In this workshop, we will plot gene expression levels from an RNAseq dataset. To do this, we’ll need two things: data and a platform to analyze the data.
We could try to use a spreadsheet program like Microsoft Excel or Google sheets that have limited access, less flexibility, and don’t easily allow for things that are critical to “reproducible” research, like easily sharing the steps used to explore and make changes to the original data.
Instead, we’ll use a programming language to test our hypothesis. Today we will use R, but we could have also used Python for the same reasons we chose R (and we teach workshops for both languages). Both R and Python are freely available, the instructions you use to do the analysis are easily shared, and by using reproducible practices, it’s straightforward to add more data or to change settings like colors or the size of a plotting symbol.
To run R, all you really need is the R program, which is available for computers running the Windows, Mac OS X, or Linux operating systems. To make your life in R easier, there is a great (and free!) program called RStudio. As we work today, we’ll use features that are available in RStudio for writing and running code, managing projects, installing packages, getting help, and much more. It is important to remember that R and RStudio are different, but complementary programs. You need R to use RStudio.
To get started, we’ll spend a little time getting familiar with the RStudio environment and setting it up to suit your tastes. When you start RStudio, you’ll have three panels.
On the left you’ll have a panel with three tabs - Console, Terminal,
and Jobs. The Console tab is what running R from the command line looks
like. This is where you can enter R code. Try typing in 2+2
at the prompt (>). In the upper right panel are tabs indicating the
Environment, History, and a few other things. If you click on the
History tab, you’ll see the command you ran at the R prompt.
In the lower right panel are tabs for Files, Plots, Packages, Help, and Viewer. You used the Packages tab to install tidyverse.
We’ll spend more time in each of these tabs as we go through the workshop, so we won’t spend a lot of time discussing them now.
You might want to alter the appearance of your RStudio window. The default appearance has a white background with black text. If you go to the Tools menu at the top of your screen, you’ll see a “Global options” menu at the bottom of the drop down; select that.
From there you will see the ability to alter numerous things about RStudio. Under the Appearances tab you can select the theme you like most. As you can see there’s a lot in Global options that you can set to improve your experience in RStudio. Most of these settings are a matter of personal preference.
However, you can update settings to help you to insure the reproducibility of your code. In the General tab, none of the selectors in the R Sessions, Workspace, and History should be selected. In addition, the toggle next to “Save workspace to .RData on exit” should be set to never. These setting will help ensure that things you worked on previously don’t carry over between sessions.
Let’s get going on our analysis!
One of the helpful features in RStudio is the ability to create a project. A project is a special directory that contains all of the code and data that you will need to run an analysis.
At the top of your screen you’ll see the “File” menu. Select that menu and then the menu for “New Project…”.
When the smaller window opens, select “New Directory” and then the “Browse” button in the next window.
Creat a new project called “heart-gene-expr-2022” and click the “Open” button.
Then click the “Create Project” button.
Did you notice anything change?
In the lower right corner of your RStudio session, you should notice that your Files tab is now your project directory. You’ll also see a file called heart-gene-expr-2022.Rproj in that directory.
From now on, you should start RStudio by double clicking on that file. This will make sure you are in the correct directory when you run your analysis.
We’d like to create a file where we can keep track of our R code.
Back in the “File” menu, you’ll see the first option is “New File”. Selecting “New File” opens another menu to the right and the first option is “R Script”. Select “R Script”.
Now we have a fourth panel in the upper left corner of RStudio that
includes an Editor tab with an untitled R Script. Let’s
save this file as gene_expression.R
in our project
directory.
We will be entering R code into the Editor tab to run in our Console panel.
On line 1 of gene_expression.R
, type
2+2
.
With your cursor on the line with the 2+2
, click the
button that says Run. You should be able to see that
2+2
was run in the Console.
As you write more code, you can highlight multiple lines and then click Run to run all of the lines you have selected.
You can use R like a calculator to add (+
), multiply
(*
), divide (/
), and more!
