old_faithful.Rmd

---
title: Old Faithful Geyser
---

The [Old Faithful Geyser](https://stat.ethz.ch/R-manual/R-devel/library/datasets/html/faithful.html) 
data set is a well-known data set that depicts the relationship 
of the waiting time between eruptions and the duration of the 
eruption for the Old Faithful geyser in Yellowstone National 
Park, Wyoming, USA [[webcam]](http://yellowstone.net/webcams/). 

`faithful` is a data set with 272 observations on 2 variables.

Column name| Description 
--- | --- 
eruptions | Duration time of previous eruption time (in mins)
waiting	| Waiting time to next eruption (in mins)

Let's load the `faithful` dataset. 
```{r}
data(faithful)
head(faithful)
summary(faithful)
```


This is a histogram of the time between eruptions. We see the are two 
groups of waiting times to the next eruption: One group with mean around 
55 minutes and a second group with a mean around 80 minutes. 

```{r, warning=FALSE, message=FALSE}
library(ggplot2)
library(dplyr) 

faithful %>% 
    ggplot(aes(x = waiting)) + geom_histogram(binwidth = 2) + 
    xlab("Waiting time to next eruption (in mins)") + 
    ylab("Frequency") + 
    labs(title="Old Faithful Geyser time between eruption")
```

This histogram indicates [Old Faithful isn't as "faithful" as you might think](http://people.stern.nyu.edu/jsimonof/classes/2301/pdf/geystime.pdf). 


Let's look at the relationship between the duration of the previous 
eruption and how it related to the waiting time until the next eruption.  

```{r}
faithful %>% 
    ggplot(aes(x = eruptions, y = waiting)) + geom_point() + 
    xlab("Duration of previous eruption time (in mins)") + 
    ylab("Waiting time to next eruption (in mins)") + 
    labs(title="Old Faithful Geyser")
```

We see that the relationship between these two variables is fairly linear, 
which suggests that we might use a linear model to predict the waiting 
time until the next eruption based on the duration of the previous eruption.