12 Exercise Solutions by Module

12.1 Module 1

12.1.1 General exercises

Exercise: Which of the following will give a different output from the other 3? Hint: Look at the help file for the log() function.

  1. log(x=6, base=4)

  2. log(4, 6)

  3. log(base=4, x=6)

  4. log(6, 4)

Solution: ?log, 2. log(4,6)

Exercise: Create a vector that goes from 5 to 25 by increments of 1.

Solution: 5:25 (or some variation)

Exercise: Create another vector that goes from 5 to 25 by increments of 1, but using a different method. Call this vector V1.

Solution: V1 <- seq(5,25,by=1) (or some variation)

Exercise: Extract the 5th element of V1.

Solution: V1[5]

Exercise: Remove the 7th element from the vector V1 and call this new vector V2.

Solution: V2 <- V1[-7]

Exercise: How many elements in your vector, V1, are greater than 11?

Solution: sum(V1>11) = 14

Exercise: Create a matrix that contains the sequence of numbers from 1 to 16, going up in increments of 1. Let the matrix have 4 rows and have the matrix elements fill by row. Call this matrix M1.

Solution: M1 <- matrix(data=1:16, nrow=4, byrow=T)

Exercise: Extract the 3rd and 4th rows and the 1st and 2nd columns of your matrix, M1. Call this matrix M2.

Solution: M2 <- M1[c(3,4), c(1,2)]

Exercise: Find the row sums of the matrix M2.

Solution: apply(M2, 1, sum) (or rowSums(M2))

12.1.2 End of module exercises

Exercise 1: Use R to find the value of the square root of 25. (\(\sqrt(25)\)) Hint: Look at the help file for the function sqrt().

Solution 1: sqrt(25)

Exercise 2: Use R to find the value of the exponential of \(6\times 14 -3\). (\(\exp(6\times 14-3)\))

Solution 2: exp(6*4-3)

Exercise 3: Use R to find the value of the absolute value of \(7\times 3 - 4\times 9 - 30\). (\(|7 \times 3 - 4 \times 9 - 30|\))

Solution 3: abs(7*3-4*9-30)

Exercise 4: Use R to find the value of \(\frac{73-42}{3}+2\times\left(\frac{36}{4}-17\right)\). Give your answer to 2 decimal places.

Solution 4: (73-42)/3+(2*((36/4)-17))

Exercise 5: How many elements does the following vector have?

seq(from = 0, to = 100, by = 3.14)

Solution 5: length(seq(0,100,by=3.14))

Exercise 6: Look at the help file for the function rnorm() and use this function to generate 100 random numbers with mean 10 and standard deviation 5.

Solution 6: rnorm(n = 100, mean = 10, sd = 5)

12.2 Module 2

12.2.1 General exercises

Exercise: What are the defaults for the header argument in the functions read.table() and read.csv()?

  • header = T in read.table() and header = T in read.csv()

  • header = T in read.table() and header = F in read.csv()

  • header = F in read.table() and header = T in read.csv()

  • header = F in read.table() and header = F in read.csv()

Solution: header = F in read.table() and header = T in read.csv()

12.2.2 End of module exercises

Exercise 1: How many cares have a miles per gallon (mpg) of less than 15 in the mtcars data?

Solution 1:

library(datasets)

cars <- mtcars

sum(cars$mpg<15) = 5

Exercise 2: How many cars have exactly 4 cylinders (cyl) in the mtcars data?

Solution 2: sum(cars$cyl==8)=14

Exercise 3: What is the mean value of horsepower (hp) to 2 decimal places in the mtcars data?

Solution 3: round(mean(cars$hp), 2)=146.69

Exercise 4: What car has the lowest miles per gallon (mpg) value for cars with 8 cylinders (cyl) in the mtcars data?

Solution 4: cars[which.min(cars$mpg),]=Cadillac Fleetwood

Exercise 5: What is the median miles per gallon (mpg) value for cars with 8 cylinders (cyl) in the mtcars data?

Solution 5: median(cars$mpg[cars$cyl==8])= 15.2

Exercise 6: What car has the highest weight (wt) for each amount of cylinders (cyl) in the mtcars data?

