Chapter 15 Data imports and graphing

Much of this chapter is based strongly (for large parts identical) on the STAT444 course by Derek Sonderegger. There is a Video Lecture that accompanies this chapter.

15.1 Importing Data

We’ll learn how to import data sets into R, including from packages, and from spreadsheets, such as Excel or .csv files. We’ll then see how to make changes to the data, or how to do simple tasks using data frames.

15.1.1 Importing From a Package

We saw in a previous chapter that one easy way to read data in is from packages- this is often used for teaching exercises . Remember, to use data from a package, we first install the package if we haven’t already. Recall to do that, we can use the Rstudio menu bar “Tools -> Install Packages…” mouse action.

So that we don’t have many data sets unnecessarily taking up R’s memory, remember from the previous chapter we have to go through a two-step process of making sure that the package is installed on the computer, and then loading the desired data set into our current R session. Once the package is installed, we can load the data into our session via the following command:

data('alfalfa', package='faraway')   # load the data set 'alfalfa' from the package 'faraway'

Because R tries to avoid loading datasets until they are needed, the object alfalfa isn’t initially loaded as a data.frame but rather as a “promise” that it eventually will be loaded whenever you first use it. So let’s first access it by viewing it.

View(alfalfa)

There are two ways to enter the view command. Either executing the View() function from the console, or perhaps more simply by clicking on either the white table or the object name in the Environment tab.

15.1.2 Import from `.csv` or `.xls` files

A common way of transmitting data is using “csv” (Comma Separated Values) files (with the file suffix of .csv). Most software packages will use this format and it’s probably the most common interchange format.

A short file might look like this:

Start,End,Name
1837,1901,Victoria
1901,1910,Edward VII
1910,1936,George V
1936,1936,Edward VIII
1936,1952,George VI
1952,2022,Elizabeth II
2022,,Charles III

where the rows in the file represent the data frame rows, and the columns are just separated by commas. The first row of the file is usually the column titles.

If data is stored as an Excel file and we just tell R where the file is and which worksheet tab to import.

The best way to import a file is using the import wizard accessed via ‘File -> Import Dataset’. This will then give you a choice of file types to read from (.csv files are in the “Text” options). Navigate to the file you want to import, and click on import. Note that R will preview the file as you import it, and here’s a good time to check the settings to make sure that you are importing the right file, and the parameters are correct.

When you import a file using the import wizard, R generates code that does the actual import. We MUST copy that code into our R Script file or else the import won’t happen when we run the script. So only use the import wizard to generate the import code! The code generated by the import wizard ends with a View() command and which can be removed. The code that I’ll paste into my R Script file typically looks like this:

# NB Not real code as the file is not a real one
library(readxl)
lotto <- read_excel("/MyFiles/DataFile/WinningLotteryNumbers.xlsx")

15.1.3 Types of data in R

It is worth thinking briefly here about how R stores data. Remember the diamondsdata set:

library(ggplot2)
head(diamonds)

## # A tibble: 6 x 10
##   carat cut       color clarity depth table price     x     y     z
##   <dbl> <ord>     <ord> <ord>   <dbl> <dbl> <int> <dbl> <dbl> <dbl>
## 1  0.23 Ideal     E     SI2      61.5    55   326  3.95  3.98  2.43
## 2  0.21 Premium   E     SI1      59.8    61   326  3.89  3.84  2.31
## 3  0.23 Good      E     VS1      56.9    65   327  4.05  4.07  2.31
## 4  0.29 Premium   I     VS2      62.4    58   334  4.2   4.23  2.63
## 5  0.31 Good      J     SI2      63.3    58   335  4.34  4.35  2.75
## 6  0.24 Very Good J     VVS2     62.8    57   336  3.94  3.96  2.48

summary(diamonds)

