Upload a PDF file, named with your UC Davis email ID and homework
number (e.g., xjw18_hw1.pdf), to Gradescope (accessible
through Canvas). You will give the commands to answer each question in
its own code block, which will also produce output that will be
automatically embedded in the output file. When asked, answer must be
supported by written statements as well as any code used.
All code used to produce your results must be shown in your PDF
file (e.g., do not use echo = FALSE or
include = FALSE as options anywhere). Rmd
files do not need to be submitted, but may be requested by the TA and
must be available when the assignment is submitted.
Students may choose to collaborate with each other on the homework, but must clearly indicate with whom they collaborated. Every student must upload their own submission.
Start to work on it as early as possible
When you want to show your result as a vector that is too long,
slice the first 10 objects. When you want to show your result as a data
frame, use head() on it. Failure to do so may lead to point
deduction.
Directly knit the Rmd file will give you an html file. Open that file in your browser and then you can print it into a PDF file.
1. What is the sum of the first 100 positive integers? The formula for the sum of integers \(1\) through \(n\) is \(n(n+1)/2\). Define \(n=100\) and then use R to compute the sum of \(1\) through \(100\) using the formula.
2. Now use the same formula to compute the sum of the integers from 1 through 1,000.
3. Look at the result of typing the following code into R:
n <- 1000
x <- seq(1, n)
sum(x)Based on the result, what do you think the functions seq
and sum do? You can use help.
sum creates a list of numbers and seq
adds them up.
seq creates a list of numbers and sum
adds them up.
seq creates a random list and sum
computes the sum of 1 through 1,000.
sum always returns the same number.
Solution: Type your solution here
4. Which of the following will always return the numeric value stored
in x? You can try out examples and use the help system if
you want.
log(10^x)log10(x^10)log(exp(x))exp(log(x, base = 2))5.Another way to create vectors is with the rep()
function. The rep() function creates a vector by
replicating a value or vector of values. Write comments inside those
code chunks to explain what happens by running these code.
The first argument of rep() is the thing to replicate.
The argument times is the number of times to replicate. The
argument each means each element of input is repeated each
times.
rep(10, times = 5)[1] 10 10 10 10 10#
rep(c("apple","banana","cream"), times = 3)[1] "apple" "banana" "cream" "apple" "banana" "cream" "apple" "banana"
[9] "cream" #
rep(c("apple","banana","cream"), each = 3)[1] "apple" "apple" "apple" "banana" "banana" "banana" "cream" "cream"
[9] "cream" #
rep(c(1,2,3),times = c(1,2,3))[1] 1 2 2 3 3 3#1. Use the function c to create a vector with the
average high temperatures in January for Beijing, Lagos, Paris, Rio de
Janeiro, San Juan, and Toronto, which are 35, 88, 42, 84, 81, and 30
degrees Fahrenheit. Call the object temp.
2. Now create a vector with the city names and call the object
city.
3. Use the names function and the objects defined in the
previous exercises to associate the temperature data with its
corresponding city. (Hint: names(vector) = name)
4. Use the [ and : operators to access the
temperature of the first three cities on the vector
5. Use the [ operator to access the temperature of Paris
and San Juan. (Hint: subset by name)
6. Use the : operator to create a sequence of numbers
\(12,13,14,\dots,73\).
7. Create a vector containing all the positive odd numbers smaller than 100.
8. Create a vector of numbers that starts at 6, does not pass 55, and
adds numbers in increments of 4/7: 6, 6 + 4/7, 6 + 8/7, and so on. How
many numbers does the list have? Hint: use seq and
length.
1. Load the US murders dataset.
# If you have not install the package, use the commented command to install it.
#install.packages(dslabs)
library(dslabs)
data(murders)Use the function str to examine the structure of the
murders object. Which of the following best describes the
variables represented in this data frame?
str shows no relevant information.Solution: Type your solution here
2. What are the column names used by the data frame for these five variables?
3. Use the accessor $ to extract the state abbreviations
and assign them to the object a. What is the class of this
object?
4. Now use the square brackets to extract the state abbreviations and
assign them to the object b. (Hint:
dataset["Column name"])
Use the identical(a, b) function to determine if
a and b are the same.
5. We saw that the region column stores a factor. You
can corroborate this by typing:
class(murders$region)With one line of code, use the function levels and
length to determine the number of regions defined by this
dataset.
6. The function table takes a vector and returns the
frequency of each element. You can quickly see how many states are in
each region by applying this function. Use this function in one line of
code to create a table of states per region.
1. Previously we created this data frame:
temp <- c(35, 88, 42, 84, 81, 30)
city <- c("Beijing", "Lagos", "Paris", "Rio de Janeiro",
"San Juan", "Toronto")
city_temps <- data.frame(name = city, temperature = temp)Remake the data frame using the code above, but add a line that converts the temperature from Fahrenheit to Celsius. The conversion formula is \(C = \frac{5}{9} \times (F - 32)\).
