In dgl5gw/geocompr: Geocomputation with R: a book

Attribute data operations {#attr}

Prerequisites {-}

This chapter requires the packages tidyverse, sf and raster:

library(sf)
library(raster)
library(tidyverse)

It also relies on spData, which loads world, worldbank_df and us_states datasets:

library(spData)

Introduction

Attribute data is non-spatial information associated with geographic (geometry) data. A bus stop provides a simple example. In a spatial vector object its position would typically be represented by latitude and longitude coordinates (geometry data), in addition to its name. The name is an attribute of the feature (to use Simple Features terminology) that bears no relation to its geometry.

Another example is the elevation value (attribute) for a specific grid cell in raster data. Unlike vector data, the raster data model stores the coordinate of the grid cell only indirectly: There is a less clear distinction between attribute and spatial information in raster data. Say, we are in the 3^rd^ row and the 4^th^ column of a raster matrix. To derive the corresponding coordinate, we have to move from the origin three cells in x-direction and four cells in y-direction with the cell resolution defining the distance for each x- and y-step. The raster header gives the matrix a spatial dimension which we need when plotting the raster or when we want to combine two rasters, think, for instance, of adding the values of one raster to another (see also next Chapter).

This chapter focuses on non-geographic operations on vector and raster data. For vector data, we will introduce subsetting, aggregating and joining attribute data in the next section. Note that the corresponding functions also have a geographic equivalent. Sometimes you can even use the same functions for attribute and spatial operations. This is the case for subsetting as base R's [ and tidyverse's filter() let you also subset spatial data based on the spatial extent of another spatial object (see Chapter \@ref(spatial-data-operations)). Therefore the skills you learn here are cross-transferable which is also why this chapter lays the foundation for the next chapter (Chapter \@ref(spatial-data-operations)) which extends the here presented methods to the spatial world.

Raster attribute data operations are covered in Section \@ref(manipulating-raster-objects), which covers the creating continuous and categorical raster layers and extracting cell values from one layer and multiple layers (raster subsetting). Section \@ref(summarizing-raster-objects) provides an overview of 'global' raster operations which can be used to characterize entire raster datasets.

Vector attribute manipulation

Geographic vector data in R are well-support by sf, a class which extends the data.frame. Thus sf objects have one column per attribute variable (such as 'name') and one row per observation, or feature (e.g. per bus station). sf objects also have a special column to contain geometry data, usually named geometry. The geometry column is special because it is a list-colum, which can contain multiple geographic entities (points, lines, polygons) per row. In Chapter \@ref(spatial-class) we saw how to perform generic methods such as plot() and summary() on sf objects. sf also provides methods that allow sf objects to behave like regular data frames:

methods(class = "sf") # methods for sf objects, first 12 shown

#>  [1] aggregate             cbind                 coerce               
#>  [4] initialize            merge                 plot                 
#>  [7] print                 rbind                 [                    
#> [10] [[<-                  $<-                   show

# Another way to show sf methods:
attributes(methods(class = "sf"))$info %>% 
  filter(!visible)

Many of these functions, including rbind() (for binding rows of data together) and $<- (for creating new columns) were developed for data frames. A key feature of sf objects is that they store spatial and non-spatial data in the same way, as columns in a data.frame (the geometry column is typically called geometry).

``{block2 type = 'rmdnote'} The geometry column ofsfobjects is typically calledgeometry` but any name can be used. The following command, for example, creates a geometry column named g:

st_sf(data.frame(n = world$name_long), g = world$geom)

This enables geometries imported from spatial databases to have a variety of names such as wkb_geometry and the_geom.

