---
title: 'Stat. 450 Section 1 or 2: Homework 5'
output:
  word_document: default
  html_notebook: default
  pdf_document: default
  html_document:
    df_print: paged
---

**Prof. Eric A. Suess**

So how should you complete your homework for this class?

- First thing to do is type all of your information about the problems you do in the text part of your R Notebook.
- Second thing to do is type all of your R code into R chunks that can be run.
- If you load the tidyverse in an R Notebook chunk, be sure to include the "message = FALSE" in the {r}, so {r message = FALSE}.
- Last thing is to spell check your R Notebook.  Edit > Check Spelling... or hit the F7 key.

Homework 5:

     Read: Chapter 7
     Do 7.3.4 Exercises 1, 2, 3, 4
     Do 7.4.1 Exercises 1, 2
     Do 7.5.1.1 Exercises 2, 3, 4, 5, 6

```{r message=FALSE}
library(tidyverse)
```


# 7.3.4

## 1.

All are skewed to the right.  The distributions of x and y are very similar.  The distributions of z looks to be less spread out.  All look to be bimodal.

I think x and y are the length and width, and z is the depth.

```{r}
diamonds

diamonds %>% select(x,y,z) %>%
  ggplot(aes(x = x )) +
  geom_histogram() +
  scale_x_continuous(limits=c(0, 10)) +
  scale_y_continuous(limits=c(0, 15000))

diamonds %>% select(x,y,z) %>%
  ggplot(aes(x = y )) +
  geom_histogram() +
  scale_x_continuous(limits=c(0, 10)) +
  scale_y_continuous(limits=c(0, 15000))

diamonds %>% select(x,y,z) %>%
  ggplot(aes(x = z )) +
  geom_histogram() +
  scale_x_continuous(limits=c(0, 10)) +
  scale_y_continuous(limits=c(0, 15000))
```



## 2.

There are not prices around $1500.

The mode of the distributions is around $750.

At the lowest levels there are spikes in the prices where the diamonds are actually priced.

```{r}
diamonds %>% select(price) %>% 
  ggplot(aes(x = price )) +
  geom_histogram() 

diamonds %>% select( price ) %>% 
  filter(price < 2500) %>%
  ggplot(aes(x = price )) +
  geom_histogram() 

diamonds %>% select( price ) %>% 
  filter(price < 2500) %>%
  ggplot(aes(x = price )) +
  geom_histogram(binwidth = 10, center = 0 ) 

diamonds %>% select( price ) %>% 
  filter(price < 900, price > 800) %>%
  ggplot(aes(x = price )) +
  geom_histogram(binwidth = 01, center = 0 ) 
  
```


## 3.

There are 23 diamonds that are .99 carats and there are 1558 diamonds that are 1 carat.  Rounding up is worth more money.

```{r}
diamonds %>% select(carat) %>% 
  count(carat == 0.99)

diamonds %>% select(carat) %>% 
  count(carat == 1)

diamonds %>%
   filter(carat >= 0.9, carat <= 1.1) %>%
   count(carat) 

diamonds %>%
   filter(carat >= 0.9, carat <= 1.1) %>%
   count(carat) %>%
   ggplot(aes(x= carat, y = n)) +
   geom_col()

```


## 4.

The *cood_cartesian* function zooms in on the original histogram.

The *xlim* and *ylim* functions limits the range of the data before counting.  So the histogram is made for a subset of the data.

```{r}
diamonds %>% select(price) %>% 
  ggplot(aes(x = price )) +
  geom_histogram() 

diamonds %>% select(price) %>% 
  ggplot(aes(x = price )) +
  geom_histogram() +
  coord_cartesian(xlim = c(0, 5000), ylim = c(0, 10000))

diamonds %>% select(price) %>% 
  ggplot(aes(x = price )) +
  geom_histogram(binwidth = 100) +
  coord_cartesian(xlim = c(0, 5000), ylim = c(0, 10000))

diamonds %>% select(price) %>% 
  ggplot(aes(x = price )) +
  geom_histogram(binwidth = 100) +
  xlim(0, 5000) +
  ylim(0, 10000)
```

# 7.4.1

## 1.

For histograms missing data is removed.

For bargraphs the NAs are considered another category.


## 2.

The option *na.rm* in the *mean* and *sum* functions remove the NAs before the values of the functions are computed.  NAs are not numeric values so they cannot be included in a sum calculation.

