Chapter 3 Data Visualization
- Geometric shapes
- Multiple smoothing lines
- Statistical transformations
Today we are going to try some more code from Chapter 3 Data Visualization.
To start we will load the tidyverse. Note that ggplot2 is the first package loaded!
library(tidyverse)
We will continue to work with the mpg dataset that is in the ggplot2 package.
mpg
Make the scatterplot along with the smoothing line.
ggplot(data = mpg) +
geom_point(mapping = aes(x = displ, y = hwy)) +
geom_smooth(mapping = aes(x = displ, y = hwy))
![](data:image/png;base64,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)
Multiple smoothing lines.
ggplot(data = mpg) +
geom_smooth(mapping = aes(x = displ, y = hwy, linetype = drv))
![](data:image/png;base64,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)
Statistical transformations
ggplot(data = diamonds) +
geom_bar(mapping = aes(x = cut))
![](data:image/png;base64,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)
Proportions
ggplot(data = diamonds) +
geom_bar(mapping = aes(x = cut, y = ..prop.., group = 1))
![](data:image/png;base64,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)
Position adjustment
ggplot(data = diamonds) +
geom_bar(mapping = aes(x = cut, fill = clarity), position = "dodge")
![](data:image/png;base64,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)
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