Read Chapter 2 to help you complete the questions in this exercise.
1. Open up your RStudio Project from Exercise 1 and either create a
new R script or continue with your previous R script. Remember to save
your R script with a suitable name (exercise_2?). Make sure you include
any metadata you feel is appropriate (title, description of task, date
of script creation etc). Don’t forget to comment out your metadata with
a # at the beginning of the line.
2. Let’s use R as a fancy calculator. Find the natural log, log to the base 10, log to the base 2, square root and the natural antilog of 12.43. See Section 2.1 of the Introduction to R book for more information on mathematical functions in R. Don’t forget to write your code in RStudio’s script editor and source the code into the console.
log(12.43) # natural log
log10(12.43) # log to base 10
log2(12.43) # log to base 2
log(12.43, base = 2) # alternative log to base 2
sqrt(12.43) # square root
exp(12.43) # exponent
3. Next, use R to determine the area of a circle with a diameter of
20 cm and assign the result to an object called
area_circle. If you can’t remember how to create and assign
objects see Section
2.2 or watch this video.
Google is your friend if you can’t remember the formula to calculate the
area of a circle! Also, remember that R already knows about
pi. Don’t worry if you’re stumped, feel free to ask one of
the instructors for guidance.
4. Now for something a little more tricky. Calculate the cube root of 14 x 0.51. You might need to think creatively for a solution (hint: think exponents), and remember that R follows the usual order of mathematical operators so you might need to use brackets in your code (see this page if you’ve never heard of this). The point of this question is not to torture you with maths (so please don’t stress!), its to get you used to writing mathematical equations in R and highlight the order of operations.
5. Ok, you’re now ready to explore one of R’s basic (but very useful)
data structures - vectors. A vector is a sequence of elements (or
components) that are all of the same data type (see Section
3.2.1 for an introduction to vectors). Although technically not
correct it might be useful to think of a vector as something like a
single column of data in a spreadsheet. There are a multitude of ways to
create vectors in R but you will use the concatenate function
c() to create a vector called weight
containing the weight (in kg) of 10 children:
69, 62, 57, 59, 59, 64, 56, 66, 67, 66 (Section
2.3 or watch this video
for more information).
6. Now you can do some useful stuff to your weight
vector. Get R to calculate the mean, variance, standard deviation, range
of weights and the number of children of your weight vector
(see Section
2.3 for more details). Now read Section 2.4 of the R book to
learn how to work with vectors. After reading this section you should be
able to extract the weights for the first five children using Positional
indexes and store these weights in a new variable called
first_five. Remember, you will need to use the square
brackets [ ] to extract (aka index, subset) elements from a
variable.
mean(weight) # calculate mean
var(weight) # calculate variance
sd(weight) # calculate standard deviation
range(weight) # range of weight values
length(weight) # number of observations
first_five <- weight[1:5] # extract first 5 weight values
first_five <- weight[c(1, 2, 3, 4, 5)] # alternative method
7. We’re now going to use the the c() function again to
create another vector called height containing the height
(in cm) of the same 10 children:
112, 102, 83, 84, 99, 90, 77, 112, 133, 112. Use the
summary() function to summarise these data in the
height object. Extract the height of the 2nd, 3rd, 9th and
10th child and assign these heights to a variable called
some_child (take a look at the section Positional
indexes in the R book if you’re stuck). We can also extract elements
using Logical
indexes. Let’s extract all the heights of children less than or
equal to 99 cm and assign to a variable called
shorter_child.
height <- c(112, 102, 83, 84, 99, 90, 77, 112, 133, 112)
summary(height) # summary statistics of height variable
some_child <- height[c(2, 3, 9, 10)] # extract the 2nd, 3rd, 9th, 10th height
shorter_child <- height[height <= 99] # extract all heights less than or equal to 99
8. Now you can use the information in your weight and
height variables to calculate the body mass index (BMI) for
each child. The BMI is calculated as weight (in kg) divided by the
square of the height (in meters).
\[bmi_i = \frac{weight_i} {height_i^2}\]
Store the results of this calculation in a variable called
bmi. Note: you don’t need to do this calculation for each
child individually, you can use both vectors in the BMI equation – this
is called vectorisation (see Section 2.4.4
of the Introduction to R book).
