hw2p3-flu-trends.Rmd

---
title: "Detecting Flu Epidemics"
author: "Terrel Shumway"
date: "04/29/2015"
output: html_document
---

This document presents answers for homework 2 part 3.

## Getting and Cleaning the Data
```{r}
baseurl = "https://courses.edx.org/c4x/MITx/15.071x_2/asset/"

getdata = function(local){
  if(!file.exists(local)){
    library(downloader)
    remote = paste0(baseurl,local)
    print(remote)
    download(remote,local)
  }
  read.csv(local)
}

train = getdata("FluTrain.csv")

```

problem 1.1:
```{r}
train[which.max(train$ILI),]
train[which.max(train$Queries),]
```

problem 1.2:
```{r}
library(ggplot2)
ggplot(train,aes(x=ILI))+geom_histogram(binwidth=1)
```

problem 1.3:
```{r}

ggplot(train,aes(x=ILI,y=Queries))+geom_point()+geom_smooth(method="lm")
ggplot(train,aes(x=log(ILI),y=Queries))+geom_point()+geom_smooth(method="lm")
m1.cor = cor(log(train$ILI),train$Queries)

```

problem 2.1,2.2:
```{r}
m1 = lm(log(ILI)~Queries,train)
s = summary(m1)

m1.cor^2
s$r.squared
```

## Performance on the Test Set


```{r}
test = getdata("FluTest.csv")
m1.pred = predict(m1,newdata=test)
target = which(test$Week=="2012-03-11 - 2012-03-17")
est = exp(m1.pred[target])
obs = test[target,"ILI"]
```
problem 3.1: `r est`

problem 3.2: `r (obs-est)/obs`

```{r}
rmse = sqrt(mean((exp(m1.pred)-test$ILI)^2))
```
problem 3.3: `r rmse`

## Training a Time Series Model
problem 4.1
```{r}
library(zoo)
lag2 = lag(zoo(train$ILI),-2,na.pad=TRUE)
train$ILILag2 = coredata(lag2)
sum(is.na(train$ILILag2))
```

problem 4.2
```{r}
ggplot(train,aes(x=log(ILI),y=log(ILILag2))) + geom_point() + geom_smooth(method="lm")
```

problem 4.3
```{r}
m2 = lm(log(ILI)~Queries+log(ILILag2),data=train)
s = summary(m2)
sig = s$coefficients[,4]<.05
s$coefficients[sig,]
s$r.squared
```


## Performance on the Test Set
problem 5.1,5.2,5.3:
```{r}
lag2 = lag(zoo(test$ILI),-2,na.pad=TRUE)
test$ILILag2 = coredata(lag2)
sum(is.na(test$ILILag2))
ilast = nrow(train)
test[1:2,"ILILag2"] = train[(ilast-1):ilast,"ILI"]
sum(is.na(test$ILILag2))
test[1:2,"ILILag2"]
```

problem 5.4:
```{r}
m2.pred = predict(m2,newdata=test)
rmse = sqrt(mean((exp(m2.pred)-test$ILI)^2))
```
rmse=`r rmse`