---
title: "perfect_separartion"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
```{r}
lines <- 
"Length  Left  Right  Bottom  Top  Diagonal  Y
214.8  131  131.1  9  9.7  141  0
214.6  129.7  129.7  8.1  9.5  141.7  0
214.8  129.7  129.7  8.7  9.6  142.2  0
214.8  129.7  129.6  7.5  10.4  142  0
215  129.6  129.7  10.4  7.7  141.8  0
215.7  130.8  130.5  9  10.1  141.4  0
215.5  129.5  129.7  7.9  9.6  141.6  0
214.5  129.6  129.2  7.2  10.7  141.7  0
214.9  129.4  129.7  8.2  11  141.9  0
215.2  130.4  130.3  9.2  10  140.7  0
215.3  130.4  130.3  7.9  11.7  141.8  0
215.1  129.5  129.6  7.7  10.5  142.2  0
215.2  130.8  129.6  7.9  10.8  141.4  0
214.7  129.7  129.7  7.7  10.9  141.7  0
215.1  129.9  129.7  7.7  10.8  141.8  0
214.5  129.8  129.8  9.3  8.5  141.6  0
214.6  129.9  130.1  8.2  9.8  141.7  0
215  129.9  129.7  9  9  141.9  0
215.2  129.6  129.6  7.4  11.5  141.5  0
214.7  130.2  129.9  8.6  10  141.9  0
215  129.9  129.3  8.4  10  141.4  0
215.6  130.5  130  8.1  10.3  141.6  0
215.3  130.6  130  8.4  10.8  141.5  0
215.7  130.2  130  8.7  10  141.6  0
215.1  129.7  129.9  7.4  10.8  141.1  0
215.3  130.4  130.4  8  11  142.3  0
215.5  130.2  130.1  8.9  9.8  142.4  0
215.1  130.3  130.3  9.8  9.5  141.9  0
215.1  130  130  7.4  10.5  141.8  0
214.8  129.7  129.3  8.3  9  142  0
215.2  130.1  129.8  7.9  10.7  141.8  0
214.8  129.7  129.7  8.6  9.1  142.3  0
215  130  129.6  7.7  10.5  140.7  0
215.6  130.4  130.1  8.4  10.3  141  0
215.9  130.4  130  8.9  10.6  141.4  0
214.6  130.2  130.2  9.4  9.7  141.8  0
215.5  130.3  130  8.4  9.7  141.8  0
215.3  129.9  129.4  7.9  10  142  0
215.3  130.3  130.1  8.5  9.3  142.1  0
213.9  130.3  129  8.1  9.7  141.3  0
214.4  129.8  129.2  8.9  9.4  142.3  0
214.8  130.1  129.6  8.8  9.9  140.9  0
214.9  129.6  129.4  9.3  9  141.7  0
214.9  130.4  129.7  9  9.8  140.9  0
214.8  129.4  129.1  8.2  10.2  141  0
214.3  129.5  129.4  8.3  10.2  141.8  0
214.8  129.9  129.7  8.3  10.2  141.5  0
214.8  129.9  129.7  7.3  10.9  142  0
214.6  129.7  129.8  7.9  10.3  141.1  0
214.5  129  129.6  7.8  9.8  142  0
214.6  129.8  129.4  7.2  10  141.3  0
215.3  130.6  130  9.5  9.7  141.1  0
214.5  130.1  130  7.8  10.9  140.9  0
215.4  130.2  130.2  7.6  10.9  141.6  0
214.5  129.4  129.5  7.9  10  141.4  0
215.2  129.7  129.4  9.2  9.4  142  0
215.7  130  129.4  9.2  10.4  141.2  0
215  129.6  129.4  8.8  9  141.1  0
215.1  130.1  129.9  7.9  11  141.3  0
215.1  130  129.8  8.2  10.3  141.4  0
215.1  129.6  129.3  8.3  9.9  141.6  0
215.3  129.7  129.4  7.5  10.5  141.5  0
215.4  129.8  129.4  8  10.6  141.5  0
214.5  130  129.5  8  10.8  141.4  0
215  130  129.8  8.6  10.6  141.5  0
215.2  130.6  130  8.8  10.6  140.8  0
214.6  129.5  129.2  7.7  10.3  141.3  0
214.8  129.7  129.3  9.1  9.5  141.5  0
215.1  129.6  129.8  8.6  9.8  141.8  0
214.9  130.2  130.2  8  11.2  139.6  0
213.8  129.8  129.5  8.4  11.1  140.9  0
