housingSubsidy_cf <- housingSubsidy %>%
  dplyr::select(-X, -y_numeric) %>%
  select_if(is.numeric) %>% 
  cbind(y = housingSubsidy$y) %>%
  gather(Variable, value, -y)

ggplot(housingSubsidy_cf, aes(y, abs(value), fill=y)) + 
  geom_bar(position = "dodge", stat = "summary", fun = "mean", width = 0.3) + 
  facet_wrap(~Variable, scales = "free") +
  scale_fill_manual(values = c(bluePalette5[2],bluePalette5[4]),
                    name = "Housing\nSubsidy") +
  labs(x="Housing Subsidy", y="Mean value",
       title = "Mean value of Feature associations with Housing Subsidy",
       subtitle = "continous features",
       caption = "Figure 2-1-1") +
  geom_hline(yintercept = 0, size = 0.25, color = greyPalette5[3]) +
  corTheme2()+
  theme(panel.background = element_blank(),
        panel.grid.major.y = element_line(linetype = "longdash", size = 0.25, color = greyPalette5[2]))

ggplot(housingSubsidy_cf) + 
  geom_density(aes(value, linetype=y, color=y, ), fill = "transparent", size = 0.8) + 
  facet_wrap(~Variable, scales = "free") +
  scale_color_manual(values = c(bluePalette5[3],bluePalette5[4])) +
  labs(title = "Feature Distribution of taking Housing Subsidy",
       subtitle = "continous features",
       caption = "Figure 2-1-2")+
  geom_hline(yintercept = 0, size = 0.25, color = greyPalette5[3]) +
  corTheme2()+
  theme(panel.background = element_blank(),
        panel.grid.major.y = element_line(linetype = "longdash", size = 0.25, color = greyPalette5[2]))+
  guides(linetype=guide_legend(title = "Housing\nSubsidy"),
         color=guide_legend(title = "Housing\nSubsidy")) 

housingSubsidy_mcf <- housingSubsidy %>%
  dplyr::select(-X, -y_numeric) %>%
  select_if(is.character) %>% 
  gather(Variable, value, -y) %>%
  count(Variable, value, y)

ggplot(housingSubsidy_mcf, aes(value, n, fill = y)) +
  geom_bar(position = "dodge", stat="identity", width = 0.9) +
  facet_wrap(~Variable, scales="free") +
  scale_fill_manual(values = c(bluePalette5[2],bluePalette5[4]),
                    name = "Housing\nSubsidy") +
  labs(x="Feature", y="Count",
       title = "Feature associations with the likelihood of taking Housing Subsidy",
       subtitle = "Two/Three category Features",
       caption = "Figure 2-2-1") +
  geom_hline(yintercept = 0, size = 0.25, color = greyPalette5[3]) +
  corTheme2()+
  theme(panel.background = element_blank(),
        panel.grid.major.y = element_line(linetype = "longdash", size = 0.25, color = greyPalette5[2]),
        axis.text.x = element_text(angle = 45, hjust = 1, size = 5))

#1 education : Bchmore / Bchless

#Bchmore : "university.degree""professional.course"
#Bchless : "basic.9y""high.school""basic.6y""basic.4y""illiterate"
#unknown : "unknown"    

housingSubsidy <- housingSubsidy %>% 
  mutate(education_min = case_when(education == "university.degree"| education == "professional.course" ~  "Bchmore",
                                   education == "basic.9y"| education == "high.school"| education == "basic.6y"| education == "basic.4y"
                                   |education == "illiterate" ~  "Bchless"
                                   ,education == "unknown" ~ "unknown")) 


#2 JOB: employed / unemployed 

#employed : "blue-collar""services""admin.""entrepreneur""self-employed" "technician""management""housemaid"      
#unemployed : "unemployed""student""retired"
#unknown : "unknown"

housingSubsidy <- housingSubsidy %>% 
  mutate(job_min = case_when(job == "blue-collar"|job =="services"|job =="admin."|job =="entrepreneur"|job =="self-employed"
                             |job =="technician"|job =="management"|job =="housemaid" ~ "employed",
                             job == "unemployed"|job =="student"|job =="retired"~ "unemployed",
                             job == "unknown"~ "unknown"))


#3 marital: single / non-single

#single :  "single""divorced"
#non-single : "married" 
#unknown : "unknown" 

housingSubsidy <- housingSubsidy %>% 
  mutate(martial_min = case_when(marital == "single"|marital =="divorced" ~ "single",
                                 marital == "married" ~ "married",
                                 marital == "unknown" ~ "unknown"))

