# Visualizing One Quantitative Variable

# Bonds

A dataset for illustrating the various available visualizations needs a certain degree of richness with manageable size. The dataset on *Bonds* contains three categorical and a few quantitative indicators sufficient to show what we might wish.

## Loading the Data

`Bonds <- read.csv(url("https://raw.githubusercontent.com/robertwwalker/DADMStuff/master/BondFunds.csv"))`

## A Summary

```
library(skimr)
Bonds %>% skim()
```

Name | Piped data |

Number of rows | 184 |

Number of columns | 9 |

_______________________ | |

Column type frequency: | |

character | 4 |

numeric | 5 |

________________________ | |

Group variables | None |

**Variable type: character**

skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace |
---|---|---|---|---|---|---|---|

Fund.Number | 0 | 1 | 4 | 6 | 0 | 184 | 0 |

Type | 0 | 1 | 20 | 23 | 0 | 2 | 0 |

Fees | 0 | 1 | 2 | 3 | 0 | 2 | 0 |

Risk | 0 | 1 | 7 | 13 | 0 | 3 | 0 |

**Variable type: numeric**

skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
---|---|---|---|---|---|---|---|---|---|---|

Assets | 0 | 1 | 910.65 | 2253.27 | 12.40 | 113.72 | 268.4 | 621.95 | 18603.50 | ▇▁▁▁▁ |

Expense.Ratio | 0 | 1 | 0.71 | 0.26 | 0.12 | 0.53 | 0.7 | 0.90 | 1.94 | ▂▇▅▁▁ |

Return.2009 | 0 | 1 | 7.16 | 6.09 | -8.80 | 3.48 | 6.4 | 10.72 | 32.00 | ▁▇▅▁▁ |

X3.Year.Return | 0 | 1 | 4.66 | 2.52 | -13.80 | 4.05 | 5.1 | 6.10 | 9.40 | ▁▁▁▅▇ |

X5.Year.Return | 0 | 1 | 3.99 | 1.49 | -7.30 | 3.60 | 4.3 | 4.90 | 6.80 | ▁▁▁▅▇ |

Most data types are represented. There is no time variable so dates and the visualizations that go with time series are omitted.

# Data Visualization

First, let us look at visualizations for one quantitative variable. Let me focus on assets..

`geom_histogram()`

A histogram divides the data into categories and counts the observations per category. The width of the categories [on x] is determined by `binwidth=`

or the binwidth can be calculated as a function of the range and the number of bins `bin=`

. I will define it as *Gen.Hist*.

### A Base Histogram

```
Gen.Hist <- Bonds %>% ggplot() + aes(x = Assets) + geom_histogram()
Gen.Hist
```

`## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.`

### Histograms [bins]

We can choose more bins. 50? That is far more than the default of 30.

```
Bin50.Hist <- Bonds %>% ggplot() + aes(x = Assets) + geom_histogram(bins = 50)
Bin50.Hist
```

We can also choose fewer bins. I will choose 10.

```
Bin10.Hist <- Bonds %>% ggplot() + aes(x = Assets) + geom_histogram(bins = 10)
Bin10.Hist
```

### Histograms [binwidth]

We can also set the width of bins in the metric of `x`

; I will choose 500 (bigger).

```
BinW500.Hist <- Bonds %>% ggplot() + aes(x = Assets) + geom_histogram(binwidth = 500)
BinW500.Hist
```

We can also set the width of bins in the metric of `x`

; I will choose 50 (smaller width makes more bins).

```
BinW50.Hist <- Bonds %>% ggplot() + aes(x = Assets) + geom_histogram(binwidth = 50)
BinW50.Hist
```

`geom_dotplot()`

`geom_dotplot()`

places a dot for every observation in the relevant bin. We can control the size of the bins [in the original metric] with `binwidth=`

.

### Small binwidth

`Bonds %>% ggplot() + aes(x = Assets) + geom_dotplot(binwidth = 10)`

### Large binwidth

`Bonds %>% ggplot() + aes(x = Assets) + geom_dotplot(binwidth = 1000)`

### An ?optimal? binwidth

Each dot represents a datum with bins of size 100.