# Using R as a calculator
# addition +
5 + 3
## [1] 8
# subtraction -
5 - 3
## [1] 2
# multiplication *
5 * 3
## [1] 15
# division /
5 / 3
## [1] 1.666667
# mod (remainder) %%
5 %% 3
## [1] 2
#exponent
5 ** 3
## [1] 125
5 ^3
## [1] 125
#combining terms together (PEMDAS)
5 - 3^2
## [1] -4
(5-3) ^ 2
## [1] 4
name <- "Kelly"
favorite_color <- "green"
height_inches <- 64
likes_cats <- TRUE
num_plants <- 14L
You can think of variables as labelled boxes where you store your belongings.
The <-
symbol is the assignment
operator. It assigns values generated or typed on the right to
objects on the left. An alternative symbol that you might see used as an
assignment operator is the =
but it is
clearer to only use <-
for assignment. We use this
symbol so often that RStudio has a keyboard short cut for it:
Alt+- on Windows, and
Option+- on Mac.
If you’re not sure of the type of a variable, you can find out with
the typeof()
function.
typeof(name)
## [1] "character"
typeof(favorite_color)
## [1] "character"
typeof(height_inches)
## [1] "double"
typeof(likes_cats)
## [1] "logical"
Comments
Sometimes you may want to write comments in your code to help you remember what your code is doing, but you don’t want R to think these comments are a part of the code you want to evaluate. That’s where comments come in! Anything after a
#
symbol in your code will be ignored by R. For example, let’s say we wanted to make a note of what each of the functions we just used do:Sys.Date() # outputs the current date
## [1] "2024-05-28"
getwd() # outputs our current working directory (folder)
## [1] "C:/Users/bmcbe/Desktop/plot-gene-expr-R"
sum(5, 6) # adds numbers
## [1] 11
Assigning values to objects
Try to assign values to some objects and observe each object after you have assigned a new value. What do you notice?
name <- "Ben" name height <- 72 height name <- "Jerry" name
Solution
When we assign a value to an object, the object stores that value so we can access it later. However, if we store a new value in an object we have already created, it replaces the old value. The
height
object does not change, because we never assign it a new value.
Guidelines on naming objects
- You want your object names to be explicit and not too long.
- They cannot start with a number (2x is not valid, but x2 is).
- R is case sensitive, so for example, weight_kg is different from Weight_kg.
- You cannot use spaces in the name.
- There are some names that cannot be used because they are the names of fundamental functions in R (e.g., if, else, for; see here for a complete list). If in doubt, check the help to see if the name is already in use (
?function_name
).- It is recommended to use nouns for object names and verbs for function names.
- Be consistent in the styling of your code, such as where you put spaces, how you name objects, etc. Using a consistent coding style makes your code clearer to read for your future self and your collaborators. One popular style guide can be found through the tidyverse.
The power of variables is that you can re-use them later!
cm_per_inch <- 2.54
height_cm <- height_inches * cm_per_inch
height_cm
## [1] 162.56
height_cm / cm_per_inch
## [1] 64
The above variables hold a single value. What if you need multiple values?
dial_numbers <- c(1, 2, 3)
dial_numbers2 <- 1:3
typeof(dial_numbers)
## [1] "double"
fan_settings <- c('low', 'medium', 'high')
typeof(fan_settings)
## [1] "character"
fan_settings <- factor(c('low', 'high', 'medium', 'high', 'medium'), levels = c('low', 'medium', 'high'))
Sometimes we make a mistake when writing code, and the code isn’t able to run. In that case, the code will give us an error message.
An error tells us, “there’s something wrong with your code or your data and R didn’t do what you asked”. A warning tells us, “you might want to know about this issue, but R still did what you asked”. You need to fix any errors that arise in order for your code to work. Warnings, are probably best to resolve or at least understand why they are coming up.
Exercise: error messages
How can you fix the error messages in these next lines of code?
heihgt_cm
## Error in eval(expr, envir, enclos): object 'heihgt_cm' not found
2 + "three"
## Error in 2 + "three": non-numeric argument to binary operator
Solution
height_cm
## [1] 162.56
2 + 3
## [1] 5
Earlier, the typeof()
function took the variable we
provided and told us the type
that the variable belonged
to. A function is a way to re-use code, either written by you or by
someone else. Functions make it easier to write code because you don’t
have to re-invent the wheel for certain tasks.
