Problem 1
cases1 <- cases %>%
pivot_longer(!Date, names_to = "Employee_student", values_to = "count")
cases1
## # A tibble: 72 × 3
## Date Employee_student count
## <dttm> <chr> <dbl>
## 1 2022-09-04 00:00:00 Employee_Cases 9
## 2 2022-09-04 00:00:00 Student_Cases 24
## 3 2022-08-28 00:00:00 Employee_Cases 21
## 4 2022-08-28 00:00:00 Student_Cases 49
## 5 2022-08-21 00:00:00 Employee_Cases 4
## 6 2022-08-21 00:00:00 Student_Cases 88
## 7 2022-08-14 00:00:00 Employee_Cases 10
## 8 2022-08-14 00:00:00 Student_Cases 22
## 9 2022-08-07 00:00:00 Employee_Cases 5
## 10 2022-08-07 00:00:00 Student_Cases 0
## # … with 62 more rows
## # ℹ Use `print(n = ...)` to see more rows
ggplot(data = cases1, mapping = aes(x = Date, y = count, color = Employee_student)) +
geom_line()
Problem 2
# making a STL model
table1 <- cases %>%
mutate(Date = yearweek(Date)) %>%
as_tsibble(index = Date, key = c(Employee_Cases, Student_Cases)) %>%
summarise(Total_Cases = Employee_Cases + Student_Cases)
table1
## # A tsibble: 36 x 2 [1W]
## Date Total_Cases
## <week> <dbl>
## 1 2021 W52 1
## 2 2022 W01 65
## 3 2022 W02 81
## 4 2022 W03 98
## 5 2022 W04 61
## 6 2022 W05 25
## 7 2022 W06 8
## 8 2022 W07 6
## 9 2022 W08 2
## 10 2022 W09 2
## # … with 26 more rows
## # ℹ Use `print(n = ...)` to see more rows
maple <- table1 %>%
model(stl = STL(Total_Cases))
maple
## # A mable: 1 x 1
## stl
## <model>
## 1 <STL>
dcmp <- components(maple)
dcmp
## # A dable: 36 x 6 [1W]
## # Key: .model [1]
## # : Total_Cases = trend + remainder
## .model Date Total_Cases trend remainder season_adjust
## <chr> <week> <dbl> <dbl> <dbl> <dbl>
## 1 stl 2021 W52 1 62.2 -61.2 1
## 2 stl 2022 W01 65 59.0 5.98 65
## 3 stl 2022 W02 81 55.9 25.1 81
## 4 stl 2022 W03 98 51.0 47.0 98
## 5 stl 2022 W04 61 43.7 17.3 61
## 6 stl 2022 W05 25 34.5 -9.54 25
## 7 stl 2022 W06 8 24.4 -16.4 8
## 8 stl 2022 W07 6 15 -9.00 6
## 9 stl 2022 W08 2 7.44 -5.44 2
## 10 stl 2022 W09 2 3.77 -1.77 2
## # … with 26 more rows
## # ℹ Use `print(n = ...)` to see more rows
# Now plotting the model with trend as the component
table1 %>%
autoplot(Total_Cases) +
autolayer(dcmp, trend, color = '#D55E00') +
labs(y = "Toal Cases", "Weeks in 2022", title = "GCSU COVID Cases for 2022")
# Looking at each component individually
dcmp %>%
autoplot()
# Looking at seasonally adj component (Keep this graph in mind for the conclusion).
table1 %>%
autoplot(Total_Cases) +
autolayer(dcmp, season_adjust, color = '#D55E00') +
labs(y = "Toal Cases", "Weeks in 2022", title = "GCSU COVID Cases for 2022")
# ^^ We will discuss these observances later in number 3.
Problem 3
# ^^ As you can see, the red line (seasonality) fits perfectly onto the black line (actual total cases),
# indicating that the data has no seasonality at all. This is because we do not have enough time
# periods of the data to find an estimation of the seasonality. If we were to include maybe a couple of
# more years, a seasonal trend would be clear. Based on observing the little data that we have, I suspect that
# there would be an increase of COVID cases at the beginning of each semester, which makes sense since
# there is more exposure to everyone at GCSU when everyone comes back from their different locations.
# On the other hand, the trend shows a smoother version of the total cases, making it obvious when there is
# a gradual increase of cases at the beginning of each semester and then a gradual decline as the semester
# continues into the Summer break.
# The remainder seems to follow the actual total cases of the data, which is an issue. Being that it
# follows basically the same trend as the actual data, we do not have a great measure
# of any white noise the data may contain. This is most likely due to the fact that we do not have enough
# data to pull out an the seasonality it would contain, leaving more exposure to the white noise.
# In conclusion, we need more observations to fully analyze and comprehend the fluctuations of the data.
Problem 4
# Since there was a spike at the beginning of the semester, and it
# now seems to follow a decreasing trend like from the Spring
# semester, my prediction for the point forecast for the amount of COVID
# cases from 09/19 to 9/25 is 15 for students and 5 for Employees. My
# prediction on a 80% PI is from 0 to 35 since spikes are possible to happen;
# however, I am given the impression that cases will continue to
# decline.