#4 month: spring_summer / autumn_winter 
 

# spring_summer: "apr" "may" "jun" "jul" "aug"
# autumn_winter: "nov" "sep" "mar" "oct" "dec"


housingSubsidy <- housingSubsidy %>% 
  mutate(month_min = case_when(month == "apr" |month == "may" |month == "jun" |month =="jul"|month == "aug" ~ "spring_summer",
                                 month == "nov" |month =="sep"|month == "mar"|month == "oct"|month == "dec" ~ "autumn_winter"))


#5 age: less55 / over55 

# less55: =< 55
# over55: > 55

housingSubsidy <- housingSubsidy %>% 
  mutate(age_min = case_when(age <= 55 ~ "less55",
                             age > 55 ~ "over55"))

#6 inflation rate: less3 / over3 

# less3: =< 3
# over3: > 3

housingSubsidy <- housingSubsidy %>% 
  mutate(inflation_rate_min = case_when(inflation_rate <= 3 ~ "less3",
                                        inflation_rate > 3 ~ "over3"))

#7 pdays: contact / non-contact 

# contact: < 999
# none-contact : >= 999

housingSubsidy <- housingSubsidy %>% 
  mutate(pdays_min = case_when(pdays < 999 ~ "contact",
                                        pdays >= 999 ~ "non-contact"))

#8 previous: less0 / over0 

# less0: =< 0
# over0: > 0

housingSubsidy <- housingSubsidy %>% 
  mutate(previous_min = case_when(previous <= 0 ~ "less0",
                                  previous > 0 ~ "over0"))

#9 spent_on_repairs: less5160 / over5160 

# less5160: =< 5160
# over5160: > 5160

housingSubsidy <- housingSubsidy %>% 
  mutate(spent_on_repairs_min = case_when(spent_on_repairs <= 5160 ~ "less5160",
                                          spent_on_repairs > 5160 ~ "over5160"))

#10 unemploy_rate: less0.5 / over0.5 

# less0.5: =< 0.5
# over0.5: > 0.5

housingSubsidy <- housingSubsidy %>% 
  mutate(unemploy_rate_min = case_when(unemploy_rate <= 0.5 ~ "less0.5",
                                          unemploy_rate > 0.5 ~ "over0.5"))



housingSubsidy_fe <- housingSubsidy %>%
    dplyr::select(y, education_min, job_min, martial_min, month_min, age_min, inflation_rate_min, pdays_min, previous_min, spent_on_repairs_min, unemploy_rate_min) %>%
    gather(Variable, value, -y) %>%
    count(Variable, value, y)

ggplot(housingSubsidy_fe, aes(value, n, fill = y)) +   
    geom_bar(position = "dodge", stat="identity", width = 0.9) +
    facet_wrap(~Variable, scales="free") +
    scale_fill_manual(values = c(bluePalette5[2],bluePalette5[4]),
                      name = "Housing\nSubsidy") +
    labs(x="Feature", y="Counts",
         title = "Feature associations with the likelihood of taking Housing Subsidy",
         subtitle = "Feature engineered category features",
         caption = "Figure 4-1-1") +
  geom_hline(yintercept = 0, size = 0.25, color = greyPalette5[3]) +
  corTheme2()+
  theme(panel.background = element_blank(),
        panel.grid.major.y = element_line(linetype = "longdash", size = 0.25, color = greyPalette5[2]),
        axis.text.x = element_text(angle = 0, hjust = 0.5, size = 5))

rm12 <- cbind(rm1, rm2)

kable(rm12, caption = "<center><span style='font-size:14px; color:black; font-family: Arial'>Table 4-2-1. Regression Summary</span></center>",
      col.names = c("Regression Model 1 : kitchen sink", "Regression Model 2 : engineered"), align = "c") %>% 
    kable_minimal(full_width = T, html_font = "Arial", font_size = 14) %>%
    row_spec(4, color = greyPalette5[5], background = greyPalette5[1], bold = T) %>%
    row_spec(0:6, extra_css = "line-height: 35px")

# model_1

testProbs_1 <- data.frame(Outcome = as.factor(housingSubsityTest$y_numeric),
                          Probs = predict(housingSubsidyModel_1, housingSubsityTest, type= "response"))

testProbs_1 <- 
  testProbs_1 %>%
  mutate(predOutcome  = as.factor(ifelse(testProbs_1$Probs > 0.5 , 1, 0)),
         Model = 1)