215.2  129.9  129.5  8.2  10.3  141.4  0
215  129.6  130.2  8.7  10  141.2  0
214.4  129.9  129.6  7.5  10.5  141.8  0
215.2  129.9  129.7  7.2  10.6  142.1  0
214.1  129.6  129.3  7.6  10.7  141.7  0
214.9  129.9  130.1  8.8  10  141.2  0
214.6  129.8  129.4  7.4  10.6  141  0
215.2  130.5  129.8  7.9  10.9  140.9  0
214.6  129.9  129.4  7.9  10  141.8  0
215.1  129.7  129.7  8.6  10.3  140.6  0
214.9  129.8  129.6  7.5  10.3  141  0
215.2  129.7  129.1  9  9.7  141.9  0
215.2  130.1  129.9  7.9  10.8  141.3  0
215.4  130.7  130.2  9  11.1  141.2  0
215.1  129.9  129.6  8.9  10.2  141.5  0
215.2  129.9  129.7  8.7  9.5  141.6  0
215  129.6  129.2  8.4  10.2  142.1  0
214.9  130.3  129.9  7.4  11.2  141.5  0
215  129.9  129.7  8  10.5  142  0
214.7  129.7  129.3  8.6  9.6  141.6  0
215.4  130  129.9  8.5  9.7  141.4  0
214.9  129.4  129.5  8.2  9.9  141.5  0
214.5  129.5  129.3  7.4  10.7  141.5  0
214.7  129.6  129.5  8.3  10  142  0
215.6  129.9  129.9  9  9.5  141.7  0
215  130.4  130.3  9.1  10.2  141.1  0
214.4  129.7  129.5  8  10.3  141.2  0
215.1  130  129.8  9.1  10.2  141.5  0
214.7  130  129.4  7.8  10  141.2  0
214.4  130.1  130.3  9.7  11.7  139.8  1
214.9  130.5  130.2  11  11.5  139.5  1
214.9  130.3  130.1  8.7  11.7  140.2  1
215  130.4  130.6  9.9  10.9  140.3  1
214.7  130.2  130.3  11.8  10.9  139.7  1
215  130.2  130.2  10.6  10.7  139.9  1
215.3  130.3  130.1  9.3  12.1  140.2  1
214.8  130.1  130.4  9.8  11.5  139.9  1
215  130.2  129.9  10  11.9  139.4  1
215.2  130.6  130.8  10.4  11.2  140.3  1
215.2  130.4  130.3  8  11.5  139.2  1
215.1  130.5  130.3  10.6  11.5  140.1  1
215.4  130.7  131.1  9.7  11.8  140.6  1
214.9  130.4  129.9  11.4  11  139.9  1
215.1  130.3  130  10.6  10.8  139.7  1
215.5  130.4  130  8.2  11.2  139.2  1
214.7  130.6  130.1  11.8  10.5  139.8  1
214.7  130.4  130.1  12.1  10.4  139.9  1
214.8  130.5  130.2  11  11  140  1
214.4  130.2  129.9  10.1  12  139.2  1
214.8  130.3  130.4  10.1  12.1  139.6  1
215.1  130.6  130.3  12.3  10.2  139.6  1
215.3  130.8  131.1  11.6  10.6  140.2  1
215.1  130.7  130.4  10.5  11.2  139.7  1
214.7  130.5  130.5  9.9  10.3  140.1  1
214.9  130  130.3  10.2  11.4  139.6  1
215  130.4  130.4  9.4  11.6  140.2  1
215.5  130.7  130.3  10.2  11.8  140  1
215.1  130.2  130.2  10.1  11.3  140.3  1
214.5  130.2  130.6  9.8  12.1  139.9  1
214.3  130.2  130  10.7  10.5  139.8  1
214.5  130.2  129.8  12.3  11.2  139.2  1
214.9  130.5  130.2  10.6  11.5  139.9  1
214.6  130.2  130.4  10.5  11.8  139.7  1
214.2  130  130.2  11  11.2  139.5  1
214.8  130.1  130.1  11.9  11.1  139.5  1
214.6  129.8  130.2  10.7  11.1  139.4  1
214.9  130.7  130.3  9.3  11.2  138.3  1
214.6  130.4  130.4  11.3  10.8  139.8  1
214.5  130.5  130.2  11.8  10.2  139.6  1
214.8  130.2  130.3  10  11.9  139.3  1
214.7  130  129.4  10.2  11  139.2  1
214.6  130.2  130.4  11.2  10.7  139.9  1
215  130.5  130.4  10.6  11.1  139.9  1
