When running R code in the Console the keyboard shortcut: CMD/Ctrl + Enter is very useful to run each R expression. When running R code in an Rnotebook the keyboard shortcut: Ctrl/Shift + Enter is useful to run each chunck of R code.
Here is the link to the RStudio Keyboard Shortcuts.
Continuing with the flights data.
library(tidyverse)
library(nycflights13)
flights
not_cancelled <- flights %>%
filter(!is.na(dep_delay), !is.na(arr_delay))
not_cancelled %>%
group_by(year, month, day) %>%
summarise(mean = mean(dep_delay))
Chapter 7 is about Exploratory Data Analysis (EDA).
EDA is an iterative cycle. You:
- Generate questions about your data.
- Search for answers by visualising, transforming, and modelling your data.
- Use what you learn to refine your questions and/or generate new questions.
A good quote that starts the Chapter:
“Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.” — John Tukey
Your goal during EDA is to develop an understanding of your data. EDA is fundamentally a creative process.
Exploring variation in the data using visualization.
Categorical variables.
In this Chapter the diamonds dataset is explored.
ggplot(data = diamonds) +
geom_bar(mapping = aes(x = cut))

diamonds %>%
count()
diamonds %>%
count(cut)
Continuous variables.
ggplot(data = diamonds) +
geom_histogram(mapping = aes(x = carat), binwidth = 0.5)

Count a continuous variable within intervals of equal length.
diamonds %>%
count(cut_width(carat, 0.5))
smaller <- diamonds %>%
filter(carat < 3)
ggplot(data = smaller, mapping = aes(x = carat)) +
geom_histogram(binwidth = 0.1)

ggplot(data = smaller, mapping = aes(x = carat, colour = cut)) +
geom_freqpoly(binwidth = 0.1)

Clusters in the data, round up!
ggplot(data = smaller, mapping = aes(x = carat)) +
geom_histogram(binwidth = 0.01)

Old Faithful data, another example of clusters.
ggplot(data = faithful, mapping = aes(x = eruptions)) +
geom_histogram(binwidth = 0.25)

Outliers:
ggplot(diamonds) +
geom_histogram(mapping = aes(x = y), binwidth = 0.5)

ggplot(diamonds) +
geom_histogram(mapping = aes(x = y), binwidth = 0.5) +
coord_cartesian(ylim = c(0, 50))

unusual <- diamonds %>%
filter(y < 3 | y > 20) %>%
select(price, x, y, z) %>%
arrange(y)
unusual
Replacing unusual values with missing values.
diamonds2 <- diamonds %>%
mutate(y = ifelse(y < 3 | y > 20, NA, y))
diamonds2
ggplot(data = diamonds2, mapping = aes(x = x, y = y)) +
geom_point()

Supress the warning.
ggplot(data = diamonds2, mapping = aes(x = x, y = y)) +
geom_point(na.rm = TRUE)

Categorical and Continuous variables.
ggplot(data = diamonds, mapping = aes(x = price)) +
geom_freqpoly(mapping = aes(colour = cut), binwidth = 500)

ggplot(diamonds) +
geom_bar(mapping = aes(x = cut))

Using a density plot.
ggplot(data = diamonds, mapping = aes(x = price, y = ..density..)) +
geom_freqpoly(mapping = aes(colour = cut), binwidth = 500)

ggplot(data = diamonds, mapping = aes(x = cut, y = price)) +
geom_boxplot()

ggplot(data = mpg, mapping = aes(x = class, y = hwy)) +
geom_boxplot()

ggplot(data = mpg) +
geom_boxplot(mapping = aes(x = reorder(class, hwy, FUN = median), y = hwy))

ggplot(data = mpg) +
geom_boxplot(mapping = aes(x = reorder(class, hwy, FUN = median), y = hwy)) +
coord_flip()

Two categorical variables. Covariation.
ggplot(data = diamonds) +
geom_count(mapping = aes(x = cut, y = color))

diamonds %>%
count(color, cut)
diamonds %>%
count(color, cut) %>%
ggplot(mapping = aes(x = color, y = cut)) +
geom_tile(mapping = aes(fill = n))

Two continuous variables.
ggplot(data = diamonds) +
geom_point(mapping = aes(x = carat, y = price))

ggplot(data = diamonds) +
geom_point(mapping = aes(x = carat, y = price), alpha = 1 / 100)

ggplot(data = smaller) +
geom_bin2d(mapping = aes(x = carat, y = price))

# install.packages("hexbin")
library(hexbin)
ggplot(data = smaller) +
geom_hex(mapping = aes(x = carat, y = price))

ggplot(data = smaller, mapping = aes(x = carat, y = price)) +
geom_boxplot(mapping = aes(group = cut_width(carat, 0.1)))

ggplot(data = smaller, mapping = aes(x = carat, y = price)) +
geom_boxplot(mapping = aes(group = cut_number(carat, 20)))

ggplot(data = diamonds) +
geom_point(mapping = aes(x = x, y = y)) +
coord_cartesian(xlim = c(4, 11), ylim = c(4, 11))

