Q3.Rmd

---
title: "Q3"
author: "Camryn Blawas"
date: "7/22/2020"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(tidyverse)
library(modelr)
library(leaps)
library(bestglm)
library(ggplot2)
library(broom)
library(purrr)
PlacementData = read_csv('PlacementData.csv')
```

```{r, echo=FALSE}
#FromNoah
RegressionData = PlacementData
RegressionData$JobStatus <-ifelse(PlacementData$JobStatus=="Placed", 1, 0)
RegressionData$SE_BoE <-ifelse(PlacementData$SE_BoE=="Central", 1, 0)
RegressionData$HSE_BoE <-ifelse(PlacementData$HSE_BoE=="Central", 1, 0)
RegressionData$WorkExp <-ifelse(PlacementData$WorkExp_1=="TRUE", 1, 0)
RegressionData$Gender <-ifelse(PlacementData$Gender=="M", 1, 0)
RegressionData$UG_Specialization <-ifelse(PlacementData$UG_Specialization=="Comm&Mgmt",1,0)
RegressionData$HSE_SpecializationD1 <-ifelse(PlacementData$HSE_Specialization=="Commerce",1,0)
RegressionData$HSE_SpecializationD2 <-ifelse(PlacementData$HSE_Specialization=="Arts",1,0)
RegressionData$MBA_Specialization <-ifelse(PlacementData$MBA_Specialization=="Mkt&Fin",1,0)
RegressionDataFinal <-select(RegressionData,"Gender","SE_Grade","SE_BoE","HSE_Grade", "HSE_BoE","HSE_SpecializationD1","HSE_SpecializationD2","UG_Grade", "UG_Specialization","WorkExp","EmploymentTest","MBA_Specialization","MBA_Grade","Salary")
RegressionDataFinal <- RegressionDataFinal[complete.cases(RegressionDataFinal),]
```

```{r, echo=FALSE}
#did not include JobStatus
models <- regsubsets(Salary~.,data=RegressionDataFinal, nvmax=13)
summary(models)

res.sum <- summary(models)
data.frame(
  Adj.R2 = which.max(res.sum$adjr2),
  CP = which.min(res.sum$cp),
  BIC = which.min(res.sum$bic), 
  RSQ = which.max(res.sum$rsq),
  RSS = which.min(res.sum$rss)
)
```

```{r, echo=FALSE}
#13 Variables
Model1 <-function(data) {glm(Salary~.,data=data)}
#12 Variables
Model2<-function(data) {glm((Salary)~(Gender+SE_Grade+SE_BoE+HSE_BoE+HSE_SpecializationD1+HSE_SpecializationD2+UG_Grade+UG_Specialization+EmploymentTest+MBA_Specialization+MBA_Grade),data=data)}
#6 Variables
Model3 <- function(data){glm((Salary)~Gender+HSE_SpecializationD2+UG_Grade+UG_Specialization+MBA_Specialization+MBA_Grade, data=data)}
#3 Variables
Model4 <- function(data) {glm((Salary)~Gender+UG_Specialization+MBA_Grade, data=data)}
#2 Variables
Model5 <- function(data) {glm((Salary)~Gender+MBA_Grade, data=data)}
```

```{r}
RMSE.func = function(actual, predict) {
  mse = mean((actual - predict)^2, na.rm=T)
  rmse = sqrt(mse)
  return(rmse)
}

RegressionDataFinal2 = RegressionDataFinal[c(1:83, 85:148), ]


#Cross Validation
set.seed(100)
cv = RegressionDataFinal2 %>% modelr::crossv_kfold(13)
pred = cv %>% dplyr::mutate(pmodel1 = map(train, Model1),
                            pmodel2 = map(train, Model2), 
                            pmodel3 = map(train, Model3), 
                            pmodel4 = map(train, Model4), 
                            pmodel5 = map(train, Model5))
pred.value = pred %>% 
  dplyr::mutate(predict1=map2(test, pmodel1, ~augment(.y, newdata=.x)), 
                predict2=map2(test, pmodel2, ~augment(.y, newdata=.x)),
                predict3=map2(test, pmodel3, ~augment(.y, newdata=.x)),
                predict4=map2(test, pmodel4, ~augment(.y, newdata=.x)),
                predict5=map2(test, pmodel5, ~augment(.y, newdata=.x)))

model1 = pred.value %>% select(predict1) %>% unnest()
model2 = pred.value %>% select(predict2) %>% unnest()
model3 = pred.value %>% select(predict3) %>% unnest()
model4 = pred.value %>% select(predict4) %>% unnest()
model5 = pred.value %>% select(predict5) %>% unnest()

rmse.table = matrix(rep(1:5, each=2), 2, 5)
rmse.table[2, 1] = RMSE.func(model1$Salary, (model1$.fitted))
rmse.table[2, 2] = RMSE.func(model2$Salary, (model2$.fitted))
rmse.table[2, 3] = RMSE.func(model3$Salary, (model3$.fitted))
rmse.table[2, 4] = RMSE.func(model4$Salary, (model4$.fitted))
rmse.table[2, 5] = RMSE.func(model5$Salary, (model5$.fitted))
rmse.table %>% data.frame() %>% dplyr::rename(Model1 = X1, Model2 = X2, Model3 = X3, Model4 = X4, Model5 = X5) %>% .[2, ]
```

```{r}
RegressionDataFinal2 %>% add_residuals(Model5(RegressionDataFinal2)) %>% ggplot(mapping=aes(x=Salary, y=resid))+geom_point(alpha=0.5)+geom_line(aes(y=rep(0, nrow(RegressionDataFinal2)), colour="red"))
ggplot(RegressionDataFinal)+
  geom_point(aes(x=as.numeric(row.names(RegressionDataFinal)),y=Salary),alpha=0.5)+
  ggtitle("All Salary Data Points")+
  xlab("Indices")
```

```{r}
RegressionDataFinal %>% add_residuals(Model5(RegressionDataFinal)) %>% ggplot(mapping=aes(x=Salary,y=resid))+
  geom_point(alpha=0.5)+
  ggtitle("")+
  ylab("Residuals")+
  theme(legend.position = "none")+
  geom_line(aes(y=rep(0, nrow(RegressionDataFinal)), colour="red"))
```


```{r}
test.model = lm(log(Salary)~polym(SE_Grade, HSE_Grade, UG_Grade, MBA_Grade, degree=3)+., data=RegressionDataFinal)
r = RegressionDataFinal
r %>% add_predictions(test.model) %>% mutate(resid=Salary - exp(pred)) %>% ggplot(mapping=aes(x=Salary, y=resid))+geom_point()+geom_line(aes(y=rep(0, nrow(r)), colour="red"))

summary(test.model)
```

```{r}
plot(Salary~EmploymentTest, data=RegressionDataFinal)

```