Viewing function documentation
Each function has a help page that documents what arguments the function expects and what value it will return. You can bring up the help page a few different ways. If you have typed the function name in the Editor windows, you can put your cursor on the function name and press F1 to open help page in the Help viewer in the lower right corner of RStudio. You can also type
?
followed by the function name in the console.For example, try running
?typeof
. A help page should pop up with information about what the function is used for and how to use it, as well as useful examples of the function in action. As you can see, the first argument oftype
is the variable name.
Whenever using a funciton, you type the name of the function followed immediately by parentheses. Any arguments, or inputs, go between the parentheses.
Do all functions need arguments? Let’s test some other functions:
Sys.Date()
## [1] "2024-05-28"
getwd()
## [1] "C:/Users/bmcbe/Desktop/plot-gene-expr-R"
While some functions don’t need any arguments, in other functions we
may want to use multiple arguments. When we’re using multiple arguments,
we separate the arguments with commas. For example, we can use the
sum()
function to add numbers together:
sum(5, 6)
## [1] 11
Learning more about functions
Look up the function
round
. What does it do? What will you get as output for the following lines of code?round(3.1415) round(3.1415,3)
Solution
round
rounds a number. By default, it rounds it to zero digits (in our example above, to 3). If you give it a second number, it rounds it to that number of digits (in our example above, to 3.142)
Position of the arguments in functions
Which of the following lines of code will give you an output of 3.14? For the one(s) that don’t give you 3.14, what do they give you?
round(x = 3.1415) round(x = 3.1415, digits = 2) round(digits = 2, x = 3.1415) round(2, 3.1415)
Solution
The 2nd and 3rd lines will give you the right answer because the arguments are named, and when you use names the order doesn’t matter. The 1st line will give you 3 because the default number of digits is 0. Then 4th line will give you 2 because, since you didn’t name the arguments, x=2 and digits=3.1415.
Sometimes it is helpful - or even necessary - to include the argument name, but often we can skip the argument name, if the argument values are passed in a certain order. If all this function stuff sounds confusing, don’t worry! We’ll see a bunch of examples as we go that will make things clearer.
So far, all of the functions we have used are part of base R. When you install R, these functions are included by default. However, anyone can write code and share it with other people by putting them in packages. A package is a collection of code that is intended to be shared and re-used. Sometimes you need to do something that isn’t included in base R, or in a different way than the way it is implemented in base R.
Let’s load our first package with
library(tidyverse)
.
Go ahead and run that line in the Console by clicking the Run button on the top right of the Editor tab and choosing Run Selected Lines. This loads a set of useful functions and sample data that makes it easier for us to do complex analyses and create professional visualizations in R.
#install.packages('tidyverse')
library(tidyverse)
## Warning: package 'tidyverse' was built under R version 4.2.3
## Warning: package 'ggplot2' was built under R version 4.2.3
## Warning: package 'tibble' was built under R version 4.2.3
## Warning: package 'purrr' was built under R version 4.2.3
## Warning: package 'dplyr' was built under R version 4.2.3
## Warning: package 'stringr' was built under R version 4.2.3
## Warning: package 'lubridate' was built under R version 4.2.3
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.4.4 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.0
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
What’s with all those messages???
When you loaded the
tidyverse
package, you probably got a message like the one we got above. Don’t panic! These messages are just giving you more information about what happened when you loadedtidyverse
. Thetidyverse
is actually a collection of several different packages, so the first section of the message tells us what packages were installed when we loadedtidyverse
(these includeggplot2
,dyplr
, andtidyr
, which we will use a lot!The second section of messages gives a list of “conflicts.” Sometimes, the same function name will be used in two different packages, and R has to decide which function to use. For example, our message says that:
dplyr::filter() masks stats::filter()
This means that two different packages (
dplyr
fromtidyverse
andstats
from base R) have a function namedfilter()
. By default, R uses the function that was most recently loaded, so if we try using thefilter()
function after loadingtidyverse
, we will be using thefilter()
function > fromdplyr()
. You can use double colons (::
) to specify which package’s version of the function you want to use. This syntax follows the patternpackage::function()
.