214.5  129.8  129.8  11.4  10  139.3  1
214.9  130.6  130.4  11.9  10.5  139.8  1
215  130.5  130.4  11.4  10.7  139.9  1
215.3  130.6  130.3  9.3  11.3  138.1  1
214.7  130.2  130.1  10.7  11  139.4  1
214.9  129.9  130  9.9  12.3  139.4  1
214.9  130.3  129.9  11.9  10.6  139.8  1
214.6  129.9  129.7  11.9  10.1  139  1
214.6  129.7  129.3  10.4  11  139.3  1
214.5  130.1  130.1  12.1  10.3  139.4  1
214.5  130.3  130  11  11.5  139.5  1
215.1  130  130.3  11.6  10.5  139.7  1
214.2  129.7  129.6  10.3  11.4  139.5  1
214.4  130.1  130  11.3  10.7  139.2  1
214.8  130.4  130.6  12.5  10  139.3  1
214.6  130.6  130.1  8.1  12.1  137.9  1
215.6  130.1  129.7  7.4  12.2  138.4  1
214.9  130.5  130.1  9.9  10.2  138.1  1
214.6  130.1  130  11.5  10.6  139.5  1
214.7  130.1  130.2  11.6  10.9  139.1  1
214.3  130.3  130  11.4  10.5  139.8  1
215.1  130.3  130.6  10.3  12  139.7  1
216.3  130.7  130.4  10  10.1  138.8  1
215.6  130.4  130.1  9.6  11.2  138.6  1
214.8  129.9  129.8  9.6  12  139.6  1
214.9  130  129.9  11.4  10.9  139.7  1
213.9  130.7  130.5  8.7  11.5  137.8  1
214.2  130.6  130.4  12  10.2  139.6  1
214.8  130.5  130.3  11.8  10.5  139.4  1
214.8  129.6  130  10.4  11.6  139.2  1
214.8  130.1  130  11.4  10.5  139.6  1
214.9  130.4  130.2  11.9  10.7  139  1
214.3  130.1  130.1  11.6  10.5  139.7  1
214.5  130.4  130  9.9  12  139.6  1
214.8  130.5  130.3  10.2  12.1  139.1  1
214.5  130.2  130.4  8.2  11.8  137.8  1
215  130.4  130.1  11.4  10.7  139.1  1
214.8  130.6  130.6  8  11.4  138.7  1
215  130.5  130.1  11  11.4  139.3  1
214.6  130.5  130.4  10.1  11.4  139.3  1
214.7  130.2  130.1  10.7  11.1  139.5  1
214.7  130.4  130  11.5  10.7  139.4  1
214.5  130.4  130  8  12.2  138.5  1
214.8  130  129.7  11.4  10.6  139.2  1
214.8  129.9  130.2  9.6  11.9  139.4  1
214.6  130.3  130.2  12.7  9.1  139.2  1
215.1  130.2  129.8  10.2  12  139.4  1
215.4  130.5  130.6  8.8  11  138.6  1
214.7  130.3  130.2  10.8  11.1  139.2  1
215  130.5  130.3  9.6  11  138.5  1
214.9  130.3  130.5  11.6  10.6  139.8  1
215  130.4  130.3  9.9  12.1  139.6  1
215.1  130.3  129.9  10.3  11.5  139.7  1
214.8  130.3  130.4  10.6  11.1  140  1
214.7  130.7  130.8  11.2  11.2  139.4  1
214.3  129.9  129.9  10.2  11.5  139.6  1"

con <- textConnection(lines)
banknotes <- read.csv(con, sep="")
banknotes$CLASS <- ifelse(banknotes$Y==1, "GENUINE", "COUNTERFEIT")
```


```{r}
library(ggplot2)
ggplot(banknotes, aes(Bottom, Diagonal)) + geom_point(aes(colour=CLASS))
```

```{r}
fit <- glm(Y~Bottom+Diagonal, data=banknotes, family=binomial())
```

```{r}
#b0+b1*Bottom+b2*Diagonal > 0
#Diagnoal > -bo/b2-(b1/b2)*Bottom
b0 <- fit$coefficients["(Intercept)"]
b1 <- fit$coefficients["Bottom"]
b2 <- fit$coefficients["Diagonal"]
banknotes$Boundary <- -b0/b2-(b1/b2)*banknotes$Bottom


ggplot(banknotes, aes(Bottom, Diagonal)) + geom_point(aes(colour=CLASS))  +geom_line(data=banknotes, aes(x=Bottom, y=Boundary))