`sf` objects also support `tibble` and `tbl` classes used in the tidyverse, allowing 'tidy' data analysis workflows for spatial data.
Thus **sf** enables the full power of R's data analysis capabilities to be unleashed on geographic data.
Before using these capabilities it's worth re-capping how to discover the basic properties of vector data objects.
Let's start by using base R functions for to get a measure of the `world` dataset:

```r
dim(world) # it is a 2 dimensional object, with rows and columns
nrow(world) # how many rows?
ncol(world) # how many columns?

Our dataset contains ten non-geographic columns (and one geometry list-column) with almost 200 rows representing the world's countries.

Extracting the attribute data of an sf object is the same as removing its geometry:

world_df = st_set_geometry(world, NULL)
class(world_df)

This can be useful if the geometry column causes problems, e.g., by occupying large amounts of RAM, or to focus the attention on the attribute data. For most cases, however, there is no harm in keeping the geometry column because non-spatial data operations on sf objects only change an object's geometry when appropriate (e.g. by dissolving borders between adjacent polygons following aggregation). This means that proficiency with attribute data in sf objects equates to proficiency with data frames in R. For many applications, the tidyverse package dplyr offers the most effective and intuitive approach of working with data frames, hence the focus on this approach in this section.^[ Unlike objects of class Spatial of the sp package, sf objects are also compatible with the tidyverse packages dplyr and ggplot2. The former provides fast and powerful functions for data manipulation (see Section 6.7 of @gillespie_efficient_2016), and the latter provides powerful plotting capabilities. ]

Vector attribute subsetting

Base R subsetting functions include [, subset() and $. dplyr subsetting functions include select(), filter(), and pull(). Both sets of functions preserve the spatial components of attribute data in sf objects.

The [ operator can subset both rows and columns. You use indices to specify the elements you wish to extract from an object, e.g., object[i, j], with i and j typically being numbers or logical vectors --- TRUEs and FALSEs --- representing rows and columns (they can also be character strings, indicating row or column names). Leaving i or j empty returns all rows or columns, so world[1:5, ] returns the first five rows and all columns. The examples below demonstrate subsetting with base R. The results are not shown; check the results on your own computer:

world[1:6, ] # subset rows by position

world[, 1:3] # subset columns by position

world[, c("name_long", "lifeExp")] # subset columns by name

A demonstration of the utility of using logical vectors for subsetting is shown in the code chunk below. This creates a new object, small_countries, containing nations whose surface area is smaller than 10,000 km^2^:

sel_area = world$area_km2 < 10000
summary(sel_area) # a logical vector
small_countries = world[sel_area, ]

The intermediary sel_object is a logical vector that shows that only seven countries match the query. A more concise command, that omits the intermediary object, generates the same result:

small_countries = world[world$area_km2 < 10000, ]

Another the base R function subset() provides yet another way to achieve the same result:

small_countries = subset(world, area_km2 < 10000)

You can use the $ operator to select a specific variable by its name. The result is a vector:

world$name_long

Base R functions are mature and widely used. However, the more recent dplyr approach has several advantages. It enables intuitive workflows. It's fast, due to its C++ backend and database integration, important when working with big data. The main dplyr subsetting functions are select(), slice(), filter() and pull().

``{block type='rmdnote'} **raster** and **dplyr** packages have a function calledselect(). If both packages are loaded, this can generate error messages containing the text:unable to find an inherited method for function ‘select’ for signature ‘"sf"’. To avoid this error message, and prevent ambiguity, we use the long-form function name, prefixed by the package name and two colons (usually omitted from R scripts for concise code):dplyr::select()`.

`select()` selects columns by name or position.
For example, you could select only two columns, `name_long` and `pop`, with the following command (note the `geom` column remains):

```r
world1 = dplyr::select(world, name_long, pop)
names(world1)

select() also allows subsetting of a range of columns with the help of the : operator:

# all columns between name_long and pop (inclusive)
world2 = dplyr::select(world, name_long:pop)

Omit specific columns with the - operator:

# all columns except subregion and area_km2 (inclusive)
world3 = dplyr::select(world, -subregion, -area_km2)

Conveniently, select() lets you subset and rename columns at the same time, for example:

world4 = dplyr::select(world, name_long, population = pop)
names(world4)

This is more concise than the base R equivalent:

world5 = world[, c("name_long", "pop")] # subset columns by name
names(world5)[2] = "population" # rename column manually

select() also works with 'helper functions' for advanced subsetting operations, including contains(), starts_with() and num_range() (see the help page with ?select for details).