# model_2

testProbs_2 <- data.frame(Outcome = as.factor(housingSubsityTest$y_numeric),
                          Probs = predict(housingSubsidyModel_2, housingSubsityTest, type= "response"))

testProbs_2 <- 
  testProbs_2 %>%
  mutate(predOutcome  = as.factor(ifelse(testProbs_2$Probs > 0.5 , 1, 0)),
         Model = 2)

testProbs_12 <- rbind(testProbs_1,testProbs_2)


gg431 <- ggplot(testProbs_1, aes(x = Probs, fill = as.factor(Outcome))) + 
  geom_density() +
  facet_grid(Outcome ~ .) +
  scale_fill_manual(values = c(bluePalette5[2], bluePalette5[4])) + xlim(0, 1) +
  geom_hline(yintercept = 0, size = 0.25, color = greyPalette5[3]) +
  geom_vline(xintercept = 0.5, size = 0.4, color = bluePalette5[3], linetype = "longdash") +
  labs(x = "Probability of Getting Subsidy", y = "Density",
       title = "Regression Model 1",
       subtitle = "kitchen sink",
       caption = "Figure 4-3-1")  +
  corTheme2()+
  theme(panel.background = element_blank(),
        panel.grid.major.y = element_line(linetype = "dashed", size = 0.25, color = greyPalette5[2]),
        legend.position = "none",
        strip.text.x = element_blank(),
        strip.text.y = element_blank())

Outcome.labs <- c("Don't Get Subsidy", "Get Subsidy")
names(Outcome.labs) <-c(0, 1)

gg432 <- ggplot(testProbs_2, aes(x = Probs, fill = as.factor(Outcome))) + 
  geom_density() +
  facet_grid(Outcome ~ .,labeller = as_labeller(Outcome.labs)) +
  scale_fill_manual(values = c(bluePalette5[2], bluePalette5[4])) + xlim(0, 1) +
  geom_hline(yintercept = 0, size = 0.25, color = greyPalette5[3]) +
  geom_vline(xintercept = 0.5, size = 0.4, color = bluePalette5[3], linetype = "longdash") +
  scale_y_continuous(position = "right")+
  labs(x = "Probability of Getting Subsidy", y = "",
       title = "Regression Model 2",
       subtitle = "engineered",
       caption = "Figure 4-3-2")  +
  corTheme2()+
  theme(panel.background = element_blank(),
        panel.grid.major.y = element_line(linetype = "dashed", size = 0.25, color = greyPalette5[2]),
        legend.position = "none")


gg431 + gg432 

# model_1

cf1 <- caret::confusionMatrix(testProbs_1$predOutcome, testProbs_1$Outcome, positive = "1")
cf2 <- caret::confusionMatrix(testProbs_2$predOutcome, testProbs_2$Outcome, positive = "1")

cf <- round(rbind(cf1$byClass, cf2$byClass),3)

rownames(cf) <- c("Kitchen sink model","Engineered model")
colnames(cf) <- c("Sens","Spec","Pos Pred","Neg Pred","Precis","Recall","F1","Preval","Det Rate","Det Preval", "Bal Accu")


kable(cf, caption = "<center><span style='font-size:14px; color:black; font-family: Arial'>Table 4-3. confusion metrics for the threshold of 50% of both model</span></center>", align = "c", booktabs = T, escape=FALSE) %>%
  kable_minimal(full_width = T, html_font = "Arial", font_size = 13)%>%
  column_spec(1, bold = T)  %>%
  row_spec(1:2, extra_css = "line-height: 30px")

auc1 <- round(pROC::auc(testProbs_1$Outcome, testProbs_1$Probs),3)
auc2 <- round(pROC::auc(testProbs_2$Outcome, testProbs_2$Probs),3)

auc1 <- paste("kitchen sink\n\n", "AUC:", auc1)
auc2 <- paste("engineered\n\n","AUC:", auc2)


