The S&P 500 is a stock market index that tracks the stock market performance of the 500 biggest publicly-listed companies in the US. The file SP500.csv contains the value of this index for each day from 2015 until 2023.
With ggplot, if you want to plot a variable x over time t from the dataframe df, you can use the command: ggplot(df, aes(t, x)) + geom_line().
Use this approach to plot the closing price (variable close) over time.
Based on your plot, during which of the following periods did the index experience the largest crash?
We begin by reading in the data:
df <- read.csv("SP500.csv")
head(df) date open high low close adj_close volume
1 2023-11-08 4384.37 4391.20 4359.76 4382.78 4382.78 3729510000
2 2023-11-07 4366.21 4386.26 4355.41 4378.38 4378.38 3791230000
3 2023-11-06 4364.27 4372.21 4347.53 4365.98 4365.98 3656340000
4 2023-11-03 4334.23 4373.62 4334.23 4358.34 4358.34 4570960000
5 2023-11-02 4268.26 4319.72 4268.26 4317.78 4317.78 4669780000
6 2023-11-01 4201.27 4245.64 4197.74 4237.86 4237.86 4224900000The date appears to be in yyyy-mm-dd format. We can format it as follows:
df$date <- as.Date(df$date, format = "%Y-%m-%d")
summary(df$date) Min. 1st Qu. Median Mean 3rd Qu. Max.
"2015-01-02" "2017-03-21" "2019-06-07" "2019-06-06" "2021-08-23" "2023-11-08" We then make the line plot with ggplot:
library(ggplot2)
ggplot(df, aes(date, close)) + geom_line() +
xlab("") + ylab("S&P 500 Index") +
theme_minimal()
We can see that the largest crash happened at the start of 2020 when the corona outbreak happened. There was also a big crash at the start of 2022, but this was not one of the possible MCQ options.
Just so you can see it, it’s also possible to make a line plot with base R. We just use the plot() function with both variables and add the type = "l" option, where "l" stands for line:
plot(df$date, df$close, type = "l")
Using the S&P 500 data, create a variable in your dataset which is the percentage change in the closing price from one day to the next. Call this the daily return.
If x_t is the closing price on date t, then the percentage change in the closing price from the previous day is given by the following equation:
100\times \frac{x_t -x_{t-1}}{x_{t-1}}
Plot the daily returns over time using ggplot with the geom_line() function.
Which of the following is true in the plot?
To create this return variable, we first need to sort the data by date:
df <- df[order(df$date), ]
head(df) date open high low close adj_close volume
2229 2015-01-02 2058.90 2072.36 2046.04 2058.20 2058.20 2708700000
2228 2015-01-05 2054.44 2054.44 2017.34 2020.58 2020.58 3799120000
2227 2015-01-06 2022.15 2030.25 1992.44 2002.61 2002.61 4460110000
2226 2015-01-07 2005.55 2029.61 2005.55 2025.90 2025.90 3805480000
2225 2015-01-08 2030.61 2064.08 2030.61 2062.14 2062.14 3934010000
2224 2015-01-09 2063.45 2064.43 2038.33 2044.81 2044.81 3364140000We then need to create the lagged closing price variable, x_{t-1}:
df$lag_close <- c(NA, df$close[1:(nrow(df)-1)])
head(df[, c("date", "close", "lag_close")]) date close lag_close
2229 2015-01-02 2058.20 NA
2228 2015-01-05 2020.58 2058.20
2227 2015-01-06 2002.61 2020.58
2226 2015-01-07 2025.90 2002.61
2225 2015-01-08 2062.14 2025.90
2224 2015-01-09 2044.81 2062.14Because we don’t have an observation before the 2nd of January 2015 we need to use NA for that value. For all subsequent values we use the value from the previous period. We index the vector from 1 to nrow(df) - 1 because for the very last row with index nrow(df), we use the value with index nrow(df) - 1 for the lag.
We then use this variable to create the percentage return variable according to the formula:
df$return <- 100 * (df$close - df$lag_close) / df$lag_close
head(df[, c("date", "close", "lag_close", "return")]) date close lag_close return
2229 2015-01-02 2058.20 NA NA
2228 2015-01-05 2020.58 2058.20 -1.8278107
2227 2015-01-06 2002.61 2020.58 -0.8893486
2226 2015-01-07 2025.90 2002.61 1.1629823
2225 2015-01-08 2062.14 2025.90 1.7888346
2224 2015-01-09 2044.81 2062.14 -0.8403891The percentage return on January 5 20215 was -1.83%.
