538e-09
Years_on_Books           0.5719999 1.422417e-04
Net_Profit_Card          0.3459799 3.096904e-02
Average_Risk_Grade      -0.5789303 1.128856e-04

head(res.pca$ind$coord)

            Dim.1      Dim.2      Dim.3      Dim.4       Dim.5
34243 -0.37589960 -0.5753707 -0.6431437 -0.8885824  0.08424434
9326   1.90290466 -3.8032097 -0.2865659  2.0146682 -0.60309285
20415 -0.08793709 -0.6820111 -0.6426179 -1.0198923 -0.29354963
2219   1.79101571  1.5519877 -0.8573422 -0.3878541 -1.06866041
35085 -0.25916907 -1.0412526 -0.8765024  0.1790552  0.07565001
7755   2.32037917  1.0636005  0.6796273 -1.1349772  1.30067377

fviz_pca_ind(res.pca)

# Contributions of the individuals to PC1
fviz_pca_contrib(res.pca, choice = "ind", axes = 1, top = 10)

The function fviz_pca_contrib() is deprecated. Please use the function fviz_contrib() which can handle outputs  of PCA, CA and MCA functions.

clusterZ <- cluster1Smple %>% mutate(marketingCost = Acquisition_Cost + 5)
cs <- clusterZ %>% mutate(Positive_ProfitabilityZ = scale(Positive_Profitability), AvRiskGrZ = scale(Average_Risk_Grade) ,AvGallCardZ = scale(Average_Gallons_Card), NetProfitCardZ = scale(Net_Profit_Card), YrZ = scale(Years_on_Books), MarketZ = scale(marketingCost))
cs <- cs %>% dplyr::select(Positive_ProfitabilityZ, AvRiskGrZ, AvGallCardZ, NetProfitCardZ, YrZ)
Customer <- seq(from=1, to=195, by=1)
clusterLong <- gather(cs, variable, value,Positive_ProfitabilityZ:YrZ)
ClusterData <- cbind.data.frame(Customer, clusterLong)
ClusterData$variable <- as.factor(ClusterData$variable)
ClusterData$Customer <- as.character(ClusterData$Customer)
ggplot(ClusterData, aes(x = value, fill = variable)) + geom_histogram() + facet_grid(~variable) + theme_bw()
ggplot(ClusterData, aes(x=value, fill=variable)) + geom_density() + theme_bw()
ggplot(ClusterData, aes(x=value, colour=variable)) + geom_density(size = 2) + facet_wrap(~variable) + theme_bw()

# Density plots with semi-transparent fill
ggplot(ClusterData, aes(x=value, fill=variable)) + geom_density(alpha=.3)

ggplot(ClusterData, aes(x=value)) + geom_histogram(binwidth=.5, colour="black", fill="white") + 
    facet_grid(~ variable) + theme_bw()

# Histogram overlaid with kernel density curve
ggplot(ClusterData, aes(x=value)) + 
    geom_histogram(aes(y=..density..),      # Histogram with density instead of count on y-axis
                   binwidth=.5,
                   colour="black", fill="white") +
    geom_density(alpha=.2, fill="#FF6666")  + facet_grid(~ variable) + theme_bw()# Overlay with transparent density plot

1

set.seed(201)
cluster2Sample <- sample_n(Cluster1, 1000) %>% na.omit()

head(cluster2Sample)
dat <- cluster2Sample[, 3:9] # without known classification 
# Kmeans clustre analysis
clus <- kmeans(dat, centers=3)
# Fig 01
plotcluster(dat, clus$cluster)

2

dat <- cluster2Sample[, 3,5:9] # without known classification 
# Kmeans clustre analysis
clus <- kmeans(dat, centers=3)
# Fig 01
plotcluster(dat, clus$cluster)

Error in plotcluster(dat, clus$cluster) : 
  could not find function "plotcluster"

3

dat <- cluster2Sample[, 3:4,6:9] # without known classification 
# Kmeans clustre analysis
clus <- kmeans(dat, centers=3)
# Fig 01
plotcluster(dat, clus$cluster)

4

dat <- cluster2Sample[, 3:5, 7:9] # without known classification 
# Kmeans clustre analysis
clus <- kmeans(dat, centers=3)
# Fig 01
plotcluster(dat, clus$cluster)

5

dat <- cluster2Sample[, 3:6, 8:9] # without known classification 
# Kmeans clustre analysis
clus <- kmeans(dat, centers=3)
# Fig 01
plotcluster(dat, clus$cluster)

6

dat <- cluster2Sample[, 3:7,9] # without known classification 
# Kmeans clustre analysis
clus <- kmeans(dat, centers=3)
# Fig 01
plotcluster(dat, clus$cluster)

ggcorr(Cluster1, label = T)

corrgram(as.matrix(Cluster1), order = NULL, panel = panel.shade, text.panel = panel.txt, main = "Correlogram") 

fit <- lm(Profitability ~  Net_Late_Fee_Count + Acquisition_Cost + Net_Profit +  Years_on_Books +  Average_Risk_Grade, data=Cluster)
summary(fit) # show results
Cluster <- Cluster %>% dplyr::select(Random, Customer_Index, Profitability, Net_Late_Fee_Count, Acquisition_Cost, Net_Profit, Years_on_Books)
Cluster <- as.matrix(Cluster)

ggplot(newdata, aes(x = Positive_Profitability, y = Max_of_Cards )) + geom_point() + geom_smooth(method = "lm")

                      #,color = factor(Years_on_Books
                                     
ggplot(newdata, aes(x = Positive_Profitability, y = Gross_Revenue_Amt )) + geom_point() + geom_smooth(method = "lm")

ggplot(newdata, aes(y = Positive_Profitability, x = Card_Fees_Amt )) + geom_point() + geom_smooth(method = "lm")