Back to Old Faithful. Seeing relationships between variables and using those relationships to build models.
ggplot(data = faithful) +
geom_point(mapping = aes(x = eruptions, y = waiting))

library(modelr)
mod <- lm(log(price) ~ log(carat), data = diamonds)
diamonds2 <- diamonds %>%
add_residuals(mod) %>%
mutate(resid = exp(resid))
ggplot(data = diamonds2) +
geom_point(mapping = aes(x = carat, y = resid))

ggplot(data = diamonds2) +
geom_boxplot(mapping = aes(x = cut, y = resid))

Same code, more consice.
ggplot(data = faithful, mapping = aes(x = eruptions)) +
geom_freqpoly(binwidth = 0.25)

ggplot(faithful, aes(eruptions)) +
geom_freqpoly(binwidth = 0.25)

Turn the end of a pipeline of data transformation into a plot. The value of the pipe.
diamonds %>%
count(cut, clarity) %>%
ggplot(aes(clarity, cut, fill = n)) +
geom_tile()

Chapter 8 is a short Chapter that introducts the getwd( ), setwd( ), and Projects. Try out Files to the right.
getwd()
[1] "/home/esuess/classes/2017-2018/Stat6864/Presentations/Chapter7"
ggplot(diamonds, aes(carat, price)) +
geom_hex()
ggsave("diamonds.pdf")
Saving 7.29 x 4.5 in image

write_csv(diamonds, "diamonds.csv")
Add a new chunk by clicking the Insert Chunk button on the toolbar or by pressing Ctrl+Alt+I.
When you save the notebook, an HTML file containing the code and output will be saved alongside it (click the Preview button or press Ctrl+Shift+K to preview the HTML file).
The preview shows you a rendered HTML copy of the contents of the editor. Consequently, unlike Knit, Preview does not run any R code chunks. Instead, the output of the chunk when it was last run in the editor is displayed.
---
title: "Code from R for Data Science - Chapter 6, 7 and 8"
output:
  html_notebook: default
  pdf_document: default
---

When running R code in the Console the keyboard shortcut: CMD/Ctrl + Enter is very useful to run each R expression.  When running R code in an Rnotebook the keyboard shortcut: Ctrl/Shift + Enter is useful to run each chunck of R code.

Here is the link to the [RStudio Keyboard Shortcuts](https://support.rstudio.com/hc/en-us/articles/200711853-Keyboard-Shortcuts).

Continuing with the flights data.
 
```{r}
library(tidyverse)
library(nycflights13)

flights

not_cancelled <- flights %>% 
  filter(!is.na(dep_delay), !is.na(arr_delay))

not_cancelled %>% 
  group_by(year, month, day) %>% 
  summarise(mean = mean(dep_delay))
```


**Chapter 7** is about Exploratory Data Analysis (EDA).

EDA is an iterative cycle. You:

1. Generate questions about your data.
2. Search for answers by visualising, transforming, and modelling your data.
3. Use what you learn to refine your questions and/or generate new questions.

A good quote that starts the Chapter:

“Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.” — John Tukey

Your goal during EDA is to develop an understanding of your data.  EDA is fundamentally a creative process.

Exploring variation in the data using visualization.

Categorical variables.

In this Chapter the diamonds dataset is explored.


```{r}
ggplot(data = diamonds) +
  geom_bar(mapping = aes(x = cut))
```


```{r}
diamonds %>% 
  count()

diamonds %>% 
  count(cut)
```


Continuous variables.

```{r}
ggplot(data = diamonds) +
  geom_histogram(mapping = aes(x = carat), binwidth = 0.5)
```

Count a continuous variable within intervals of equal length.

```{r}
diamonds %>% 
  count(cut_width(carat, 0.5))
```

```{r}
smaller <- diamonds %>% 
  filter(carat < 3)
  
ggplot(data = smaller, mapping = aes(x = carat)) +
  geom_histogram(binwidth = 0.1)
```

```{r}
ggplot(data = smaller, mapping = aes(x = carat, colour = cut)) +
  geom_freqpoly(binwidth = 0.1)
```


Clusters in the data, round up!

```{r}
ggplot(data = smaller, mapping = aes(x = carat)) +
  geom_histogram(binwidth = 0.01)
```

Old Faithful data, another example of clusters.

```{r}
ggplot(data = faithful, mapping = aes(x = eruptions)) + 
  geom_histogram(binwidth = 0.25)
```

Outliers:

```{r}
ggplot(diamonds) + 
  geom_histogram(mapping = aes(x = y), binwidth = 0.5)
```

```{r}
ggplot(diamonds) + 
  geom_histogram(mapping = aes(x = y), binwidth = 0.5) +
  coord_cartesian(ylim = c(0, 50))
```


```{r}
unusual <- diamonds %>% 
  filter(y < 3 | y > 20) %>% 
  select(price, x, y, z) %>%
  arrange(y)
unusual
```