2. What is the following sum to \(n = 100\) terms of the series? Calculate using vector arithmetics. \[\frac{2n-1}{n(n+1)(n+2)}\]
Hint: The theoretical result should be:
\[\sum_{k=1}^n \frac{2k-1}{k(k+1)(k+2)} = \frac{1}{4}(3-\frac{10}{n+2}+\frac{2}{n+1})\]
Start by loading the library and data.
library(dslabs)
data(murders)
# This will give you the column names of the murders.
colnames(murders)[1] "state" "abb" "region" "population" "total" The total murder for each state is murders$total, and
the total population for each state is murders$population.
per 100,000 murder rate is defined as
total/population * 100000.
1. Compute the per 100,000 murder rate for each state and store it in
an object called murder_rate. Then use logical operators to
create a logical vector named low that tells us which
entries of murder_rate are lower than 1.
2. Now use the results from the previous exercise and the function
which to determine the indices of murder_rate
associated with values lower than 1.
3. Use the results from the previous exercise to report the names of the states with murder rates lower than 1. (Hint: subset based on the index in 2)
4. Now extend the code from exercises 2 and 3 to report the states in
the Northeast with murder rates lower than 1. Hint: 1. use the
previously defined logical vector low and the logical
operator &. 2. Define a new logical vector to determine
the indices of murder_rate that region is
exactly "Northeast" using == operator.
5. In a previous exercise we computed the murder rate for each state and the average of these numbers. How many states are below the average?
6. Use the %in% operator to create a logical vector that
answers the question: which of the following are actual abbreviations:
MA, ME, MI, MO, MU?
7. Extend the code you used in exercise 6 to report the one entry
that is not an actual abbreviation. Hint: use the
! operator, which turns FALSE into
TRUE and vice versa.
1. Create an empty list with 4 elements. Fill in the first element with the numbers 1 through 10, the second element with the letters “a” through “j”, the third element with a data frame with two columns and two rows, and the fourth element with a list containing a numeric vector and a character vector.
2. Here is an example of paste() function in R:
paste("I love", "Data science", sep = " ")[1] "I love Data science"Where the first 2 arguments are strings (If one argument is not
string, it will be first converted into string automatically), the
sep = " " indicates we concatenate the two strings using a
space.
Now create vector: names with student names “Andy”,
“Bob”, “Catherine”, vector: scores with score 80, 90, 85.
Use paste() function to output: “Andy STA32 score is 80”,
“Bob STA32 score is 90”, “Catherine STA32 score is 85”.
(Hint: What should the sep=? be?)
For these exercises we will use the US murders dataset. Make sure you load it prior to starting.
library(dslabs)
data("murders")For this problem you may need to use ?sort,
?order, ?ranks or Google the usage of these
functions. They are not covered in lecture note. But it’s common to use
new functions, so start learning how to know using new functions by your
own is crucial.
1. Use the $ operator to access the population size data
and store it as the object pop. Then use the
sort function to redefine pop so that it is
sorted. Finally, use the [ operator to report the smallest
population size.
2. Now instead of the smallest population size, find the index of the
entry with the smallest population size. Hint: use order
instead of sort.
3. We can actually perform the same operation as in the previous
exercise using the function which.min. Write one line of
code that does this.
4. Now we know how small the smallest state is and we know which row
represents it. Which state is it? Define a variable states
to be the state names from the murders data frame. Report
the name of the state with the smallest population.
5. You can create a data frame using the data.frame
function. Here is a quick example:
temp <- c(35, 88, 42, 84, 81, 30)
city <- c("Beijing", "Lagos", "Paris", "Rio de Janeiro",
"San Juan", "Toronto")
city_temps <- data.frame(name = city, temperature = temp)Use the rank function to determine the population rank
of each state from smallest population size to biggest. Save these ranks
in an object called ranks, then create a data frame with
the state name and its rank. Call the data frame my_df.
6. The na_example vector represents a series of counts.
You can quickly examine the object using:
data("na_example")
str(na_example) int [1:1000] 2 1 3 2 1 3 1 4 3 2 ...However, when we compute the average with the function
mean, we obtain an NA:
mean(na_example)[1] NAThe is.na function returns a logical vector that tells
us which entries are NA. Assign this logical vector to an
object called ind and determine how many NAs
does na_example have. (Hint: use sum on the
logical object)
7. Now compute the average again, but only for the entries that are
not NA. Hint: the ! operator, try
!(c(TRUE, FALSE, TRUE)).
Names:
sessionInfo()R version 4.2.3 (2023-03-15 ucrt)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 22621)
Matrix products: default
locale:
[1] LC_COLLATE=English_United States.utf8
[2] LC_CTYPE=English_United States.utf8
[3] LC_MONETARY=English_United States.utf8
[4] LC_NUMERIC=C
[5] LC_TIME=English_United States.utf8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] dslabs_0.7.4
loaded via a namespace (and not attached):
[1] digest_0.6.31 R6_2.5.1 jsonlite_1.8.4 evaluate_0.20
[5] cachem_1.0.7 rlang_1.1.0 cli_3.6.0 rstudioapi_0.14
[9] jquerylib_0.1.4 bslib_0.4.2 rmarkdown_2.20 tools_4.2.3
[13] xfun_0.37 yaml_2.3.7 fastmap_1.1.1 compiler_4.2.3
[17] htmltools_0.5.4 knitr_1.42 sass_0.4.5