Module 9 Assignment

Question 1: Simple Table

assignment_data <- data.frame(
  Country = c("France", "Spain", "Germany", "Spain", "Germany",
              "France", "Spain", "France", "Germany", "France"),
  age = c(44, 27, 30, 38, 40, 35, 52, 48, 45, 37),
  salary = c(6000, 5000, 7000, 4000, 8000,
             5500, 4500, 6000, 7500, 5000),
  Purchased = c("No", "Yes", "No", "No", "Yes",
                "Yes", "No", "Yes", "No", "Yes")
)
knitr::kable(assignment_data)

Country	age	salary	Purchased
France	44	6000	No
Spain	27	5000	Yes
Germany	30	7000	No
Spain	38	4000	No
Germany	40	8000	Yes
France	35	5500	Yes
Spain	52	4500	No
France	48	6000	Yes
Germany	45	7500	No
France	37	5000	Yes

The table contains 10 observations and four columns: Country, age, salary, and Purchased.

Question 2: Contingency Table

data(mtcars)
assignment9 <- table(mtcars$gear, mtcars$cyl,
                     dnn = c("gears", "cylinders"))
assignment9

##      cylinders
## gears  4  6  8
##     3  1  2 12
##     4  8  4  0
##     5  2  1  2

The table shows the number of cars for each combination of gears and cylinders. For example, 12 cars have 3 gears and 8 cylinders.

Question 2.1: Row and Column Totals

addmargins(assignment9)

##      cylinders
## gears  4  6  8 Sum
##   3    1  2 12  15
##   4    8  4  0  12
##   5    2  1  2   5
##   Sum 11  7 14  32

There are 32 cars in total. The row totals show that 15 cars have 3 gears, 12 have 4 gears, and 5 have 5 gears. The column totals show that 11 cars have 4 cylinders, 7 have 6 cylinders, and 14 have 8 cylinders.

Question 2.2: Overall Proportions

prop.table(assignment9)

##      cylinders
## gears       4       6       8
##     3 0.03125 0.06250 0.37500
##     4 0.25000 0.12500 0.00000
##     5 0.06250 0.03125 0.06250

Each cell is divided by the total of 32 cars. These proportions sum to 1 across the entire table. For example, cars with 3 gears and 8 cylinders account for 12/32 = 0.375, or 37.5% of all cars.

Question 2.3: Row Proportions

prop.table(assignment9, margin = 1)

##      cylinders
## gears          4          6          8
##     3 0.06666667 0.13333333 0.80000000
##     4 0.66666667 0.33333333 0.00000000
##     5 0.40000000 0.20000000 0.40000000

Each cell is divided by its row total, so each row sums to 1.

Among cars with 3 gears, approximately 6.67% have 4 cylinders, 13.33% have 6 cylinders, and 80% have 8 cylinders.

Among cars with 4 gears, approximately 66.67% have 4 cylinders, 33.33% have 6 cylinders, and 0% have 8 cylinders.

Among cars with 5 gears, 40% have 4 cylinders, 0% have 6 cylinders, and 60% have 8 cylinders.