The tidyverse vs Base R
If you’ve used R before, you may have learned commands that are different than the ones we will be using during this workshop. We will be focusing on functions from the tidyverse. The “tidyverse” is a collection of R packages that have been designed to work well together and offer many convenient features that do not come with a fresh install of R (aka “base R”). These packages are very popular and have a lot of developer support including many staff members from RStudio. These functions generally help you to write code that is easier to read and maintain. We believe learning these tools will help you become more productive more quickly.
The variable types we discussed above are useful for simple variables, but what if you want to store attributes about lots of different things, like patient samples? For that we use data frames. Just about anything that you can store as rows and columns, like in an Excel spreadsheet, are a great use for data frames. Let’s find out how to read in a dataset as a data frame.
# READING DATA INTO R
expression_data <- read_csv("https://tinyurl.com/UMGWCDFB")
## Rows: 2448 Columns: 4
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (2): Sample_Num, gene
## dbl (2): weeks, log2_expr
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
read_csv
gave us lots of useful information about the
data frames we just loaded. Take a look at the column names and their
types.
The dataset is curated from this paper:
Cui Y et al. 2019. Single-Cell Transcriptome Analysis Maps the Developmental Track of the Human Heart. Cell Reports 26:1934-1950.e5. https://doi.org/10.1016/j.celrep.2019.01.079
If you want to take a peak at just the first 6 rows of the data
frame, you can do so with head
, or to peak at the last 6
rows using tail()
,or look at the whole data frame
interactively with View
:
# LOOKING AT OUR DATA
View(expression_data)
head(expression_data)
tail(expression_data)
We can see that the data type of our weeks column is currently a double. We want to split this data to look at what is going on at 6 weeks and 24 weeks separately, so we need to make this column into categories, or “factors”.
expression_data$weeks <- factor(expression_data$weeks)
Now, we are going to use filter()
to split the data into
two separate data frames, one for each time point.
six_weeks <- expression_data %>%
filter(weeks == 6)
twenty_four_weeks <- expression_data %>%
filter(weeks == 24)
Now, let’s more closely at the six week data:
ncol(six_weeks)
## [1] 4
nrow(six_weeks)
## [1] 864
dim(six_weeks)
## [1] 864 4
colnames(six_weeks)
## [1] "Sample_Num" "gene" "weeks" "log2_expr"
As we see from above, there are 864 rows, so let’s just look at
head()
of row names to see the first few row names.
head(rownames(six_weeks))
## [1] "1" "2" "3" "4" "5" "6"
#reference things in the data frame
#data_frame[row,column]
dim(six_weeks)
## [1] 864 4
six_weeks[1,1]
## # A tibble: 1 × 1
## Sample_Num
## <chr>
## 1 Sample1
six_weeks[4,]
## # A tibble: 1 × 4
## Sample_Num gene weeks log2_expr
## <chr> <chr> <fct> <dbl>
## 1 Sample1 COL3A1 6 8.33
six_weeks[,4]
## # A tibble: 864 × 1
## log2_expr
## <dbl>
## 1 0
## 2 3.38
## 3 6.29
## 4 8.33
## 5 3.98
## 6 4.46
## 7 4.64
## 8 0
## 9 3.42
## 10 0.621
## # ℹ 854 more rows
six_weeks[,2]
## # A tibble: 864 × 1
## gene
## <chr>
## 1 ACTN2
## 2 COL1A1
## 3 COL1A2
## 4 COL3A1
## 5 COL5A1
## 6 COL5A2
## 7 GATA4
## 8 MYH6
## 9 MYH7
## 10 MYL2
## # ℹ 854 more rows
The method above automatically shows us the first 10 rows of our
column of interest. Let’s compare this to another method of looking at a
particular column, also focusing on the first 10 rows using
head()
again.
head(six_weeks$gene, 10)
## [1] "ACTN2" "COL1A1" "COL1A2" "COL3A1" "COL5A1" "COL5A2" "GATA4" "MYH6"
## [9] "MYH7" "MYL2"
# USING FUNCTIONS
mean(six_weeks$log2_expr)
## [1] 3.102636
mean(twenty_four_weeks$log2_expr)
## [1] 3.258743
summary(six_weeks$log2_expr)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.000 1.667 3.103 5.757 11.551
summary(twenty_four_weeks$log2_expr)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.000 3.041 3.259 5.926 12.670
Now we’re ready to make our first plot!
