Time series plot, Moving Average model, AR model, forecasting

Foster_Opoku · July 15, 2024, 7:01pm

I have this data set

Flu_data <- Filtered_data %>% filter(Surveillance.Network == "FluSurv-NET")

str(Flu_data)
'data.frame': 190 obs. of 12 variables:
Surveillance.Network: chr "FluSurv-NET" "FluSurv-NET" "FluSurv-NET" "FluSurv-NET" ... Season : chr "2018-19" "2018-19" "2018-19" "2018-19" ...
MMWR.Year : int 2018 2018 2018 2018 2018 2018 2018 2018 2018 2018 ... MMWR.Week : int 40 41 42 43 44 45 46 47 48 49 ...
Age.group : chr "Overall" "Overall" "Overall" "Overall" ... Sex : chr "Overall" "Overall" "Overall" "Overall" ...
Race.Ethnicity : chr "Overall" "Overall" "Overall" "Overall" ... Site : chr "Overall" "Overall" "Overall" "Overall" ...
Weekly.Rate : num 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.6 0.7 ... Cumulative.Rate : num 0.1 0.2 0.3 0.4 0.5 0.7 1 1.3 1.8 2.5 ...
Week.Ending.Date : chr "2018-10-06T00:00:00.000" "2018-10-13T00:00:00.000" "2018-10-20T00:00:00.000" "2018-10-27T00:00:00.000" ... Type : chr "Unadjusted Rate" "Unadjusted Rate" "Unadjusted Rate" "Unadjusted Rate" ...
unique(Flu_data$Season)
[1] "2018-19" "2019-20" "2020-21" "2021-22" "2022-23" "2023-24" that spans about six seasons. it is weekly report of flu starting from 2018-2019 season to 2023-2024 seasons.

First, write a code to have only these variables. Surveillance.Network: chr "FluSurv-NET" "FluSurv-NET" "FluSurv-NET" "FluSurv-NET" ... Season
MMWR.Year . MMWR.Week
$ Week.Ending.Date

my goal is to build moving Average model to forecast for the weekly rates for the the next 10 seasons. Can i have some ideas about how to go about it. first how to plot it a time series data from it. how to make a time series data and then build the model.

williaml · July 15, 2024, 10:37pm

What have you tried? Can you make your data reproducible?

Have a look at:

Forecasting: Principles and Practice (3rd ed) (otexts.com)

jrkrideau · July 16, 2024, 4:39pm

A handy way to supply some sample data is the dput() function. In the case of a large dataset something like dput(head(mydata, 100)) should supply the data we need. Just do dput(mydata) where mydata is your data. Copy the output and paste it here between
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Foster_Opoku · July 16, 2024, 7:02pm