##      carat               cut        color        clarity          depth      
##  Min.   :0.2000   Fair     : 1610   D: 6775   SI1    :13065   Min.   :43.00  
##  1st Qu.:0.4000   Good     : 4906   E: 9797   VS2    :12258   1st Qu.:61.00  
##  Median :0.7000   Very Good:12082   F: 9542   SI2    : 9194   Median :61.80  
##  Mean   :0.7979   Premium  :13791   G:11292   VS1    : 8171   Mean   :61.75  
##  3rd Qu.:1.0400   Ideal    :21551   H: 8304   VVS2   : 5066   3rd Qu.:62.50  
##  Max.   :5.0100                     I: 5422   VVS1   : 3655   Max.   :79.00  
##                                     J: 2808   (Other): 2531                  
##      table           price             x                y                z         
##  Min.   :43.00   Min.   :  326   Min.   : 0.000   Min.   : 0.000   Min.   : 0.000  
##  1st Qu.:56.00   1st Qu.:  950   1st Qu.: 4.710   1st Qu.: 4.720   1st Qu.: 2.910  
##  Median :57.00   Median : 2401   Median : 5.700   Median : 5.710   Median : 3.530  
##  Mean   :57.46   Mean   : 3933   Mean   : 5.731   Mean   : 5.735   Mean   : 3.539  
##  3rd Qu.:59.00   3rd Qu.: 5324   3rd Qu.: 6.540   3rd Qu.: 6.540   3rd Qu.: 4.040  
##  Max.   :95.00   Max.   :18823   Max.   :10.740   Max.   :58.900   Max.   :31.800  
##

You will see in the summary command above for the diamonds data set that R knows that the mean of price can be explained, but for example, that color is categorical data, and does not attempt to find a mean color, which would not make sense.

R stores data as different types, and if we look at the structure of the diamonds dataset using the str command, we can see this structure:

str(diamonds)

## tibble [53,940 x 10] (S3: tbl_df/tbl/data.frame)
##  $ carat  : num [1:53940] 0.23 0.21 0.23 0.29 0.31 0.24 0.24 0.26 0.22 0.23 ...
##  $ cut    : Ord.factor w/ 5 levels "Fair"<"Good"<..: 5 4 2 4 2 3 3 3 1 3 ...
##  $ color  : Ord.factor w/ 7 levels "D"<"E"<"F"<"G"<..: 2 2 2 6 7 7 6 5 2 5 ...
##  $ clarity: Ord.factor w/ 8 levels "I1"<"SI2"<"SI1"<..: 2 3 5 4 2 6 7 3 4 5 ...
##  $ depth  : num [1:53940] 61.5 59.8 56.9 62.4 63.3 62.8 62.3 61.9 65.1 59.4 ...
##  $ table  : num [1:53940] 55 61 65 58 58 57 57 55 61 61 ...
##  $ price  : int [1:53940] 326 326 327 334 335 336 336 337 337 338 ...
##  $ x      : num [1:53940] 3.95 3.89 4.05 4.2 4.34 3.94 3.95 4.07 3.87 4 ...
##  $ y      : num [1:53940] 3.98 3.84 4.07 4.23 4.35 3.96 3.98 4.11 3.78 4.05 ...
##  $ z      : num [1:53940] 2.43 2.31 2.31 2.63 2.75 2.48 2.47 2.53 2.49 2.39 ...

carat, for example is noted as num (numerical data, meaning continuous), where price is an int, or an integer, as price has only taken integer prices. The unusual thing R does, as a statistical language, is to have a data type which is a factor, which is how R stores categorical data. factorscan be ordered (ordinal data), as here with cut,color,and clarity, or unordered (nominal data).

Other data types that R uses are strings (str), and logicals.

oneName<-"Kier"
myNames<-c("Tony", "Gordon", "David", "Jeremy")
leader<-TRUE
myFriend<-c(FALSE,TRUE,FALSE,TRUE)

R is generally pretty good at recognising which data type is which, but if we explicitly want to define something as a categorical data, we usually have to tell R

# This is just a vector containing two strings
y<-c("Bert","Ernie")
y

## [1] "Bert"  "Ernie"

# Here we tell R that this is categorical data
z<-as.factor(c("Bert","Ernie"))
z

## [1] Bert  Ernie
## Levels: Bert Ernie

More details on the types can be found in the appendix

15.2 More general graphs: ggplot2

We have seen how to do simple graphs in a previouis chapter. A more general approach, and increasingly popular, is the ‘tidyverse’ which is a collection of modern packages that do some very useful things. One part of this tidyverse package is an advanced graphing library called ggplot2.

To install the package the very first time, we either use the “Tools-> Import Packages” menu and install tidyverse, or use the following command.

install.packages("tidyverse")

We must load the package into memory using the library command every time:

library(tidyverse)

To make the most of ggplot2 it is important to wrap your mind around “The Grammar of Graphics”. Briefly, the act of building a graph can be broken down into three steps.