ggauc1 <- ggplot(testProbs_1, aes(d = as.numeric(testProbs_1$Outcome), m = Probs)) +
  geom_roc(n.cuts = 30, labels = FALSE, colour = bluePalette5[3], pointsize = 0.4, size = 0.6) +
  style_roc(theme = theme_grey) +
  geom_abline(slope = 1, intercept = 0, size = 0.4, color = greyPalette5[3]) +
  labs(title = "ROC curve",
       subtitle = auc1,
       caption = "Figure 4-3-3",
       y = "True Positive Fraction") +
  corTheme2()+
  theme(panel.background = element_blank(),
        panel.grid.major.y = element_line(linetype = "dashed", size = 0.25, color = greyPalette5[2]),
        panel.grid.major.x = element_line(linetype = "dashed", size = 0.25, color = greyPalette5[2]),
        legend.position = "none")


ggauc2 <- ggplot(testProbs_2, aes(d = as.numeric(testProbs_2$Outcome), m = Probs)) +
  geom_roc(n.cuts = 30, labels = FALSE, colour = bluePalette5[4], pointsize = 0.4, size = 0.6) +
  style_roc(theme = theme_grey) +
  geom_abline(slope = 1, intercept = 0, size = 0.4, color = greyPalette5[3]) +
  scale_y_continuous(position = "right")+
  labs(title = "ROC curve",
       subtitle = auc2,
       caption = "Figure 4-3-4",
       y = "True Positive Fraction")+
  corTheme2()+
  theme(panel.background = element_blank(),
        panel.grid.major.y = element_line(linetype = "dashed", size = 0.25, color = greyPalette5[2]),
        panel.grid.major.x = element_line(linetype = "dashed", size = 0.25, color = greyPalette5[2]),
        legend.position = "none")


ggauc1 + ggauc2

ctrl2 <- trainControl(method = "cv", number = 100, classProbs=TRUE, summaryFunction=twoClassSummary)

cv_1 <- train(y ~ .,
              data=housingSubsidy %>%
                dplyr::select(-X, -inflation_rate_min, -pdays_min, -previous_min, -spent_on_repairs_min, -unemploy_rate_min,
                              -education_min, -job_min, -martial_min, -month_min, -age_min, -y_numeric), 
                method="glm", family="binomial", metric="ROC", trControl = ctrl2)

cv_gfm1 <- round(cv_1$results[2:4],4)

cv_2 <- train(y ~ .,
              data=housingSubsidy %>% 
                dplyr::select(-X, -education, -job, -marital, -month, -age, -day_of_week, -inflation_rate_min, -pdays_min, -previous_min, -spent_on_repairs_min, -unemploy_rate_min, -y_numeric), 
                method="glm", family="binomial",
                metric="ROC", trControl = ctrl2)

cv_gfm2 <- round(cv_2$results[2:4],4)

cv_gfm <- rbind(cv_gfm1, cv_gfm2) 

rownames(cv_gfm) <- c("Kitchen sink model","Engineered model")
colnames(cv_gfm) <- c("ROC(AUC)","Sensitivity","Specificity")

cv_gfm <- cv_gfm %>% mutate(Sensitivity = cell_spec(Sensitivity, background = ifelse(Sensitivity > 0.982, bluePalette5[2], "white"),
                                                     bold = ifelse(Sensitivity > 0.982, T, F)))

kable(cv_gfm, caption = "<center><span style='font-size:14px; color:black; font-family: Arial'>Table 4-4-1. The Sensitivity(True Positive Rate) of each model</span></center>", align = "c", booktabs = T, escape=FALSE) %>%
  kable_minimal(full_width = F, html_font = "Arial", font_size = 16)%>%
  column_spec(2:4, width = "5.3cm") %>%
  column_spec(1, bold = T)  %>%
  row_spec(1:2, extra_css = "line-height: 30px")

cv_1_resample <- cv_1$resample %>%
  dplyr::select(-Resample) %>%
  gather(metric, value) %>% # column to row with value (100obj > 300obj)
  left_join(gather(cv_1$results[2:4], metric, mean)) %>% #metric is key to left join
  mutate(Model = "Kitchen Sink Model")


cv_2_resample <- cv_2$resample %>%
  dplyr::select(-Resample) %>%
  gather(metric, value) %>% # column to row with value (100obj > 300obj)
  left_join(gather(cv_2$results[2:4], metric, mean)) %>% #metric is key to left join
  mutate(Model = "Engineered_Model")

cv_12_resample <- rbind(cv_1_resample,cv_2_resample)