slice() is the row-equivalent of select(). The following code chunk, for example, selects the 3^rd^ to 5^th^ rows:

slice(world, 3:5)

filter() is dplyr's equivalent of base R's subset() function. It keeps only rows matching given criteria, e.g., only countries with a very high average of life expectancy:

# Countries with a life expectancy longer than 82 years
world6 = filter(world, lifeExp > 82)

The standard set of comparison operators can be used in the filter() function, as illustrated in Table \@ref(tab:operators):

operators = c("`==`", "`!=`", "`>, <`", "`>=, <=`", "`&, |, !`")
operators_exp = c("Equal to", "Not equal to", "Greater/Less than", "Greater/Less than or equal", "Logical operators: And, Or, Not")
knitr::kable(data_frame(Symbol = operators, Name = operators_exp), caption = "Table of comparison operators that result in boolean (TRUE/FALSE) outputs.")

A benefit of dplyr is its compatibility with the pipe operator %>%. This 'R pipe', which takes its name from the Unix pipe | and is part of the magrittr package, enables expressive code by 'piping' the output of a previous command into the first argument of the next function. This allows chaining data analysis commands, with the data frame being passed from one function to the next.

``{block2 type='rmdnote'} The **dplyr** functionpull()` extracts a single variable as a vector.

This is illustrate below, in which the `world` dataset is subset by columns (`name_long` and `continent`) and the first five rows (result not shown).

```r
world7 = world %>%
  dplyr::select(name_long, continent) %>%
  slice(1:5)

The above chunk shows how the pipe operator allows commands to be written in a clear order: the above run from top to bottom (line-by-line) and left to right. Without %>% one would be forced to create intermediary objects or use nested function calls, e.g.:

world8 = dplyr::select(
  slice(world, 1:5),
  name_long, continent)

This generates the same result --- verify this with identical(world7, world8) --- in the same number of lines of code, but in a much more confusing way, starting with the function that is called last!

There are additional advantages of pipes from a communication perspective: they encourage adding comments to self-contained functions and allow single lines commented-out without breaking the code.

Vector attribute aggregation

Aggregation operations summarize datasets by a grouping variable, which can be either another attribute column or a spatial object. Imagine we would like to calculate the number of people per continent. Fortunately, our world dataset has the necessary ingredients, with the pop column containing the population per country and the grouping variable continent. In base R this can be done with aggregate() as follows:

aggregate(pop ~ continent, FUN = sum, data = world, na.rm = TRUE)

The result is a non-spatial data frame with six rows, one per continent, and two columns (see Table \@ref(tab:continents) with results for the top 3 most populous continents).

summarize() is the dplyr equivalent of aggregate(), which uses the function group_by() to create the grouping variable. The tidy equivalent of the aggregate() method is as follows:

group_by(world, continent) %>%
  summarize(pop = sum(pop, na.rm = TRUE))

This approach is flexible, allowing the resulting columns to be named. Further, omitting the grouping variable puts everything on in one group. This means summarize() can be used to calculate Earth's total population (~7 billion) and number of countries:

world %>% 
  summarize(pop = sum(pop, na.rm = TRUE), n_countries = n())

world %>% 
  st_set_geometry(NULL) %>%
  summarize(pop = sum(pop, na.rm = TRUE), n_countries = n())

The result is a spatial data frame of class sf (only the non-spatial results are shown): the aggregation procedure dissolves boundaries within continental land masses. In the previous code chunk pop and n_countries are column names in the result. sum() and n() were the aggregating functions.

Let's combine what we've learned so far about dplyr by chaining together functions to find the world's 3 most populous continents (with dplyr::n() ) and the number of countries they contain. The output of the following code is presented in Table \@ref(tab:continents)):

world %>% 
  dplyr::select(pop, continent) %>% 
  group_by(continent) %>% 
  summarize(pop = sum(pop, na.rm = TRUE), n_countries = n()) %>% 
  top_n(n = 3, wt = pop) %>%
  st_set_geometry(value = NULL)

world %>% 
  dplyr::select(pop, continent) %>% 
  group_by(continent) %>% 
  summarize(pop = sum(pop, na.rm = TRUE), n_countries = n()) %>% 
  top_n(n = 3, wt = pop) %>%
  st_set_geometry(value = NULL) %>% 
  knitr::kable(caption = "The top 3 most populous continents, and the number of countries in each.")

Vector attribute joining