Define what data set we are using.
What is the major relationship we wish to examine?
In what way should we present that relationship? These relationships can be presented in multiple ways, and the process of creating a good graph relies on building layers upon layers of information. For example, we might start with printing the raw data and then overlay a regression line over the top.

Next, it should be noted that ggplot2 is designed to act on data frames. It is actually hard to just draw three data points and for simple graphs it might be easier to use the base graphing system in R. However for any real data analysis project, the data will already be in a data frame and this is not an annoyance.

These notes are sufficient for creating simple graphs using ggplot2, but are not intended to be exhaustive. There are many places online to get help with ggplot2. One very nice resource is the website, http://www.cookbook-r.com/Graphs/, which gives much of the information available in the book R Graphics Cookbook which I highly recommend. Second is just googling your problems and see what you can find on websites such as StackExchange.

One way that ggplot2 makes it easy to form very complicated graphs is that it provides a large number of basic building blocks that, when stacked upon each other, can produce extremely complicated graphs. A full list is available at http://docs.ggplot2.org/current/ but the following list gives some idea of different building blocks. These different geometries are different ways to display the relationship between variables and can be combined in many interesting ways.

Geom	Description	Required Aesthetics
`geom_histogram`	A histogram	`x`
`geom_bar`	A barplot (y is number of rows)	`x`
`geom_col`	A barplot (y is given by a column)	`x, y`
`geom_density`	A density plot of data. (smoothed histogram)	`x`
`geom_boxplot`	Boxplots	`x, y`
`geom_line`	Draw a line (after sorting x-values)	`x, y`
`geom_path`	Draw a line (without sorting x-values)	`x, y`
`geom_point`	Draw points (for a scatterplot)	`x, y`
`geom_smooth`	Add a ribbon that summarizes a scatterplot	`x, y`
`geom_ribbon`	Enclose a region, and color the interior	`ymin, ymax`
`geom_errorbar`	Error bars	`ymin, ymax`
`geom_text`	Add text to a graph (with box)	`x, y, label`
`geom_label`	Add text to a graph (without box)	`x, y, label`
`geom_tile`	Create Heat map	`x, y, fill`

A graph can be built up layer by layer, where:

Each layer corresponds to a geom, each of which requires a dataset and a mapping between an aesthetic and a column of the data set.
- If you don’t specify either, then the layer inherits everything defined in the ggplot() command.
- You can have different datasets for each layer!
Layers can be added with a +, or you can define two plots and add them together (second one over-writes anything that conflicts).

15.2.1 Scatterplots

We’ll again use the iris dataset to demonstrate here.

ggplot( data=iris, aes(x=Sepal.Length, y=Petal.Length) ) +  
    geom_point(  )

The data set we wish to use is specified using data=iris.
The relationship we want to explore is x=Sepal.Length and y=Petal.Length. This means the x-axis will be the Sepal Length and the y-axis will be the Petal Length.
The way we want to display this relationship is through graphing 1 point for every observation.

We can define other attributes that might reflect other aspects of the data. For example, we might want for the color of the data point to change dynamically based on the species of iris.

ggplot( data=iris, aes(x=Sepal.Length, y=Petal.Length) ) +  
    geom_point( aes(color=Species) )

The aes() command (short for aesthetic) inside the previous section of code is quite mysterious. The way to think about the aes() is that it gives you a way to define relationships that are data dependent. In the previous graph, the x-value and y-value for each point was defined dynamically by the data, as was the color. If we just wanted all the data points to be colored blue and larger, then the following code would do that

ggplot( data=iris, aes(x=Sepal.Length, y=Petal.Length) ) +  
    geom_point( color='blue', size=4 )

The important part isn’t that color and size were defined in the geom_point() but that they were defined outside of an aes() function!

Anything set inside an aes() command will be of the form attribute=Column_Name and will change based on the data.
Anything set outside an aes() command will be in the form attribute=value and will be fixed.

15.2.2 Box Plots

Boxplots are a common way to show a categorical variable on the x-axis and continuous on the y-axis.

ggplot(iris, aes(x=Species, y=Petal.Length)) +
  geom_boxplot()

The boxes show the \(25^{th}\), \(50^{th}\), and \(75^{th}\) percentile and the lines coming off the box extend to the smallest and largest non-outlier observation.