First, let’s try just plotting the ACTN2 gene. We’ll use
filter()
to get rows for this gene only:
expression_data %>%
filter(gene == 'ACTN2')
## # A tibble: 136 × 4
## Sample_Num gene weeks log2_expr
## <chr> <chr> <fct> <dbl>
## 1 Sample1 ACTN2 6 0
## 2 Sample1 ACTN2 24 0
## 3 Sample2 ACTN2 6 0
## 4 Sample2 ACTN2 24 0
## 5 Sample3 ACTN2 6 0.642
## 6 Sample3 ACTN2 24 3.68
## 7 Sample4 ACTN2 6 0
## 8 Sample4 ACTN2 24 0
## 9 Sample5 ACTN2 6 0
## 10 Sample5 ACTN2 24 6.19
## # ℹ 126 more rows
We will be using the ggplot2
package today to make our
plots. This is a very powerful package that creates professional looking
plots and is one of the reasons people like using R so much. All plots
made using the ggplot2
package start by calling the
ggplot()
function.
expression_data %>%
filter(gene == 'ACTN2') %>%
ggplot()
Now we need to start telling it what we actually want to draw in this
plot. The elements of a plot have a bunch of properties like an x and y
position, a size, a color, etc. These properties are called
aesthetics. When creating a data visualization, we map
a variable in our dataset to an aesthetic in our plot. In ggplot, we can
do this by creating an “aesthetic mapping”, which we do with the
aes()
function.
To create our plot, we need to map variables from our data frame to
ggplot aesthetics using the aes()
function. Since we have
already told ggplot
that we are using the data in the
dat_joined_long
object, we can access the columns of the
data frame using the object’s column names. Remember, R is
case-sensitive, so we have to be careful to match the column names
exactly!
expression_data %>%
filter(gene == 'ACTN2') %>%
ggplot() +
aes(weeks, log2_expr)
Note that we’ve added this new function call to a second line just to
make it easier to read. To do this we make sure that the +
is at the end of the first line otherwise R will assume your command
ends when it starts the next row. The +
sign indicates not
only that we are adding information, but to continue on to the next line
of code.
We still haven’t told ggplot how we want it to draw the data. There are many different plot types (bar charts, scatter plots, histograms, etc). We tell our plot object what to draw by adding a “geometry” (“geom” for short) to our object. We will talk about many different geometries today, but for our first plot, let’s draw our data using a boxplot.
expression_data %>%
filter(gene == 'ACTN2') %>%
ggplot() +
aes(weeks, log2_expr) +
geom_boxplot()
Finally, we can make it look nicer by adding labels:
expression_data %>%
filter(gene == 'ACTN2') %>%
ggplot() +
aes(weeks, log2_expr) +
geom_boxplot() +
labs(title = 'ACTN2', x = '# of weeks', y = 'log2 gene expression')
boxplot_actn2 <- expression_data %>%
filter(gene == 'ACTN2') %>%
ggplot() +
aes(weeks, log2_expr) +
geom_boxplot() +
labs(title = 'ACTN2', x = '# of weeks', y = 'log2 gene expression')
ggsave(filename = 'boxplot_actn2.png', plot = boxplot_actn2)
Exercise: make a boxplot
Make a boxplot plot for expression of the gene GATA4 at 6 weeks compared to 24 weeks.