Combining data from different sources is a common task in data preparation. Joins do this by combining tables based on a shared 'key' variable. dplyr has powerful functions for joining: left_join(), right_join(), inner_join(), full_join, semi_join() and anti_join(). These function names follow conventions used in the database language SQL [@grolemund_r_2016, Chapter 13]. Using them with sf objects is the focus of this section. dplyr join functions work the same on data frames and sf objects, the only important difference being the geometry list column. The result of data joins can be either an sf or data.frame object.

Most joins involving spatial data will have an sf object as the first argument and a data.frame object as the second argument, resulting in a new sf object (the reverse order is also possible and will return a data.frame). We will focus on the commonly used left and inner joins, which use the same syntax as the other join types [see @grolemund_r_2016 for more join types].

The easiest way to understand the concept of joins is to show how they work with a smaller dataset. We will use an sf object north_america with country codes (iso_a2), names and geometries, as well as a data.frame object wb_north_america containing information about urban population and unemployment for three countries. Note that north_america contains data about Canada, Greenland and the United States but the World Bank dataset (wb_north_america) contains information about Canada, Mexico and the United States:

north_america = world %>%
  filter(subregion == "Northern America") %>%
  dplyr::select(iso_a2, name_long)
north_america$name_long

wb_north_america = worldbank_df %>% 
  filter(name %in% c("Canada", "Mexico", "United States")) %>%
  dplyr::select(name, iso_a2, urban_pop, unemploy = unemployment)

We will use a left join to combine the two datasets. Left joins are the most commonly used operation for adding attributes to spatial data, as they return all observations from the left object (north_america) and the matched observations from the right object (wb_north_america) in new columns. Rows in the left object without matches in the right (Greenland in this case) result in NA values.

To join two objects we need to specify a key. This is a variable (or a set of variables) that uniquely identifies each observation (row). The by argument of dplyr's join functions lets you identify the key variable. In simple cases, a single, unique variable exist in both objects like the iso_a2 column in our example (you may need to rename columns with identifying information for this to work):

left_join1 = north_america %>% 
  left_join(wb_north_america, by = "iso_a2")

This has created a spatial dataset with the new variables added. The utility of this is shown in Figure \@ref(fig:unemploy), which shows the unemployment rate (a World Bank variable) across the countries of North America.

tmap::qtm(left_join1, "unemploy", fill.breaks = c(6, 6.5, 7), fill.title="Unemployment: ")

It is also possible to join objects by different variables. Both of the datasets have variables with names of countries, but they are named differently. The north_america has a name_long column and the wb_north_america has a name column. In these cases a named vector, such as c("name_long" = "name"), can specify the connection:

left_join2 = north_america %>% 
  left_join(wb_north_america, by = c("name_long" = "name"))
names(left_join2)

Note that the result contains two duplicated variables - iso_a2.x and iso_a2.y because both x and y objects have the column iso_a2. This can be solved by specifying all the keys:

left_join3 = north_america %>% 
  left_join(wb_north_america, by = c("iso_a2", "name_long" = "name"))

Joins also work when a data frame is the first argument. This keeps the geometry column but drops the sf class, returning a data.frame object.

# keeps the geom column, but drops the sf class
left_join4 = wb_north_america %>%
  left_join(north_america, by = c("iso_a2"))
class(left_join4)

``{block2 type='rmdnote'} In most cases the geometry column is only useful in ansfobject. The geometry column can only be used for creating maps and spatial operations if R 'knows' it is a spatial object, defined by a spatial package such as **sf**. Fortunately non-spatial data frames with a geometry list column (likeleft_join4) can be coerced into ansfobject as follows:st_as_sf(left_join4)`.

<!-- On the other hand, it is also possible to remove the geometry column of `left_join4` using base R functions or `dplyr`. -->
<!-- Here, this is this simple because the geometry column is just another `data.frame` column and no longer the sticky geometry column of an `sf` object (see also Chapter \@ref(spatial-class)): -->

<!-- ```r -->
<!-- # base R -->
<!-- left_join4_df = subset(left_join4, select = -geom) -->
<!-- # or dplyr -->
<!-- left_join4_df = left_join4 %>% dplyr::select(-geom) -->
<!-- left_join4_df -->
<!-- class(left_join4_df) -->
<!-- ``` -->

In contrast to `left_join()`, `inner_join()` keeps only observations from the left object (`north_america`) where there are matching observations in the right object (`wb_north_america`). 
All columns from the left and right object are still kept:

```r
inner_join1 = north_america %>% 
  inner_join(wb_north_america, by = c("iso_a2", "name_long" = "name"))
inner_join1$name_long

Creating attributes and removing spatial information

Often, we would like to create a new column based on already existing columns. For example, we want to calculate population density for each country. For this we need to divide a population column, here pop, by an area column , here area_km2 with unit area in square km. Using base R, we can type:

world_new = world # do not overwrite our original data
world_new$pop_dens = world_new$pop / world_new$area_km2

Alternatively, we can use one of dplyr functions - mutate() or transmute(). mutate() adds new columns at the penultimate position in the sf object (the last one is reserved for the geometry):

world %>% 
  mutate(pop_dens = pop / area_km2)

The difference between mutate() and transmute() is that the latter skips all other existing columns (except for the sticky geometry column):

world %>% 
  transmute(pop_dens = pop / area_km2)

Existing columns could be also paste together using unite(). For example, we want to stick together continent and region_un columns into a new con_reg column. We could specify a separator to use between values and if input columns should be removed:

world_unite = world %>%
  unite("con_reg", continent:region_un, sep = ":", remove = TRUE)

The separate() function is the complement of the unite() function. Its role is to split one column into multiple columns using either a regular expression or character position.

world_separate = world_unite %>% 
  separate(con_reg, c("continent", "region_un"), sep = ":")

identical(world, world_separate)

Two helper functions, rename() and set_names can be used to change columns names. The first one, rename() replace an old name with a new one. For example, we want to change a name of column from name_long to name:

world %>% 
  rename(name = name_long)

set_names can be used to change names of many columns. In this function, we do not need to provide old names:

new_names = c("ISO_A2", "Name", "Continent", "Region", "Subregion", 
              "Country_type", "Area_in_km2", "Population", "Life_Expectancy",
              "GDP_per_capita", "geom")
world %>% 
  set_names(new_names)

It is important to note that the attribute data operations preserve the geometry of the simple features. As mentioned at the outset of the chapter, however, it can be useful to remove the geometry. Do do this, you have to explicitly remove it because sf explicitly makes the geometry column sticky. This behavior ensures that data frame operations do not accidentally remove the geometry column. Hence, an approach such as select(world, -geom) will be unsuccessful instead use st_set_geometry()^[Note that st_geometry(world_st) = NULL also works to remove the geometry from world but overwrites the original object. ].

world_data = world %>% st_set_geometry(NULL)
class(world_data)

``{block2 type='rmdnote'} More details are provided in the help pages (which can be accessed via?summarizeandvignette(package = "dplyr")` and Chapter 5 of R for Data Science.

## Manipulating raster objects

In contrast to the vector data model underlying simple features (which represents points, lines and polygons as discrete entities in space), raster data represent continuous surfaces.
This section shows how raster objects work, by creating them *from scratch*, building on section \@ref(an-introduction-to-raster).
Because of their unique structure, subsetting and other operations on raster datasets work in a different way, as demonstrated in section \@ref(raster-subsetting).