15.3 Faceting

The goal with faceting is to make many panels of graphics where each panel represents the same relationship between variables, but something changes between each panel. For example using the iris dataset we could look at the relationship between Sepal.Length and Petal.Length either with all the data in one graph, or one panel per species.

library(ggplot2)
ggplot(iris, aes(x=Sepal.Length, y=Petal.Length)) +
  geom_point() +
  facet_grid( . ~ Species )

The line facet_grid( formula ) tells ggplot2 to make panels, and the formula tells how to orient the panels. In R, formulas are always interpreted in the order y ~ x. Because I want the species to change as we go across the page, but don’t have anything I want to change vertically we use . ~ Species to represent that. If we had wanted three graphs stacked then we could use Species ~ ..

For a second example, we look at a dataset that examines the amount a waiter was tipped by 244 parties. Covariates that were measured include the day of the week, size of the party, total amount of the bill, amount tipped, whether there were smokers in the group and the gender of the person paying the bill

library(reshape)

## Warning: package 'reshape' was built under R version 4.1.3

## 
## Attaching package: 'reshape'

## The following object is masked from 'package:dplyr':
## 
##     rename

## The following objects are masked from 'package:tidyr':
## 
##     expand, smiths

data(tips, package='reshape')
head(tips)

##   total_bill  tip    sex smoker day   time size
## 1      16.99 1.01 Female     No Sun Dinner    2
## 2      10.34 1.66   Male     No Sun Dinner    3
## 3      21.01 3.50   Male     No Sun Dinner    3
## 4      23.68 3.31   Male     No Sun Dinner    2
## 5      24.59 3.61 Female     No Sun Dinner    4
## 6      25.29 4.71   Male     No Sun Dinner    4

It is easy to look at the relationship between the size of the bill and the percentage tipped.

ggplot(tips, aes(x = total_bill, y = tip / total_bill )) +
  geom_point()

Next we ask if there is a difference in tipping percent based on gender or day of the week by plotting this relationship for each combination of gender and day.

ggplot(tips, aes(x = total_bill, y = tip / total_bill, color=time )) +
  geom_point() +
  facet_grid( sex ~ day )

#  facet_grid( day ~ sex )  # changing orientation emphasizes certain comparisons!

Sometimes we want multiple rows and columns of the facets, but there is only one categorical variable with many levels. In that case we use facet_wrap which takes a one-sided formula.

ggplot(tips, aes(x = total_bill, y = tip / total_bill )) +
  geom_point() +
#  facet_grid( . ~ day)  # Four graphs in a row, Too Squished left/right!
  facet_wrap( ~ day )   # spread graphs out both left/right and up/down.

Finally we can allow the x and y scales to vary between the panels by setting “free”, “free_x”, or “free_y”. In the following code, the y-axis scale changes between the gender groups.

ggplot(tips, aes(x = total_bill, y = tip / total_bill )) +
  geom_point() +
  facet_grid( sex ~ day, scales="free_y" )

15.4 Annotation

15.4.1 Axis Labels and Titles

To make a graph more understandable, it is necessary to tweak the axis labels and add a main title and such. Here we’ll adjust labels in a graph, including the legend labels.

# Save the graph before I add more to it.
P <-
  ggplot( data=iris, aes(x=Sepal.Length, y=Petal.Length, color=Species) ) +  
    geom_point( aes(color=Species)  ) +
  labs( title='Sepal Length vs Petal Length' ) +
  labs( x="Sepal Length (cm)", y="Petal Length (cm)" ) +
  labs( color="Species Name")  + 
  labs( caption = "Iris data from Edgar Anderson (1935)" )

# Print out the plot
P

You could either call the labs() command repeatedly with each label, or you could provide multiple arguments to just one labs() call.

15.4.2 Text Labels

One way to improve the clarity of a graph is to remove the legend and label the points directly on the graph. For example, we could instead have the species names near the cloud of data points for the species.

Usually our annotations aren’t stored in the data.frame that contains our data of interest. So we need to either create a new (usually small) data.frame that contains all the information needed to create the annotation or we need to set the necessary information in-place. Either way, we need to specify the x and y coordinates, and the label to be printed, as well as any other attribute that is set in the global aes() command. That means if color has been set globally, the annotation layer also needs to address the color attribute.

15.4.2.1 Using a `data.frame`

To do this in ggplot, we need to make a data frame that has the columns Sepal.Length and Petal.Length so that we can specify where each label should go, as well as the label that we want to print. Also, because color is matched to the Species column, this small dataset should also have a the Species column.