`Bonds %>% ggplot() + aes(x = Assets) + geom_dotplot(binwidth = 100) + labs(y = "")`

`geom_freqpoly()`

`geom_freqpoly()`

is the line equivalent of a histogram. The arguments are similar, the output doesn’t include the bars as it does in the histogram.

`Bonds %>% ggplot(., aes(x = Assets)) + geom_freqpoly()`

`## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.`

### More bins

`Bonds %>% ggplot(., aes(x = Assets)) + geom_freqpoly(bins = 50)`

### Fewer bins

`Bonds %>% ggplot(., aes(x = Assets)) + geom_freqpoly(bins = 10)`

`geom_area()`

Is a relative of the histogram with lines connecting the midpoints of the bins and an associated fill from zero.

### Defaults to 30 bins

`Bonds %>% ggplot(., aes(x = Assets)) + geom_area(stat = "bin")`

`## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.`

### Small binwidth with a large number of bins

I will color in the area with magenta and clean up the theme.

```
Bonds %>% ggplot(., aes(x = Assets)) + geom_area(stat = "bin", bins = 100, fill = "magenta") +
theme_minimal()
```

`geom_density()`

A relative of the histogram and the area plots above, the density plot smooths out the blocks of a histogram with a moving window [known as the bandwidth].

`geom_density()`

outlines

`Bonds %>% ggplot(., aes(x = Assets)) + geom_density(outline.type = "upper")`

`Bonds %>% ggplot(., aes(x = Assets)) + geom_density(outline.type = "lower")`

`Bonds %>% ggplot(., aes(x = Assets)) + geom_density(outline.type = "full")`

`geom_density()`

adjust

Adjust applies a numeric correction to the bandwidth. Numbers greater than 1 make the bandwidth bigger [and the graphic smoother] and numbers less than 1 [but greater than zero] make the bandwidth smaller and the graphic more jagged.

`Bonds %>% ggplot(., aes(x = Assets)) + geom_density(adjust = 2)`

`Bonds %>% ggplot(., aes(x = Assets)) + geom_density(adjust = 1/2)`

`geom_boxplot`

A boxplot shows a box of the first and third quartiles and a notch at the median. The dots above or below denote points outside the hinges. The hinges [default to 1.5*IQR] show a range of expected data while the individual dots show possible outliers outside the hinges. To adjust the hinges, the argument `coef=1.5`

can be adjusted.

`Bonds %>% ggplot(., aes(x = Assets)) + geom_boxplot()`

`geom_qq()`

To compare empirical and theoretical quantiles. Comparing a distribution to the normal or others is common and this provides the tool for doing so. The default is a normal.

The empirical cumulative distribution function arises when we sort a quantitative variable and show the percentiles below said value.

`Bonds %>% ggplot(aes(sample = Assets)) + geom_qq()`

`stat_ecdf(geom = )`

We could do this with most geometries. I will show a few.

`stat_ecdf(geom = "step")`

```
Bonds %>% ggplot(aes(x = Assets)) + stat_ecdf(geom = "point") + stat_ecdf(geom = "step",
alpha = 0.1) + labs(y = "ECDF: Proportion less than Assets") + theme_minimal()
```

`stat_ecdf(geom = "point")`

```
Bonds %>% ggplot(aes(x = Assets)) + stat_ecdf(geom = "point") + stat_ecdf(geom = "step",
alpha = 0.1) + labs(y = "ECDF: Proportion less than Assets") + theme_minimal()
```

### Combining two

```
Bonds %>% ggplot(aes(x = Assets)) + stat_ecdf(geom = "point") + stat_ecdf(geom = "step",
alpha = 0.1) + labs(y = "ECDF: Proportion less than Assets") + theme_minimal()
```

`stat_ecdf(geom = "line")`

```
Bonds %>% ggplot(aes(x = Assets)) + stat_ecdf(geom = "line") + labs(y = "ECDF: Proportion less than Assets") +
theme_minimal()
```

`stat_ecdf(geom = "area")`

```
Bonds %>% ggplot(aes(x = Assets)) + stat_ecdf(geom = "area", alpha = 0.2) + labs(y = "ECDF: Proportion less than Assets") +
theme_minimal()
```