Solution 6:

unique(cars$cyl

cars[which.max(cars$wt[cars$cyl==4]),]=Mazda RX4 Wag

cars[which.max(cars$wt[cars$cyl==6]),]=Hornet 4 Drive

cars[which.max(cars$wt[cars$cyl==8]),]=Duster 360

Exercise 7: Create a bar plot that shows the number of cars with each gear type (gear) in the mtcars data.

Solution 7:

gear_types <- table(cars$gear)

barplot(gear_types, names.arg=c("Type 3", "Type 4", "Type 5"),

xlab = "Gear types", ylab = "Total count",

main = "Distribution of gear types")

Exercise 8: Create a bar plot that shows the number of cars with each gear type (gear) with the distribution of cylinders (cyl) for each type in the mtcars data. Add a legend for the cylinders.

Solution 8:

cyl_gear_types <- table(cars$cyl, cars$gear)

colours <- c("#004C92", "#FF0000", "#FFC600")

barplot(cyl_gear_types, names.arg=c("Type 3", "Type 4", "Type 5"),

xlab = "Gear types", ylab = "Total count",

main = "Distribution of gear types vs cylinders",

col = colours)

legend("topright", rownames(cyl_gear_types), cex = 1.3, fill = colours)

Exercise 9: Create a scatter plot to show the relationship between weight (wt) and miles per gallon (mpg) in the mtcars data.

Solution 9:

plot(x = cars$wt,y = cars$mpg,

xlab = "Weight",

ylab = "Miles per gallon",

xlim = c(1,6),

ylim = c(10,35),

main = "Weight vs miles per gallon")

ggplot(cars, aes(x = wt, y = mpg)) +

geom_point(col="#004C92")+

labs(x="Weight", y="Miles per gallon")+

ggtitle("Weight vs miles per gallon")

Exercise 10: Create a scatter plot to show the relationship between weight (wt) and miles per gallon (mpg) by cylinder (cyl) in the mtcars data.

Solution 10:

plot(cars$wt, cars$mpg, col = cars$cyl,

xlab="Weight", ylab="Miles per gallon",

main="Weight vs miles per gallon by cylinder")

lapply(cars$cyl, function(x) {

abline(lm(mpg ~ wt, cars, subset = (cyl == x)), col = x)})

legend("topright", rownames(cyl_gear_types),

col = c(4,6,8), pch = 1, bty = "n")

ggplot(cars, aes(x = wt, y = mpg, group=cyl, col=cyl)) +

geom_point() +

geom_smooth(method="lm", se=FALSE)+

labs(x="Weight", y="Miles per gallon")+

ggtitle("Weigth vs miles per gallon by cylinder")

12.3 Module 3

12.3.1 General exercises

Exercise: How can you add multiple layers, such as polygons for states and points for health facilities, to a single map using tmap?

  1. By using tm_shape() and tm_fill()

  2. By using tm_shape() and tm_dots()

  3. By using multiple tm_shape() functions with different elements

  4. By using tm_shape() and tm_lines()

Solution: 3. By using multiple tm_shape() functions with different elements

12.3.2 End of module exercises

Exercise 1: What is the primary purpose of the .prj file in a shapefile set, and which package is commonly used to handle this file type in R?

  1. Stores map projection information, handled by raster package.

  2. Stores attribute information, handled by sp package

  3. Stores projection information, handled by sf package

  4. Stores metadata information, handled by terra package

Solution 1: 3. Stores projection information, handled by sf package

Exercise 2: Create a map of Nigeria that combines the raster layer for building count and the vector layer for region.

Solution 2:

library(terra)     
library(sf)       
library(tmap)     

#load data
building_raster <- rast(nga_building_count.tif) #raster data
regions_vector <- st_read(nga_regions.shp) #vector data

#both are in same CRS
if (st_crs(regions_vector)$epsg != crs(building_raster, describe=TRUE)$code) {
 regions_vector <- st_transform(regions_vector, crs(building_raster))
}
 
#plot tmap
tmap_mode("plot")
tm_shape(building_raster) +
 tm_raster(style = "quantile", palette = "YlOrRd", title = "Building Count") +
tm_shape(regions_vector) +
 tm_borders(lwd = 1, col = "black")

Exercise 3: Create a choropleth map that shows the variation in population density for Nigeria at region level. Export the results as a .png file.