This step always requires a bit of fussing with the graph because the text size and location should be chosen based on the size of the output graphic and if I rescale the image it often looks awkward. Typically I leave this step until the figure is being prepared for final publication.

# create another data frame that has the text labels I want to add to the graph.
annotation.data <- data.frame(
  Sepal.Length = c(4.5,  6.5,  7.0),  # Figured out the label location by eye.
  Petal.Length = c(2.25, 3.75, 6.5),  # If I rescale the graph, I would redo this step.
  Species = c('setosa', 'versicolor', 'virginica'),
  Text = c('SETOSA', 'VERSICOLOR', 'VIRGINICA')
)

# Use the previous plot I created, along with the 
# aes() options already defined.
P +
  geom_text( data=annotation.data, aes(label=Text), size=2.5) +   # write the labels
  theme( legend.position = 'none' )                               # remove the legend

15.4.2.2 Setting attributes in-line

Instead of creating a new data frame, we could just add a new layer and just set all of the graph attributes manually. To do this, we have to have one layer for each text we want to add to the graph. The annotate function takes a geom layer type and the necessary inputs an allows us to avoid the annoyance of building a labels data frame.

P +
  annotate('text', x=4.5, y=2.25, size=6, color='#F8766D', label='SETOSA'     ) +
  annotate('text', x=6.5, y=3.75, size=6, color='#00BA38', label='VERSICOLOR' ) +
  annotate('text', x=7.0, y=6.50, size=6, color='#619CFF', label='VIRGINICA'  ) +
  theme(legend.position = 'none')

Finally there is a geom_label layer that draws a nice box around what you want to print.

P +
  annotate('label', x=4.5, y=2.25, size=6, color='#F8766D', label='SETOSA'     ) +
  annotate('label', x=6.5, y=3.50, size=6, color='#00BA38', label='VERSICOLOR' ) +
  annotate('label', x=7.0, y=6.75, size=6, color='#619CFF', label='VIRGINICA'  ) +
  theme(legend.position = 'none')

My recommendation is to just set the x, y, and label attributes manually inside an annotate() call if you have one or two annotations to print on the graph. If you have many annotations to print, the create a data frame that contains all of them and use data= argument in the geom to use that created annotation data set.