here is the data. it's too large so it got trimmed

 dput(Flu_data)
structure(list(Surveillance.Network = c("FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", "FluSurv-NET", 
"FluSurv-NET", "FluSurv-NET", "FluSurv-NET"), Season = c("2018-19", 
"2018-19", "2018-19", "2018-19", "2018-19", "2018-19", "2018-19", 
"2018-19", "2018-19", "2018-19", "2018-19", "2018-19", "2018-19", 
"2018-19", "2018-19", "2018-19", "2018-19", "2018-19", "2018-19", 
"2018-19", "2018-19", "2018-19", "2018-19", "2018-19", "2018-19", 
"2018-19", "2018-19", "2018-19", "2018-19", "2018-19", "2018-19", 
"2019-20", "2019-20", "2019-20", "2019-20", "2019-20", "2019-20", 
"2019-20", "2019-20", "2019-20", "2019-20", "2019-20", "2019-20", 
"2019-20", "2019-20", "2019-20", "2019-20", "2019-20", "2019-20", 
"2019-20", "2019-20", "2019-20", "2019-20", "2019-20", "2019-20", 
"2019-20", "2019-20", "2019-20", "2019-20", "2019-20", "2019-20", 
"2019-20", "2020-21", "2020-21", "2020-21", "2020-21", "2020-21", 
"2020-21", "2020-21", "2020-21", "2020-21", "2020-21", "2020-21", 
"2020-21", "2020-21", "2020-21", "2020-21", "2020-21", "2020-21", 
"2020-21", "2020-21", "2020-21", "2020-21", "2020-21", "2020-21", 
"2020-21", "2020-21", "2020-21", "2020-21", "2020-21", "2020-21", 
"2020-21", "2020-21", "2021-22", "2021-22", "2021-22", "2021-22", 
"2021-22", "2021-22", "2021-22", "2021-22", "2021-22", "2021-22", 
"2021-22", "2021-22", "2021-22", "2021-22", "2021-22", "2021-22", 
"2021-22", "2021-22", "2021-22", "2021-22", "2021-22", "2021-22", 
"2021-22", "2021-22", "2021-22", "2021-22", "2021-22", "2021-22", 
"2021-22", "2021-22", "2021-22", "2021-22", "2021-22", "2021-22", 
"2021-22", "2021-22", "2022-23", "2022-23", "2022-23", "2022-23", 
"2022-23", "2022-23", "2022-23", "2022-23", "2022-23", "2022-23", 
"2022-23", "2022-23", "2022-23", "2022-23", "2022-23", "2022-23", 
"2022-23", "2022-23", "2022-23", "2022-23", "2022-23", "2022-23", 
"2022-23", "2022-23", "2022-23", "2022-23", "2022-23", "2022-23", 
"2022-23", "2022-23", "2022-23", "2023-24", "2023-24", "2023-24", 
"2023-24", "2023-24", "2023-24", "2023-24", "2023-24", "2023-24", 
"2023-24", "2023-24", "2023-24", "2023-24", "2023-24", "2023-24", 
"2023-24", "2023-24", "2023-24", "2023-24", "2023-24", "2023-24", 
"2023-24", "2023-24", "2023-24", "2023-24", "2023-24", "2023-24", 
"2023-24", "2023-24", "2023-24"), MMWR.Year = c(2018L, 2018L, 
2018L, 2018L, 2018L, 2018L, 2018L, 2018L, 2018L, 2018L, 2018L, 
2018L, 2018L, 2019L, 2019L, 2019L, 2019L, 2019L, 2019L, 2019L, 
2019L, 2019L, 2019L, 2019L, 2019L, 2019L, 2019L, 2019L, 2019L, 
2019L, 2019L, 2019L, 2019L, 2019L, 2019L, 2019L, 2019L, 2019L, 
2019L, 2019L, 2019L, 2019L, 2019L, 2019L, 2020L, 2020L, 2020L, 
2020L, 2020L, 2020L, 2020L, 2020L, 2020L, 2020L, 2020L, 2020L, 
2020L, 2020L, 2020L, 2020L, 2020L, 2020L, 2020L, 2020L, 2020L, 
2020L, 2020L, 2020L, 2020L, 2020L, 2020L, 2020L, 2020L, 2020L, 
2020L, 2020L, 2021L, 2021L, 2021L, 2021L, 2021L, 2021L, 2021L, 
2021L, 2021L, 2021L, 2021L, 2021L, 2021L, 2021L, 2021L, 2021L, 
2021L, 2021L, 2021L, 2021L, 2021L, 2021L, 2021L, 2021L, 2021L, 
2021L, 2021L, 2021L, 2021L, 2021L, 2022L, 2022L, 2022L, 2022L, 
2022L, 2022L, 2022L, 2022L, 2022L, 2022L, 2022L, 2022L, 2022L, 
2022L, 2022L, 2022L, 2022L, 2022L, 2022L, 2022L, 2022L, 2022L, 
2022L, 2022L, 2022L, 2022L, 2022L, 2022L, 2022L, 2022L, 2022L, 
2022L, 2022L, 2022L, 2022L, 2022L, 2023L, 2023L, 2023L, 2023L, 