Solution 3:

library(sf)         
library(tmap)       
library(dplyr)     
 
#load data
nigeria_regions <- st_read(nga_regions.shp)
 
#calculate population density
nigeria_regions <- nigeria_regions %>%
 mutate(pop_density = nga_pop / nga_area)
 
#create choropleth map
tmap_mode("plot")
choropleth_map <- tm_shape(nigeria_regions) +
tm_polygons("pop_density",
             style = "quantile",     
             palette = "Blues") +
 tm_layout(title = "Nigeria: Population Density by Region")
 
#save as PNG
tmap_save(choropleth_map, filename = "nigeria_population_density.png", 
          width = 2000, height = 1500, dpi = 300)

Exercise 4: How do you plot a raster dataset using tmap, ensuring it can handle large datasets efficiently?

  1. tm_shape(raster_data) + tm_fill()
  2. tm_shape(raster_data) + tm_raster()
  3. tm_shape(raster_data) + tm_polygons()
  4. tm_shape(raster_data) + tm_dots()

Solution 4: 2. tm_shape(raster_data) + tm_raster()

12.4 Module 4

12.4.1 General exercises

Exercise: Identify the dependent and independent variables in the following sentence:

‘A researcher investigates the effects of school density on the grades of its pupils.’

Solution: Dependent variable: the grades of the pupils, independent variable: school density

Exercise: Fit a Poisson GLM using the ccancer dataset exploring the relationship between the count of cancer deaths and the covariates for the cancer site and region in Canada. Is the relationship between the dependent and independent variables significant?

Solution: ccancer_glm_exercise <- glm(Count ~ Site + Region, family = "poisson", data = ccancer)

summary(ccancer_glm_exercise)

Yes, the relationships are significant.

Exercise: What is the expected birth weight for a baby boy at a gestational age of 39.5 weeks?

Solution: \[Weight = -1447.24 -163.04\times 0+120.89\times 39.5 = 3327.92g\]

12.5 Module 5

12.5.1 General exercises

Exercise: Following on from the example above, what is the probability that an individual that is vaccincated but has a high fever is infected with disease A?

Solution: 0.19

Exercise: Following on from the example above, what is the conditional probability of drawing a purple button given that the button drawn is not blue?

Solution:

\[ \begin{aligned} P(A|B)&=\frac{P(A\cap B)}{P(B)}\\ &= \frac{\text{number of pruple buttons}/\text{total number of buttons}}{\text{blue}/\text{total number of buttons}}\\ &=\frac{4/10}{6/10}\\ &=\frac{2}{3}=0.67. \end{aligned} \]

Exercise: Following on from the example above, what would the probability be of selecting 2 men from the island without replacement?

Solution: \[ \begin{aligned} P(M_1 \cap M_2)&=P(M_1)P(M_2|M_1)\\ &= \frac{\text{number of men}}{\text{total number of people}}\times\frac{\text{number of men left}}{\text{total number of people left}}\\ &=\frac{4}{10}\times\frac{3}{9}\\ &=\frac{2}{15}. \end{aligned} \] ## Module 6

12.5.2 General exercises

Exercise: Following on from the example above, what is the probability that someone who is vaccinated is from region C?

Solution: \[P(A|Vaccinated) = \frac{P(C)P(Vaccinated|C)}{P(Vaccinated)} = \frac{0.3 \times 0.74}{0.728} = 0.305\]

Exercise: Create a histogram of posterior values for hospital D.

Solution:

#histogram of posterior values for hospital D
ggplot(data = predicted_values_df , aes(x = D)) +
  geom_histogram(bins = 20, color = "#00b4d8", alpha = 1, fill = "#1d3557") +
  theme_bw() +
  labs(title = "Posterior Predicted values for D",
       x = "Posteriors",
       y = "Frequency")

Exercise: Create a density plot of the posterior values for hospital G.

Solution:

#density plot of posterior values for hospital G
ggplot(data = predicted_values_df , aes(x = G)) +
  geom_density(alpha = 1, fill = "#1d3557") +
  theme_bw() +
  labs(title = "Posterior predicted Values for G",
       x = "Posteriors",
       y = "Density")