A22

---
title: "A22 By Noah Perry and Andrew Hall"
output:
  pdf_document: default
  html_notebook: default
---

Build a neural network for the Manheim data with a range of hidden layers and decide which model gives the best fit. Compare your result with a general linear model.

```{r}
library(tidyverse)
library(Metrics)
library(neuralnet)
library(ggplot2)

url<-"http://www.richardtwatson.com/data/manheim.csv"
t<-read_csv(url)

#Create general linear model
lm <- lm(t$price~t$miles +t$model+t$sale)
summary(lm)
predict.lm <- round(predict(lm),0)
MSE.lm <- rmse(t$price,predict.lm)

# Recoding
t$saleCode <- case_when(
 t$sale == 'Auction' ~1,
 t$sale == 'Online' ~2
 )
t$modelCode <- case_when(
 t$model == 'X' ~1,
 t$model == 'Y' ~2,
 t$model == 'Z' ~3
 )
t$sale <- NULL
t$model <- NULL

# Normalize data
maxs <- apply(t, 2, max)
mins <- apply(t, 2, min)
n <- as.data.frame(scale(t, center = mins, scale = maxs - mins))

#Create Neural Nets with 2:6 Hidden layers
mseList <- list()
for (x in c(2,3,4,5,6)) {
  # Build neural net
  set.seed(2)
  net <- neuralnet(price ~ miles +
  saleCode + modelCode, data = n, hidden
  = x, linear.output = T)
  pr.net <- compute(net, n[,2:4])
  # rescale
  predict.net <- pr.net$net.result*(max(t$price)-min(t$price))+min(t$price)
  mseList[x] <- rmse(t$price, predict.net)
}

#Graph with x-axis as number of layers, y-axis MSE
mseDf <- data.frame(matrix(unlist(mseList)))
mseDf$layers = c(2,3,4,5,6)
ggplot(mseDf, aes(mseDf$layers)) + geom_point(aes(y=mseDf$matrix.unlist.mseList..)) +
 xlab('Layers') +
 ylab('Mean Squared Error')

#Neural Net with 4 Hidden Layers results in lowest MSE, so compare with linear model
#First, recreate Neural Net
set.seed(2)
net <- neuralnet(price ~ miles +
  saleCode + modelCode, data = n, hidden
  = 4, linear.output = T)
pr.net <- compute(net, n[,2:4])
# rescale
predict.net <- pr.net$net.result*(max(t$price)-min(t$price))+min(t$price)
MSE.net <- rmse(t$price, predict.net)

#Graph results
t <- t %>% mutate(diff = predict.lm - predict.net)
ggplot(t, aes(x=price)) +
 geom_point(aes(y=diff, color='Prediction difference')) +
 geom_point(aes(y=predict.lm, color='Linear model')) +
 geom_point(aes(y=predict.net,color='Neural net')) +
 geom_abline(intercept = 0, slope = 1) +
 xlab('Actual price') +
 ylab('Predicted price')

# Compare the two models' mean square error
paste('MSEs for linear regression and neural net ',round(MSE.lm,
0),round(MSE.net,0))
paste('Percent difference ', round(((MSE.net - MSE.lm)/MSE.lm*100),2))


```