# CHALLENGE: # Make a boxplot plot for expression of the gene GATA4 at 6 weeks compared to 24 weeks. expression_data %>% filter(gene == 'GATA4') %>% ggplot() + aes(weeks, log2_expr) + geom_boxplot() + labs(title = 'GATA4', x = '# of weeks', y = 'log2 gene expression')
We can map the color of the boxplot to a variable using
aes(color = colname)
. Let’s see what it looks like using
the default options:
# R color palettes
# change the colors with scale_color_
expression_data %>%
filter(gene == 'ACTN2') %>%
ggplot() +
aes(weeks, log2_expr, color = weeks) +
geom_boxplot() +
labs(title = 'ACTN2', x = '# of weeks', y = 'log2 gene expression')
That changed the outline, but not the inside. We can instead use fill:
# R color palettes
# change the colors with scale_color_
expression_data %>%
filter(gene == 'ACTN2') %>%
ggplot() +
aes(weeks, log2_expr, fill = weeks) +
geom_boxplot() +
labs(title = 'ACTN2', x = '# of weeks', y = 'log2 gene expression')
Our plot is looking prettier now that we have some color! But what if
we want to use different colors? We can use
scale_fill_manual
to manually set them and specify colors
by name:
# R color palettes
# change the colors with scale_color_
expression_data %>%
filter(gene == 'ACTN2') %>%
ggplot() +
aes(weeks, log2_expr, fill = weeks) +
geom_boxplot() +
scale_fill_manual(values = c('green', 'blue')) +
labs(title = 'ACTN2', x = '# of weeks', y = 'log2 gene expression')
Or you can look up the hexadecimal code of your favorite colors and specify them exactly. There are a lot of websites that will tell you the hex code of a color. Here’s one: https://www.rapidtables.com/web/color/RGB_Color.html Let’s use “plum” (#DDA0DD) and “light steel blue” (#B0C4DE).
# R color palettes
# change the colors with scale_color_
expression_data %>%
filter(gene == 'ACTN2') %>%
ggplot() +
aes(weeks, log2_expr, fill = weeks) +
geom_boxplot() +
scale_fill_manual(values = c('#DDA0DD', '#B0C4DE')) +
labs(title = 'ACTN2', x = '# of weeks', y = 'log2 gene expression')
You can even specify both the fill and the color at the same time:
# R color palettes
# change the colors with scale_color_
expression_data %>%
filter(gene == 'ACTN2') %>%
ggplot() +
aes(weeks, log2_expr, fill = weeks, color = weeks) +
geom_boxplot() +
scale_fill_manual(values = c('#DDA0DD', '#B0C4DE')) +
scale_color_manual(values = c('#B0C4DE', '#DDA0DD'))
labs(title = 'ACTN2', x = '# of weeks', y = 'log2 gene expression')
## $x
## [1] "# of weeks"
##
## $y
## [1] "log2 gene expression"
##
## $title
## [1] "ACTN2"
##
## attr(,"class")
## [1] "labels"
Exercise: custom colors
modify your boxplot for GATA4. Make each box a different color or fill (or both!)
Once you’ve finished, use
ggsave()
to save the file.pretty_boxplot_gata4 = expression_data %>% filter(gene == 'GATA4') %>% ggplot() + aes(weeks, log2_expr, fill = weeks, color = weeks) + geom_boxplot() + scale_fill_manual(values = c('#DDA0DD', '#B0C4DE')) + scale_color_manual(values = c('#B0C4DE', '#DDA0DD')) labs(title = 'GATA4', x = '# of weeks', y = 'log2 gene expression')
## $x ## [1] "# of weeks" ## ## $y ## [1] "log2 gene expression" ## ## $title ## [1] "GATA4" ## ## attr(,"class") ## [1] "labels"
#ggsave(filename = 'boxplot_GATA4.png', plot = pretty_boxplot_gata4)
# PLOT ALL THE GENES
# facet wrap
expression_data %>%
ggplot(aes(weeks, log2_expr)) +
geom_boxplot() +
facet_wrap('gene')
expression_data %>%
filter(weeks == '6', !is.na(log2_expr)) %>%
ggplot(aes(gene, Sample_Num, fill = log2_expr)) +
geom_tile() +
theme(axis.text.x = element_text(angle = 90))
expression_data %>%
filter(weeks == '24', !is.na(log2_expr)) %>%
ggplot(aes(gene, Sample_Num, fill = log2_expr)) +
geom_tile() +
theme(axis.text.x = element_text(angle = 90))
tibble(linear = 0:10,
x = linear) %>%
mutate(log2 = log2(linear),
log10 = log10(linear)) %>%
pivot_longer(c(linear, log2, log10),
names_to = 'scale',
values_to = 'y') %>%
ggplot() +
aes(x, y, color = scale) +
geom_point() +
geom_line() +
theme_bw()