# 7.5.1.1

## 1.

The cancelled flights tend to occur later in the day, but have a wider range of scheduled departure hour.

```{r}
library(nycflights13)

flights %>% mutate(
  cancelled = is.na(dep_time),
  sched_hour = sched_dep_time %/% 100,
  sched_min  = sched_dep_time %% 100
  ) %>%
  ggplot(aes(x = cancelled, y = sched_hour)) +
  geom_boxplot() + 
  coord_flip()
```


## 2.

The most important variable is carat.

```{r}
diamonds %>% select (price, carat, depth, table, x, y , z) %>%
  cor()

diamonds %>% select (price, carat, depth, table, x, y , z) %>%
  ggplot(aes(x = carat, y = price)) +
  geom_point()

diamonds %>% ggplot(aes(x = carat, y = price)) +
  geom_boxplot(aes(group = cut_width(carat, 0.1)))
```

Examining the caregorical variables.

Weak positive relationship of price with color.

Weak neagative relationship of price with clarity and cut.

```{r}
diamonds %>% ggplot( aes(x = color, y = price)) +
  geom_boxplot()

diamonds %>% ggplot(aes(x = clarity, y = price)) +
  geom_boxplot()

ggplot(diamonds, aes(x = cut, y = carat)) +
  geom_boxplot()

```


## 3.

Looks the same, but x and y need to be switched for the boxploth()

```{r}
flights %>% mutate(
  cancelled = is.na(dep_time),
  sched_hour = sched_dep_time %/% 100,
  sched_min  = sched_dep_time %% 100
  ) %>%
  ggplot(aes(x = cancelled, y = sched_hour)) +
  geom_boxplot() + 
  coord_flip()

library(ggstance)

flights %>% mutate(
  cancelled = is.na(dep_time),
  sched_hour = sched_dep_time %/% 100,
  sched_min  = sched_dep_time %% 100
  ) %>%
  ggplot(aes(y = cancelled, x = sched_hour)) +
  geom_boxploth()

```




## 4.

The boxes in the lvplot correspond to percentiles, every 10%.

Outliers are in the direction of the thinner percentiles.

```{r}
library(lvplot)

diamonds %>% select(price, cut) %>%
  ggplot(aes(x = cut, y = price)) +
  geom_lv() + 
  coord_flip()

flights %>% mutate(
  cancelled = is.na(dep_time),
  sched_hour = sched_dep_time %/% 100,
  sched_min  = sched_dep_time %% 100
  ) %>%
  ggplot(aes(x = cancelled, y = sched_hour)) +
  geom_lv() + 
  coord_flip()
```

## 5.

The facted histograms are printed in the reverse order of the violin plots.  I would be good to have the vertical scales the same.


```{r}
flights %>% mutate(
  cancelled = is.na(dep_time),
  sched_hour = sched_dep_time %/% 100,
  sched_min  = sched_dep_time %% 100
  ) %>%
  ggplot(aes(x = cancelled, y = sched_hour)) +
  geom_violin() + 
  coord_flip()

flights %>% mutate(
  cancelled = is.na(dep_time),
  sched_hour = sched_dep_time %/% 100,
  sched_min  = sched_dep_time %% 100
  ) %>%
  ggplot(aes( x = sched_hour )) +
  geom_histogram() +
  facet_wrap(~ cancelled, nrow = 2) 

```

## 6.

method | description
-------|------------
default | jitters the point horizontally
tukey   | jitters more
tukeyDense | jitters but less than tukey
frowney | jitters downward
smiley  | jitters upward


```{r}
library(ggbeeswarm)

mpg %>% ggplot(aes(x = reorder(class, hwy, FUN = median),y = hwy) ) +
  geom_beeswarm()

mpg %>% ggplot(aes(x = reorder(class, hwy, FUN = median),y = hwy) ) +
  geom_quasirandom()

mpg %>% ggplot(aes(x = reorder(class, hwy, FUN = median),y = hwy) ) +
  geom_quasirandom(method = "tukey")

mpg %>% ggplot(aes(x = reorder(class, hwy, FUN = median),y = hwy) ) +
  geom_quasirandom(method = "tukeyDense")


mpg %>% ggplot(aes(x = reorder(class, hwy, FUN = median),y = hwy) ) +
  geom_quasirandom(method = "frowney")

mpg %>% ggplot(aes(x = reorder(class, hwy, FUN = median),y = hwy) ) +
  geom_quasirandom(method = "smiley")

```