9. Now let’s practice a very useful skill - creating sequences
(honestly it is…). Take a look at Section
2.3 in the R book (the bit on creating sequences) to see the myriad
ways you can create sequences in R. Let’s use the seq()
function to create a sequence of numbers ranging from 0 to 1 in steps of
0.1 (this is also a vector by the way) and assign this sequence to a
variable called seq1.
10. Next, see if you can figure out how to create a sequence from 10
to 1 in steps of 0.5. Assign this sequence to a variable called
seq2. Hint: you may find it useful to include the
rev() function in your code (use the search facility in the
Introduction to R book to search for 'rev').
11. Let’s go sequence crazy! Generate the following sequences. You
will need to experiment with the arguments of the rep()
function to generate these sequences (see Section
2.3 for some clues):
rep(1:3, times = 3)
rep(c("a", "c", "e", "g"), each = 3)
rep(c("a", "c", "e", "g"), times = 3)
rep(1:3, each = 3, times = 2)
rep(1:5, times = 5:1)
rep(c(7, 2, 8, 1), times = c(4, 3, 1, 5))
12. OK, back to the variable height you created in Q7.
Sort the values of height into ascending order (shortest to
tallest) and assign the sorted vector to a new variable called
height_sorted. Take a look at Section 2.4.3 in the
R book to see how to do this. Now sort all heights into descending order
and assign the new vector a name of your choice.
13. Let’s give the children some names. Create a new vector called
child_names with the following names of the 10 children:
"Alfred", "Barbara", "James", "Jane", "John", "Judy", "Louise", "Mary", "Ronald", "William".
child_names <- c("Alfred", "Barbara", "James", "Jane", "John", "Judy", "Louise", "Mary", "Ronald", "William")
14. A really useful (and common) task is to order the values of one
variable by the order of another variable. To do this you will need to
use the order() function in combination with the square
bracket notation [ ]. Have a peep at Section 2.4.3 for
some details. Create a new variable called names_sort to
store the names of the children ordered by child height (from shortest
to tallest). Who is the shortest? who is the tallest child? If you’re
not sure how to do this, please ask one of the instructors.
height_ord <- order(height) # get the indexes of the heights, smallest to tallest
names_sort <- child_names[height_ord] # Louise is shortest, Ronald is tallest
15. Now order the names of the children by
descending values of weight and assign the result to a
variable called weight_rev (Hint: perhaps include the
rev() function?). Who is the heaviest? Who is the
lightest?
weight_ord <- rev(order(weight))
weight_rev <- child_names[weight_ord] # Alfred is heaviest, Louise is lightest
16. Almost there! In R, missing values are usually represented with
an NA. Missing data can be tricky to deal with in R (and in
statistics more generally) and cause some surprising behaviour when
using some functions. Take a look at Section 2.4.5 of the
R book for more information about missing values. To explore this a
little further let’s create a vector called mydata with the
values 2, 4, 1, 6, 8, 5, NA, 4, 7. Notice the value of the
7th element of mydata is missing and represented
with an NA. Now use the mean() function to
calculate the mean of the values in mydata. What does R
return? If you’re confused by this output take a look at the help page
for the function mean(). Can you figure out how to alter
your use of the mean() function to calculate the mean
ignoring this missing value?
mydata <- c(2, 4, 1, 6, 8, 5, NA, 4, 7)
mean(mydata) # returns NA!
mean(mydata, na.rm = TRUE) # returns 4.625
17. Finally, list all variables in your workspace that you have
created in this exercise. Remove the variable seq1 from the
workspace using the rm() function.
ls() # list all variables in workspace
rm(seq1) # remove variable seq1 from the workspace
ls() # check seq1 has been removed
End of Exercise 2