ggplot(cv_12_resample, aes(value)) + 
    geom_histogram(bins=35, fill = bluePalette5[3], color = "white") +
    facet_wrap(vars(Model, metric)) +
    geom_hline(yintercept = 0, size = 0.25, color = greyPalette5[3]) +
    geom_vline(aes(xintercept = mean), colour = bluePalette5[4], linetype = 4, size = 0.7) +
    scale_x_continuous(limits = c(0, 1)) +
    labs(x="Goodness of Fit", y="Count", title="CV Goodness of Fit Metrics",
         subtitle = "Across-fold mean reprented as dotted lines",
         caption = "Figure 4-4-2")+
  corTheme2()+
  theme(panel.background = element_blank(),
        panel.grid.major.y = element_line(linetype = "dashed", size = 0.25, color = greyPalette5[2]),
        panel.grid.major.x = element_line(linetype = "dashed", size = 0.25, color = greyPalette5[2]),
        legend.position = "none")

cost_benefit_table <-
   testProbs_2 %>%
      count(predOutcome, Outcome) %>%
      summarize(True_Negative = sum(n[predOutcome==0 & Outcome==0]),
                True_Positive = sum(n[predOutcome==1 & Outcome==1]),
                False_Negative = sum(n[predOutcome==0 & Outcome==1]),
                False_Positive = sum(n[predOutcome==1 & Outcome==0])) %>%
       gather(Variable, Count) %>%
       mutate(Revenue =
               ifelse(Variable == "True_Negative", Count * 0,
               ifelse(Variable == "True_Positive",(Count * (-2850-5000*0.25+10000*0.25+56000*0.25)),
               ifelse(Variable == "False_Negative", Count * 0,
               ifelse(Variable == "False_Positive", Count * (-2850), 0))))) %>%
    bind_cols(data.frame(Description = c(
              "We predicted correctly homeowner would not take the credit",
              "We predicted correctly homeowner would enter credit program",
              "We predicted that a homeowner would not take the credit but they did",
              "We predicted incorrectly homeowner would take the credit")))


kable(cost_benefit_table, caption = "<center><span style='font-size:14px; color:black; font-family: Arial'>Table 5-1. Cost/Benefit Table of 50% thresholds</span></center>",
      align = "c") %>% 
      kable_minimal(full_width = T, html_font = "Arial", font_size = 15) %>%
      column_spec(1, bold = TRUE) %>%
      row_spec(c(2,4), background = greyPalette5[1]) %>%
      row_spec(1:4, extra_css = "line-height: 35px") 

iterateThresholds <- function(data) {
  x = .01
  all_prediction <- data.frame()
  while (x <= 1) {
    this_prediction <- testProbs_2 %>%
      mutate(predOutcome = ifelse(Probs > x, 1, 0)) %>%
      count(predOutcome, Outcome) %>%
      summarize(True_Negative = sum(n[predOutcome==0 & Outcome==0]),
                True_Positive = sum(n[predOutcome==1 & Outcome==1]),
                False_Negative = sum(n[predOutcome==0 & Outcome==1]),
                False_Positive = sum(n[predOutcome==1 & Outcome==0])) %>%
       gather(Variable, Count) %>%
       mutate(Revenue =
               ifelse(Variable == "True_Negative", Count * 0,
               ifelse(Variable == "True_Positive",(Count * (-2850-5000*0.25+10000*0.25+56000*0.25)),
               ifelse(Variable == "False_Negative", Count * 0,
               ifelse(Variable == "False_Positive", Count * (-2850), 0)))),
              Threshold = x)
    all_prediction <- rbind(all_prediction, this_prediction)
    x <- x + .01
  }
return(all_prediction)
}

whichThreshold <- iterateThresholds(testProbs2)

whichThreshold %>%
  ggplot(.,aes(Threshold, Revenue, colour = Variable)) +
  geom_point() +
  scale_colour_manual(values = bluePalette5[2:5]) +    
  labs(title = "Revenue by confusion matrix type and threshold",
       y = "Revenue",
       caption = "Figure 5-2-1") +
  corTheme2()+
  theme(panel.background = element_blank(),
        panel.grid.major.y = element_line(linetype = "dashed", size = 0.35, color = greyPalette5[2]),
        panel.grid.major.x = element_line(linetype = "dashed", size = 0.35, color = greyPalette5[2]),
        legend.position = "bottom",
        legend.background = element_rect(fill = "white")) +
  guides(colour=guide_legend(title = "Confusion Matrix")) 