We then make a plot of the returns:
ggplot(df, aes(date, return)) + geom_line() +
xlab("") + ylab("S&P 500 Index Daily Return") +
theme_minimal()Warning: Removed 1 row containing missing values (`geom_line()`).
We can see that early 2020 had the largest swings in returns, where it had both the largest positive and negative daily returns.
Download the dataset toyota-camry-ads.csv. This contains information on classified advertisements placed on Craigslist for used Toyota Camry cars, one of the most common sedan cars in the US. The variables are:
condition: what kind of condition the car is in (good, like new, etc).odometer: how many miles the car has travelled in its lifetime (the car’s “mileage”).paint_color: the car’s color.price: the asking price of the car.year: the year the car was bought new.Create a histogram of the year variable. Based on this histogram, choose the answer below which contains a correct statement about the data.
We can read in and plot the data as follows:
df <- read.csv("toyota-camry-ads.csv")
ggplot(df, aes(year)) + geom_histogram()`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
We can see that most cars were bought after the year 2000. We can confirm this by checking the proportion of cars bought after 2000:
mean(df$year > 2000)[1] 0.8953975About 89.5% of the cars were bought after 2000, which is a clear majority.
The other options are wrong for the following reasons.
mean(df$year %in% 2007:2009)[1] 0.2538354mean(df$year > 2010)[1] 0.3514644mean(df$year <= 1990)[1] 0.00209205Create a bar plot of the condition variable. Based on this plot, what is the most common condition for Toyota Camry cars for sale on this site to be in?
Plotting tip: ggplot will by default order the “conditions” alphabetically. But sometimes it makes more sense for categorical variables like this to be ordered differently. We might want to order the bars from worst condition to best condition. We can do this by converting the condition variable to a factor variable and specifying the order we want:
ordered_levels <- c("salvage", "fair", "good", "excellent", "like new", "new")
df$condition <- factor(df$condition, levels = ordered_levels)Variables like this are called “ordinal”.
If we create a bar plot of the condition variable without ordering the levels, we get:
ggplot(df, aes(condition)) + geom_bar()
From this we can see that the most common condition for the cars to be in is “excellent”. But this is not a very satisfactory way of making the plot because there is a natural ordering to the condition types that isn’t alphabetical:
salvage < fair < good < excellent < like\;new < new We can use the plotting tip to re-order the levels and re-make the bar plot:
ordered_levels <- c("salvage", "fair", "good", "excellent", "like new", "new")
df$condition <- factor(df$condition, levels = ordered_levels)
ggplot(df, aes(condition)) + geom_bar()
Now the bars are in the right order. We still get the same answer to the question, however, that excellent is the most common condition for the cars to be in.
Create a scatter plot with:
odometer on the horizontal axis.price on the vertical axis.In addition, make the colors of the points represent the values of the year variable.
Choose the answer below which best interprets this scatter plot.
Hint: To make a scatter plot with x and y with colors representing z we do ggplot(df, aes(x, y, color = z)) + geom_point()
We create the plot as follows:
ggplot(df, aes(odometer, price, color = year)) +
geom_point()
We can make the following conclusions from this:
Therefore the option “Higher values of odometer are usually associated with lower prices. In addition, newer cars usually sell for a higher price” best matches what we observe.
We can customize the plot a bit the following way:
if (!require(viridis)) install.packages("viridis")Loading required package: viridisLoading required package: viridisLitelibrary(viridis)
ggplot(df, aes(odometer/1000, price/1000, color = year)) +
geom_point() +
xlab("Mileage (in 1,000s)") +
ylab("Asking Price (in $1,000)") +
scale_color_viridis(name = "Year", option = "C") +
theme_minimal()
The line if (!require(viridis)) install.packages("viridis") checks if the package viridis is installed, and if it isn’t, it installs it. The viridis package is used to change the colors of the points. Note: you won’t be asked to use this package in the exam, but I’m just showing you how to use this package here in case you want to make colorful plots after this course.
The reason I divided the variables by 1,000 is to make them easier to read. We then adjust the axis labels accordingly to make this clear.