The following code recreates the raster dataset used in section \@ref(raster-classes), the result of which is illustrated in Figure \@ref(fig:cont-cate-rasters).
This demonstrates how the `raster()` function works to create an example raster named `elev` (representing elevations).

```r
elev = raster(nrow = 6, ncol = 6, res = 0.5,
              xmn = -1.5, xmx = 1.5, ymn = -1.5, ymx = 1.5,
              vals = 1:36)

The result is a raster object with 6 rows and 6 columns (specified by the nrow and ncol arguments), and minimum and a minimum and maximum spatial extent (specified by xmn, xmx and equivalent arguments for the y axis). The vals argument sets the values that each cell contains: numeric data ranging from 1 to 36 in this case. Raster objects can also contain categorical values of class logical or factor variables in R. The following code creates a raster representing grain sizes (Figure \@ref(fig:cont-cate-rasters)):

grain_order = c("clay", "silt", "sand")
grain_char = sample(grain_order, 36, replace = TRUE)
grain_fact = factor(grain_char, levels = grain_order)
grain = raster(nrow = 6, ncol = 6, res = 0.5, 
               xmn = -1.5, xmx = 1.5, ymn = -1.5, ymx = 1.5,
               vals = grain_fact)

``{block2 type='rmdnote'}rasterobjects can contain values of classnumeric,integer,logicalorfactor, but notcharacter. To use character values they must first be converted into an appropriate class, for example using the functionfactor(). Thelevels` argument was used in the preceding code chunk to create an ordered factor: clay < silt < sand in terms of grain size. See the Data structures chapter of [@wickham_advanced_2014] for further details on classes.

`raster` objects represent categorical variables as integers, so `grain[1, 1]` returns a number that represents a unique identifiers, rather than "clay", "silt" or "sand". 
The raster object stores the corresponding look-up table or "Raster Attribute Table" (RAT) as a data frame in a new slot named `attributes`, which can be viewed with `ratify(grain)` (see `?ratify()` for more information).
Use the function `levels()` to retrieve the attribute table and add additional factor values:

```r
levels(grain)[[1]] = cbind(levels(grain)[[1]], wetness = c("wet", "moist", "dry"))
levels(grain)

This behavior demonstrates that raster cells can only possess one value, an identifier which can be used to look up the attributes in the corresponding attribute table (stored in a slot named attributes). This is illustrated in command below, which returns the grain size and wetness of cell IDs 1, 12 and 36, we can run:

factorValues(grain, grain[c(1, 12, 36)])

knitr::include_graphics("figures/03_cont_categ_rasters.png")

Raster subsetting

Raster subsetting is done with the base R operator [, which accepts a variety of inputs:

row-column indexing
cell IDs
coordinates
another raster object

The latter two represent spatial subsetting (see the next chapter). The first two subsetting options are demonstrated in the commands below --- both return the value of the top left pixel in the raster object elev (results not shown):

# row 1, column 1
elev[1, 1]
# cell ID 1
elev[1]

To extract all values or complete rows, you can use values() and getValues(). For multi-layered raster objects stack or brick, this will return the cell value(s) for each layer. For example, stack(elev, grain)[1] returns a matrix with one row and two columns --- one for each layer. For multi-layer raster objects another way to subset is with raster::subset(), which extracts layers from a raster stack or brick. The [[ and $ operators can also be used:

r_stack = stack(elev, grain)
names(r_stack) = c("elev", "grain")
# three ways to extract a layer of a stack
raster::subset(r_stack, "elev")
r_stack[["elev"]]
r_stack$elev

Cell values can be modified by overwriting existing values in conjunction with a subsetting operation. The following code chunk, for example, sets the upper left cell of elev to 0:

elev[1, 1] = 0
elev[]

Leaving the square brackets empty is a shortcut version of values() for retrieving all values of a raster. Multiple cells can also be modified in this way:

elev[1, 1:2] = 0

Summarizing raster objects

raster contains functions for extracting descriptive statistics for entire rasters. Printing a raster object to the console by default, by typing its name, returns minimum and maximum values of a raster. summary() provides common descriptive statistics (minimum, maximum, interquartile range and number of NAs). Further summary operations such as the standard deviation (see below) or custom summary statistics can be calculated with cellStats().

cellStats(elev, sd)

``{block2 type='rmdnote'} If you provide thesummary()andcellStats()functions with a raster stack or brick object, they will summarize each layer separately, as can be illustrated by runningsummary(brick(elev, grain))`.