whichThreshold_revenue_subsidy <- 
whichThreshold %>% 
    mutate(Credits = 
             ifelse(Variable == "True_Positive", Count*0.25,
             ifelse(Variable == "False_Negative", Count, 0))) %>%
    group_by(Threshold) %>% 
    summarize(Revenue = sum(Revenue)/1000,
              Total_Count_of_Credits = sum(Credits))

gg522 <- ggplot(whichThreshold_revenue_subsidy, aes(Threshold, Revenue)) +
  geom_point(color = bluePalette5[3], size = 1.2) +
  scale_colour_manual(values = bluePalette5) +    
  labs(title = "Revenue by threshold",
       y = "Revenue(1,000$)",
       caption = "Figure 5-2-2") +
  corTheme2()+
  theme(panel.background = element_blank(),
        panel.grid.major.y = element_line(linetype = "dashed", size = 0.45, color = greyPalette5[2]),
        panel.grid.major.x = element_line(linetype = "dashed", size = 0.45, color = greyPalette5[2]),
        legend.position = "bottom",
        axis.text.y = element_text(angle = 90)) +
  guides(colour=guide_legend(title = "Confusion Matrix")) 

gg523 <- ggplot(whichThreshold_revenue_subsidy, aes(Threshold, Total_Count_of_Credits)) +
  geom_point(color = bluePalette5[4], size = 1.2) +
  scale_colour_manual(values = bluePalette5) +
  scale_y_continuous(position = "right")+
  labs(title = "Total Counts of Credits by threshold",
       y = "Total Counts of Credits",
       caption = "Figure 5-2-3") +
  corTheme2()+
  theme(panel.background = element_blank(),
        panel.grid.major.y = element_line(linetype = "dashed", size = 0.45, color = greyPalette5[2]),
        panel.grid.major.x = element_line(linetype = "dashed", size = 0.45, color = greyPalette5[2]),
        legend.position = "bottom",
        axis.text.y = element_text(angle = 270)) +
  guides(colour=guide_legend(title = "Confusion Matrix")) 


gg522 + gg523

whichThreshold_revenue_subsidy <- 
whichThreshold %>% 
    mutate(Credits = 
             ifelse(Variable == "True_Positive", Count*0.25,
             ifelse(Variable == "False_Negative", Count, 0))) %>%
    group_by(Threshold) %>% 
    summarize(Revenue = sum(Revenue),
              Total_Count_of_Credits = sum(Credits))


finalTable <- whichThreshold_revenue_subsidy %>%
  filter(Threshold >= 0.50 & Threshold < 0.51 | Threshold >= pull(arrange(whichThreshold_revenue_subsidy, -Revenue)[1,1]) & Threshold < pull(arrange(whichThreshold_revenue_subsidy, -Revenue)[1,1])+0.01 )

kable(finalTable, caption = "<center><span style='font-size:14px; color:black; font-family: Arial'>Table 5-3. Cost/Benefit Comparison Table</span></center>",
      align = "c") %>% 
      kable_minimal(full_width = T, html_font = "Arial", font_size = 16)%>%
      column_spec(1:2, bold = TRUE) %>%
      row_spec(1, color = orangePalette5[5]) %>%
      row_spec(2, color = bluePalette5[4]) %>%
      row_spec(1:2, extra_css = "line-height: 30px") 

ggplot(whichThreshold_revenue_subsidy)+
  geom_line(aes(x = Threshold, y = Revenue), color = greyPalette5[3], size = 0.8)+
  geom_vline(xintercept =  pull(arrange(whichThreshold_revenue_subsidy, -Revenue)[1,1]), color = orangePalette5[5], size = 0.8, linetype = "longdash")+
  geom_vline(xintercept = 0.5, color = bluePalette5[4], size = 0.8, linetype = "longdash")+
  scale_x_continuous(minor_breaks = seq(0, 1, 0.05))+
  labs(title = "Model Revenues By Threshold",
       subtitle = "Orange line : 0.17 Optimal Threshold           Blue line : 0.5 Threshold",
       caption = "Figure 5-3-1")+
  corTheme2()+
  theme(panel.background = element_blank(),
        panel.grid.major.y = element_line(linetype = "dashed", size = 0.45, color = greyPalette5[2]),
        panel.grid.major.x = element_line(linetype = "dashed", size = 0.45, color = greyPalette5[2]),
        panel.grid.minor.x = element_line(linetype = "dotted", size = 0.45, color = greyPalette5[2]),
        legend.position = "bottom",
        axis.text.y = element_text(angle = 90))