Replacing unusual values with missing values.

```{r}
diamonds2 <- diamonds %>% 
  mutate(y = ifelse(y < 3 | y > 20, NA, y))

diamonds2
```

```{r}
ggplot(data = diamonds2, mapping = aes(x = x, y = y)) + 
  geom_point()
```

Supress the warning.

```{r}
ggplot(data = diamonds2, mapping = aes(x = x, y = y)) + 
  geom_point(na.rm = TRUE)
```


Categorical and Continuous variables.

```{r}
ggplot(data = diamonds, mapping = aes(x = price)) + 
  geom_freqpoly(mapping = aes(colour = cut), binwidth = 500)
```

```{r}
ggplot(diamonds) + 
  geom_bar(mapping = aes(x = cut))
```

Using a density plot.

```{r}
ggplot(data = diamonds, mapping = aes(x = price, y = ..density..)) + 
  geom_freqpoly(mapping = aes(colour = cut), binwidth = 500)
```


```{r}
ggplot(data = diamonds, mapping = aes(x = cut, y = price)) +
  geom_boxplot()
```


```{r}
ggplot(data = mpg, mapping = aes(x = class, y = hwy)) +
  geom_boxplot()
```


```{r}
ggplot(data = mpg) +
  geom_boxplot(mapping = aes(x = reorder(class, hwy, FUN = median), y = hwy))
```

```{r}
ggplot(data = mpg) +
  geom_boxplot(mapping = aes(x = reorder(class, hwy, FUN = median), y = hwy)) +
  coord_flip()
```


Two categorical variables.  Covariation.

```{r}
ggplot(data = diamonds) +
  geom_count(mapping = aes(x = cut, y = color))
```

```{r}
diamonds %>% 
  count(color, cut)
```

```{r}
diamonds %>% 
  count(color, cut) %>%  
  ggplot(mapping = aes(x = color, y = cut)) +
    geom_tile(mapping = aes(fill = n))
```


Two continuous variables.

```{r}
ggplot(data = diamonds) +
  geom_point(mapping = aes(x = carat, y = price))
```


```{r}
ggplot(data = diamonds) + 
  geom_point(mapping = aes(x = carat, y = price), alpha = 1 / 100)
```


```{r}
ggplot(data = smaller) +
  geom_bin2d(mapping = aes(x = carat, y = price))

# install.packages("hexbin")

library(hexbin)

ggplot(data = smaller) +
  geom_hex(mapping = aes(x = carat, y = price))
```

```{r}
ggplot(data = smaller, mapping = aes(x = carat, y = price)) + 
  geom_boxplot(mapping = aes(group = cut_width(carat, 0.1)))
```

```{r}
ggplot(data = smaller, mapping = aes(x = carat, y = price)) + 
  geom_boxplot(mapping = aes(group = cut_number(carat, 20)))
```


```{r}
ggplot(data = diamonds) +
  geom_point(mapping = aes(x = x, y = y)) +
  coord_cartesian(xlim = c(4, 11), ylim = c(4, 11))
```


Back to Old Faithful.  Seeing relationships between variables and using those relationships to build models.

```{r}
ggplot(data = faithful) + 
  geom_point(mapping = aes(x = eruptions, y = waiting))
```

```{r}
library(modelr)

mod <- lm(log(price) ~ log(carat), data = diamonds)

diamonds2 <- diamonds %>% 
  add_residuals(mod) %>% 
  mutate(resid = exp(resid))

ggplot(data = diamonds2) + 
  geom_point(mapping = aes(x = carat, y = resid))
```

```{r}
ggplot(data = diamonds2) + 
  geom_boxplot(mapping = aes(x = cut, y = resid))
```

Same code, more consice.

```{r}
ggplot(data = faithful, mapping = aes(x = eruptions)) + 
  geom_freqpoly(binwidth = 0.25)

ggplot(faithful, aes(eruptions)) + 
  geom_freqpoly(binwidth = 0.25)
```

Turn the end of a pipeline of data transformation into a plot.  The value of the pipe.

```{r}
diamonds %>% 
  count(cut, clarity) %>% 
  ggplot(aes(clarity, cut, fill = n)) + 
    geom_tile()
```

**Chapter 8** is a short Chapter that introducts the *getwd( )*, *setwd( )*, and Projects.  Try out Files to the right.

```{r}
getwd()
```

```{r}
ggplot(diamonds, aes(carat, price)) + 
  geom_hex()
ggsave("diamonds.pdf")

write_csv(diamonds, "diamonds.csv")
```


Add a new chunk by clicking the *Insert Chunk* button on the toolbar or by pressing *Ctrl+Alt+I*.

When you save the notebook, an HTML file containing the code and output will be saved alongside it (click the *Preview* button or press *Ctrl+Shift+K* to preview the HTML file).

The preview shows you a rendered HTML copy of the contents of the editor. Consequently, unlike *Knit*, *Preview* does not run any R code chunks. Instead, the output of the chunk when it was last run in the editor is displayed.