15.5 Exercises

Examine the dataset trees, which should already be pre-loaded. Look at the help file using ?trees for more information about this data set. We wish to build a scatterplot that compares the height and girth of these cherry trees to the volume of lumber that was produced.
1. Create a graph using ggplot2 with Height on the x-axis, Volume on the y-axis, and Girth as the either the size of the data point or the color of the data point. Which do you think is a more intuitive representation?
2. Add appropriate labels for the main title and the x and y axes.
3. The R-squared value for a regression through these points is 0.36 and the p-value for the statistical significance of height is 0.00038. Add text labels “R-squared = 0.36” and “p-value = 0.0004” somewhere on the graph.
Consider the following small dataset that represents the number of times per day a mother played “Ring around the Rosy” with her daughter relative to the number of days since she has learned this game. The column yhat represents the best fitting line through the data, and lwr and upr represent a 95% confidence interval for the predicted value on that day. Because these questions ask you to produce several graphs and evaluate which is better and why, please include each graph and response with each sub-question.
```
Rosy <- data.frame(
  times = c(15, 11, 9, 12, 5, 2, 3),
  day   = 1:7,
  yhat  = c(14.36, 12.29, 10.21, 8.14, 6.07, 4.00,  1.93),
  lwr   = c( 9.54,  8.5,   7.22, 5.47, 3.08, 0.22, -2.89),
  upr   = c(19.18, 16.07, 13.2, 10.82, 9.06, 7.78,  6.75))
```
1. Using ggplot() and geom_point(), create a scatterplot with day along the x-axis and times along the y-axis.
2. Add a line to the graph where the x-values are the day values but now the y-values are the predicted values which we’ve called yhat. Notice that you have to set the aesthetic y=times for the points and y=yhat for the line. Because each geom_ will accept an aes() command, you can specify the y attribute to be different for different layers of the graph.
3. Add a ribbon that represents the confidence region of the regression line. The geom_ribbon() function requires an x, ymin, and ymax columns to be defined. For examples of using geom_ribbon() see the online documentation: http://docs.ggplot2.org/current/geom_ribbon.html.
4. What happened when you added the ribbon? Did some points get hidden? If so, why?
5. Reorder the statements that created the graph so that the ribbon is on the bottom and the data points are on top and the regression line is visible.
6. The color of the ribbon fill is ugly. Use Google to find a list of named colors available to ggplot2. For example, I googled “ggplot2 named colors” and found the following link: http://sape.inf.usi.ch/quick-reference/ggplot2/colour. Choose a color for the fill that is pleasing to you.
7. Add labels for the x-axis and y-axis that are appropriate along with a main title.
We’ll next make some density plots that relate several factors towards the birth weight of a child. Because these questions ask you to produce several graphs and evaluate which is better and why, please include each graph and response with each sub-question.
1. The MASS package contains a dataset called birthwt which contains information about 189 babies and their mothers. In particular there are columns for the mother’s race and smoking status during the pregnancy. Load the birthwt by either using the data() command or loading the MASS library.
2. Read the help file for the dataset using MASS::birthwt. The covariates race and smoke are not stored in a user friendly manner. For example, smoking status is labeled using a 0 or a 1. Because it is not obvious which should represent that the mother smoked, we’ll add better labels to the race and smoke variables. For more information about dealing with factors and their levels, see the Factors chapter in these notes.
```
library(tidyverse)
data('birthwt', package='MASS')
birthwt <- birthwt %>% mutate(
  race  = factor(race,  labels=c('White','Black','Other')),
  smoke = factor(smoke, labels=c('No Smoke', 'Smoke')))
```
3. Graph a histogram of the birth weights bwt using ggplot(birthwt, aes(x=bwt)) + geom_histogram().
4. Make separate graphs that denote whether a mother smoked during pregnancy by appending + facet_grid() command to your original graphing command.
5. Perhaps race matters in relation to smoking. Make our grid of graphs vary with smoking status changing vertically, and race changing horizontally (that is the formula in facet_grid() should have smoking be the y variable and race as the x).
6. Remove race from the facet grid, (so go back to the graph you had in part d). I’d like to next add an estimated density line to the graphs, but to do that, I need to first change the y-axis to be density (instead of counts), which we do by using aes(y=..density..) in the ggplot() aesthetics command.
7. Next we can add the estimated smooth density using the geom_density() command.
8. To really make this look nice, lets change the fill color of the histograms to be something less dark, lets use fill='cornsilk' and color='grey60'. To play with different colors that have names, check out the following: http://www.stat.columbia.edu/~tzheng/files/Rcolor.pdf.
9. Change the order in which the histogram and the density line are added to the plot. Does it matter and which do you prefer?
10. Finally consider if you should have the histograms side-by-side or one ontop of the other (i.e. . ~ smoke or smoke ~ .). Which do you think better displayes the decrease in mean birthweight and why?
Load the dataset ChickWeight, which comes preloaded in R, and get the background on the dataset by reading the manual page ?ChickWeight. Because these questions ask you to produce several graphs and evaluate which is better and why, please include each graph and response with each sub-question.
1. Produce a separate scatter plot of weight vs age for each chick. Use color to distinguish the four different Diet treatments.
2. We could examine these data by producing a scatterplot for each diet. Most of the code below is readable, but if we don’t add the group aesthetic the lines would not connect the dots for each Chick but would instead connect the dots across different chicks.
```
data(ChickWeight)
ggplot(ChickWeight, aes(x=Time, y=weight, group=Chick )) +
  geom_point() + geom_line() +
  facet_grid( ~ Diet) 
```
There is a spreadsheet with the football (soccer) results from the English Premiership 2019-2020 season available at this url. Because the readr package doesn’t care whether a file is on your local computer or on the Internet, we’ll use this file.
1. Start the import wizard using: “File -> Import Dataset -> From Text (readr) …” and input the above web URL. Click the update button near the top to cause the wizard to preview the result.
2. Save the generated code to your R Script file and show the first few rows using the head() command.
3. The goals scored by the home side are in the ‘FTHG’ column. Calculate the mean number of goals for the home side.
4. The result of the match (Home win, Draw, Away Win) are in the FTR column. Produce a crosstab using the table command to show the number of times each HomeTeam achieved each result. Which team had the most draws in the season?
5. Produce bar charts showing the number of goals scored in each game (from the FTHG column)