Raster value statistics can be visualized in a variety of ways.
Raster values, e.g. returned by `values()` or `getValues()`, can be plotted in a variety of ways, including with `boxplot()`, `density()`, `hist()` and `pairs()`, which work for raster objects, as demonstrated in the histogram created with the command below (not shown):

```r
hist(elev)

Descriptive raster statistics belong to the so-called global raster operations. These and other typical raster processing operations are part of the map algebra scheme which are covered in the next chapter.

``{block type='rmdnote'} Some function names clash between packages (e.g.,select, as discussed in a previous note). In addition to not loading packages by referring to functions verbosely (e.g.,dplyr::select()) another way to prevent function names clashes is by unloading the offending package withdetach(). The following command, for example, unloads the **raster** package (this can also be done in the *package* tab in the right-bottom pane in RStudio):detach("package:raster", unload = TRUE, force = TRUE). Theforce` argument makes sure that the package will be detached even if other packages depend on it. This, however, may lead to a restricted usability of packages depending on the detached package, and is therefore not recommended.

## Exercises

For these exercises we will use the `us_states` and `us_states_df` datasets from the **spData** package:

```r
library(spData)
data(us_states)
data(us_states_df)

us_states is a spatial object (of class sf), containing geometry and a few attributes (including name, region, area, and population) of states within the contiguous United States. us_states_df is a data frame (of class data.frame) containing the name and additional variables (including median income and poverty level, for years 2010 and 2015) of US states, including Alaska, Hawaii and Puerto Rico. The data comes from the US Census Bureau, and is documented in ?us_states and ?us_states_df.

Create a new object called us_states_name that contains only the NAME column from the us_states object. What is the class of the new object?
Select columns from the us_states object which contain population data. Obtain the same result using a different command (bonus: try to find three ways of obtaining the same result). Hint: try to use helper functions, such as contains or starts_with from dplyr (see ?contains).
Find all states with the following characteristics (bonus find and plot them):
- Belong to the Midwest region.
- Belong to the West region, have an area below 250,000 km^2^ and in 2015 a population greater than 5,000,000 residents (hint: you may need to use the function units::set_units() or as.numeric()).
- Belong to the South region, had an area larger than 150,000 km^2^ or a total population in 2015 larger than 7,000,000 residents.
What was the total population in 2015 in the us_states dataset? What was the minimum and maximum total population in 2015?
How many states are there in each region?
What was the minimum and maximum total population in 2015 in each region? What was the total population in 2015 in each region?
Add variables from us_states_df to us_states, and create a new object called us_states_stats. What function did you use and why? Which variable is the key in both datasets? What is the class of the new object?
us_states_df has two more variables than us_states. How you can find them? (hint: try to use the dplyr::anti_join function)
What was the population density in 2015 in each state? What was the population density in 2010 in each state?
How much has population density changed between 2010 and 2015 in each state? Calculate the change in percentages and map them.
Change the columns names in us_states to lowercase. (Hint: helper functions - tolower() and colnames() may help).
Using us_states and us_states_df create a new object called us_states_sel. The new object should have only two variables - median_income_15 and geometry. Change the name of the median_income_15 column to Income.
Calculate the change in median income between 2010 and 2015 for each state. Bonus: what was the minimum, average and maximum median income in 2015 for each region? What is the region with the largest increase of the median income?
Create a raster from scratch with nine rows and columns and a resolution of 0.5 decimal degrees (WGS84). Fill it with random numbers. Extract the values of the four corner cells.
What is the most common class of our example raster grain (hint: modal())?
Plot the histogram and the boxplot of the data(dem, package = "RQGIS") raster.
Now attach also data(ndvi, package = "RQGIS"). Create a raster stack using dem and ndvi, and make a pairs() plot