2023L, 2023L, 2023L, 2023L, 2023L, 2023L, 2023L, 2023L, 2023L, 
2023L, 2023L, 2023L, 2023L, 2023L, 2023L, 2023L, 2023L, 2023L, 
2023L, 2023L, 2023L, 2023L, 2023L, 2023L, 2023L, 2023L, 2023L, 
2024L, 2024L, 2024L, 2024L, 2024L, 2024L, 2024L, 2024L, 2024L, 
2024L, 2024L, 2024L, 2024L, 2024L, 2024L, 2024L, 2024L), MMWR.Week = c(40L, 
41L, 42L, 43L, 44L, 45L, 46L, 47L, 48L, 49L, 50L, 51L, 52L, 1L, 
2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 
16L, 17L, 18L, 40L, 41L, 42L, 43L, 44L, 45L, 46L, 47L, 48L, 49L, 
50L, 51L, 52L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L, 
12L, 13L, 14L, 15L, 16L, 17L, 18L, 40L, 41L, 42L, 43L, 44L, 45L, 
46L, 47L, 48L, 49L, 50L, 51L, 52L, 53L, 1L, 2L, 3L, 4L, 5L, 6L, 
7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 40L, 41L, 
42L, 43L, 44L, 45L, 46L, 47L, 48L, 49L, 50L, 51L, 52L, 1L, 2L, 
3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 
17L, 18L, 19L, 20L, 21L, 22L, 23L, 40L, 41L, 42L, 43L, 44L, 45L, 
46L, 47L, 48L, 49L, 50L, 51L, 52L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 
8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 40L, 41L, 
42L, 43L, 44L, 45L, 46L, 47L, 48L, 49L, 50L, 51L, 52L, 1L, 2L, 
3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 
17L), Age.group = c("Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall"
), Sex = c("Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall"), Race.Ethnicity = c("Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall"), Site = c("Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall", "Overall", "Overall", "Overall", "Overall", 
"Overall", "Overall"), Weekly.Rate = c(0.1, 0.1, 0.1, 0.1, 0.2, 
0.2, 0.2, 0.3, 0.6, 0.7, 1.2, 1.9, 2.9, 3, 2.5, 2.1, 2.3, 3, 
3.5, 3.8, 4.6, 4.6, 5.2, 5.5, 4.8, 3.6, 2.7, 1.8, 1.1, 0.6, 0.2, 
0.1, 0.1, 0.2, 0.2, 0.2, 0.3, 0.4, 0.6, 0.9, 1.3, 1.7, 2.4, 4.5, 
5.3, 4.5, 4.2, 4.6, 5.3, 6, 5, 5, 4.4, 4, 2.8, 1.3, 0.3, 0.1, 
0.1, 0.1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.1, 0, 0, 0, 0.1, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0.1, 0.1, 0.2, 0.3, 0.4, 0.6, 0.7, 1, 0.6, 0.4, 0.3, 0.2, 
0.2, 0.2, 0.2, 0.3, 0.3, 0.4, 0.6, 0.7, 0.9, 1.1, 1.1, 1.2, 1.2, 
1.1, 1, 0.8, 0.6, 0.5, 0.3, 0.4, 0.6, 0.9, 1.7, 2.5, 3.2, 3.9, 
6.9, 8.7, 7.3, 6.4, 5.6, 5.2, 3, 1.3, 0.8, 0.5, 0.4, 0.3, 0.3, 
0.3, 0.2, 0.3, 0.3, 0.3, 0.2, 0.2, 0.2, 0.2, 0.1, 0, 0.2, 0.2, 
0.3, 0.2, 0.5, 0.8, 0.9, 1.4, 2.1, 2.9, 4.2, 6.7, 9, 6.9, 5.5, 
4.2, 4, 3.5, 3.5, 3.4, 3.3, 3.4, 2.7, 2.2, 1.9, 1.7, 1.6, 1.2, 
0.9, 0.5), Cumulative.Rate = c(0.1, 0.2, 0.3, 0.4, 0.5, 0.7, 
1, 1.3, 1.8, 2.5, 3.7, 5.6, 8.6, 11.6, 14.1, 16.3, 18.6, 21.6, 
25, 28.9, 33.5, 38.1, 43.3, 48.8, 53.6, 57.2, 59.9, 61.7, 62.8, 
63.4, 63.6, 0.1, 0.2, 0.4, 0.6, 0.8, 1.1, 1.5, 2.2, 3.1, 4.3, 
6.1, 8.5, 12.9, 18.3, 22.8, 27, 31.6, 36.9, 42.9, 48, 53, 57.4, 
61.3, 64.2, 65.4, 65.7, 65.9, 65.9, 66, 66, 66, 0, 0, 0, 0.1, 
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9.8, 10.9, 12, 13.3, 14.3, 15.4, 16.1, 16.8, 17.2, 17.5, 0.4, 
1, 1.9, 3.6, 6.1, 9.3, 13.2, 20.1, 28.8, 36.1, 42.4, 48, 53.2, 
56.1, 57.4, 58.2, 58.7, 59.1, 59.4, 59.8, 60, 60.3, 60.5, 60.8, 
61, 61.3, 61.5, 61.7, 61.9, 62.1, 62.1, 0.2, 0.4, 0.7, 0.9, 1.4, 
2.2, 3.1, 4.5, 6.6, 9.5, 13.7, 20.4, 29.4, 36.3, 41.7, 45.9, 
49.9, 53.3, 56.8, 60.2, 63.5, 66.9, 69.6, 71.8, 73.7, 75.5, 77.1, 
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