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<h1 class="title toc-ignore">Exercises</h1>
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<p> </p>
<div id="exercise-2-basic-r-operations" class="section level2">
<h2>Exercise 2 : Basic R operations</h2>
<p> </p>
<p>Read <a href="https://intro2r.com/basics_r.html">Chapter 2</a> to
help you complete the questions in this exercise.</p>
<p> </p>
<p>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 <code>#</code> at the beginning of the line.</p>
<p> </p>
<p>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 <a
href="https://intro2r.com/getting-started.html#getting-started">Section
2.1</a> 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.</p>
<p> </p>
<p>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
<code>area_circle</code>. If you can’t remember how to create and assign
objects see <a
href="https://intro2r.com/objects-in-r.html#objects-in-r">Section
2.2</a> or watch this <a
href="https://alexd106.github.io/PGR-R/howto.html#objs-vid">video</a>.
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
<code>pi</code>. Don’t worry if you’re stumped and feel free to ask one
of the instructors for guidance.</p>
<p> </p>
<p>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 <a href="https://en.wikipedia.org/wiki/Order_of_operations">this
page</a> 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.</p>
<p> </p>
<p>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 <a
href="https://intro2r.com/data-structures.html#scal_vecs">Section
3.2.1</a> 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
<code>c()</code> to create a vector called <code>weight</code>
containing the weight (in kg) of 10 children:
<code>69, 62, 57, 59, 59, 64, 56, 66, 67, 66</code> (<a
href="https://intro2r.com/using-functions-in-r.html#using-functions-in-r">Section
2.3</a> or watch this <a
href="https://alexd106.github.io/PGR-R/howto.html#vec-vid">video</a> for
more information).</p>
<p> </p>
<p>6. Now you can do some useful stuff to your <code>weight</code>
vector. Get R to calculate the mean, variance, standard deviation, range
of weights and the number of children of your <code>weight</code> vector
(see <a href="https://intro2r.com/using-functions-in-r.html">Section
2.3</a> for more details). Now read <a
href="https://intro2r.com/vectors.html">Section 2.4</a> 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 <a
href="https://intro2r.com/vectors.html#positional-index">Positional
indexes</a> and store these weights in a new variable called
<code>first_five</code>. Remember, you will need to use the square
brackets <code>[ ]</code> to extract (aka index, subset) elements from a
variable.</p>
<p> </p>
<p>7. We’re now going to use the the <code>c()</code> function again to
create another vector called <code>height</code> containing the height
(in cm) of the same 10 children:
<code>112, 102, 83, 84, 99, 90, 77, 112, 133, 112</code>. Use the
<code>summary()</code> function to summarise these data in the
<code>height</code> object. Extract the height of the 2nd, 3rd, 9th and
10th child and assign these heights to a variable called
<code>some_child</code> (take a look at the section <a
href="https://intro2r.com/vectors.html#positional-index">Positional
indexes</a> in the R book if you’re stuck). We can also extract elements
using <a href="https://intro2r.com/vectors.html#logical-index">Logical
indexes</a>. Let’s extract all the heights of children less than or
equal to 99 cm and assign to a variable called
<code>shorter_child</code>.</p>
<p> </p>
<p>8. Now you can use the information in your <code>weight</code> and
<code>height</code> 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 (<strong>in meters</strong>).</p>
<p><span class="math display">\[bmi_i = \frac{weight_i}
{height_i^2}\]</span></p>
<p>Store the results of this calculation in a variable called
<code>bmi</code>. 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 <a
href="https://intro2r.com/vectors.html#vectorisation">Section 2.4.4</a>
of the Introduction to R book).</p>
<p> </p>
<p>9. Now let’s practice a very useful skill - creating sequences
(honestly it is…). Take a look at <a
href="https://intro2r.com/using-functions-in-r.html#using-functions-in-r">Section
2.3</a> in the R book (the bit on creating sequences) to see the myriad
ways you can create sequences in R. Let’s use the <code>seq()</code>
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 <code>seq1</code>.</p>
<p> </p>
<p>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
<code>seq2</code>. Hint: you may find it useful to include the
<code>rev()</code> function in your code (use the search facility in the
Introduction to R book to search for <code>'rev'</code>).</p>
<p> </p>
<p>11. Let’s go sequence crazy! Generate the following sequences. You
will need to experiment with the arguments of the <code>rep()</code>
function to generate these sequences (see <a
href="https://intro2r.com/using-functions-in-r.html#using-functions-in-r">Section
2.3</a> for some clues):</p>
<ul>
<li>1 2 3 1 2 3 1 2 3</li>
<li>a a a c c c e e e g g g</li>
<li>a c e g a c e g a c e g</li>
<li>1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3</li>
<li>1 1 1 1 1 2 2 2 2 3 3 3 4 4 5</li>
<li>7 7 7 7 2 2 2 8 1 1 1 1 1</li>
</ul>
<p> </p>
<p>12. OK, back to the variable <code>height</code> you created in Q7.
Sort the values of <code>height</code> into ascending order (shortest to
tallest) and assign the sorted vector to a new variable called
<code>height_sorted</code>. Take a look at <a
href="https://intro2r.com/vectors.html#vec_ord">Section 2.4.3</a> 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.</p>
<p> </p>
<p>13. Let’s give the children some names. Create a new vector called
<code>child_names</code> with the following names of the 10 children:
<code>"Alfred", "Barbara", "James", "Jane", "John", "Judy", "Louise", "Mary", "Ronald", "William"</code>.</p>
<p> </p>
<p>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 <code>order()</code> function in combination with the square
bracket notation <code>[ ]</code>. Have a peep at <a
href="https://intro2r.com/vectors.html#vec_ord">Section 2.4.3</a> for
some details. Create a new variable called <code>names_sort</code> 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.</p>
<p> </p>
<p>15. Now order the names of the children by
<strong>descending</strong> values of weight and assign the result to a
variable called <code>weight_rev</code> (Hint: perhaps include the
<code>rev()</code> function?). Who is the heaviest? Who is the
lightest?</p>
<p> </p>
<p>16. Almost there! In R, missing values are usually represented with
an <code>NA</code>. 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 <a
href="https://intro2r.com/vectors.html#na_vals">Section 2.4.5</a> of the
R book for more information about missing values. To explore this a
little further let’s create a vector called <code>mydata</code> with the
values <code>2, 4, 1, 6, 8, 5, NA, 4, 7</code>. Notice the value of the
7<sup>th</sup> element of <code>mydata</code> is missing and represented
with an <code>NA</code>. Now use the <code>mean()</code> function to
calculate the mean of the values in <code>mydata</code>. What does R
return? If you’re confused by this output take a look at the help page
for the function <code>mean()</code>. Can you figure out how to alter
your use of the <code>mean()</code> function to calculate the mean
ignoring this missing value?</p>
<p> </p>
<p>17. Finally, list all variables in your workspace that you have
created in this exercise. Remove the variable <code>seq1</code> from the
workspace using the <code>rm()</code> function.</p>
<p> </p>
<p>End of Exercise 2</p>
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