library(tidyverse)
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library(ggthemes)
library(ggrepel)
library(xts)
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library(tsibble)
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theme_set(theme_minimal())
options(scipen = 6)
astro <- read_delim('/Users/sneha/H510-Statistics/astronaut-data.csv')
## Rows: 1277 Columns: 23
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## chr (10): name, sex, nationality, military_civilian, selection, occupation, ...
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Select a column of your data that encodes time (e.g., “date”, “timestamp”, “year”, etc.). Convert this into a Date in R.

astro$mission_date <- as.Date(paste(astro$year_of_mission, "01", "01", sep = "-"))
response <- astro |> select(mission_date, total_hrs_sum)
#ts_data <- response |> as_tsibble(index = mission_date)

Since i ended up getting error, i will have to remove duplicates from this column. tsibble objects should have unique rows for each combination of key and index.

duplicates <- response |> duplicates(index = mission_date)
print(duplicates)
## # A tibble: 1,276 × 2
##    mission_date total_hrs_sum
##    <date>               <dbl>
##  1 1961-01-01            1.77
##  2 1961-01-01           25.3 
##  3 1962-01-01          218   
##  4 1998-01-01          218   
##  5 1962-01-01            5   
##  6 1962-01-01          519.  
##  7 1970-01-01          519.  
##  8 1962-01-01          448.  
##  9 1974-01-01          448.  
## 10 1962-01-01          295.  
## # ℹ 1,266 more rows

Removing duplicates and keeping the first instance:

response_data <- response |> distinct(mission_date, .keep_all = TRUE)
ts_data <- response_data |> as_tsibble(index = mission_date)

Plotting data over time:

ts_data |> 
  ggplot(aes(x = mission_date, y = total_hrs_sum)) + 
  geom_line() + 
  labs(title = "Total Hours in Space Over Time", x = "Date", y = "Total Hours in Space")

The line graph titled “Total Hours in Space Over Time” shows a clear upward trend in the number of hours spent in space over the years.

1)The overall trend is upward, indicating that the amount of time humans have spent in space has been increasing over the decades.

2)There are significant fluctuations within this upward trend. Some years see a sharp increase in hours spent in space, while others show a decrease.

3)there appear to be a few peaks in the graph, which might correspond to specific events or missions that involved extended stays in space.

My Interpretations:

The upward trend likely reflects the advancements in space technology and the growing interest in space exploration.

Linear Regression:

model <- lm(total_hrs_sum ~ mission_date, data = ts_data)
summary(model)
## 
## Call:
## lm(formula = total_hrs_sum ~ mission_date, data = ts_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8751.1 -3169.6  -344.5  2120.4 11401.8 
## 
## Coefficients:
##                Estimate Std. Error t value     Pr(>|t|)    
## (Intercept)  -121.43840  939.56018  -0.129        0.898    
## mission_date    0.62588    0.09793   6.391 0.0000000327 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4679 on 57 degrees of freedom
## Multiple R-squared:  0.4175, Adjusted R-squared:  0.4072 
## F-statistic: 40.85 on 1 and 57 DF,  p-value: 0.00000003265

Below is my analysis:

The coefficient for mission date is 0.625, with a very low p-value (0.00000003), indicating that it is highly statistically significant.This suggests a clear relationship between between mission date and total hrs sum.

A positive coefficient for mission date suggests an upward trend in total hrs sum over time. This means that, on average, the total mission hours are increasing as the mission date gets later.

ts_data |>
  ggplot(aes(x = mission_date, y = total_hrs_sum)) +
  geom_line() +
  geom_smooth(method = "lm", color = "red", se = FALSE) +
  labs(title = "Trend in Total Hours in Space", x = "Date", y = "Total Hours in Space")
## `geom_smooth()` using formula = 'y ~ x'

I think this model captures the general upward trajectory of the “Total Hours in Space” over time.

The red line, representing the linear regression, clearly shows an upward slope, suggesting that the total hours spent in space have been increasing over the years.

subset_data <- ts_data |> filter(mission_date >= as.Date("1990-01-01"))

Trying to smooth out the graph for better clarity:

smoothed_data <- ts_data |>
  mutate(smoothed = forecast::ma(total_hrs_sum, order = 5))
## Registered S3 method overwritten by 'quantmod':
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I saw this forcast package which might be helpful with analysing trend

library(forecast)
smoothed_data |>
  ggplot(aes(x = mission_date)) +
  geom_line(aes(y = total_hrs_sum), alpha = 0.5) +
  geom_line(aes(y = smoothed), color = "blue") +
  labs(title = "Smoothed Trend of Total Hours in Space", x = "Date", y = "Total Hours in Space")
## Warning: Removed 4 rows containing missing values or values outside the scale range
## (`geom_line()`).

acf(ts_data$total_hrs_sum, main = "ACF of Total Hours in Space")

pacf(ts_data$total_hrs_sum, main = "PACF of Total Hours in Space")

In this specific ACF graph, there is no clear evidence of seasonality. The ACF values do not show any significant spikes at regular intervals that would suggest a repeating seasonal pattern.

Initial Spikes:We observe a few initial spikes in the ACF values, suggesting some degree of autocorrelation in the short term. However, these spikes quickly decay.

The ACF values generally reduces as the lag increases, indicating that the correlation between the time series and its lagged values weakens over time.

PACF:

We observe a few initial spikes in the PACF values, suggesting some degree of direct correlation between the time series and its immediate past values.

There is no clear pattern or significant spikes at regular intervals in the PACF, suggesting that there is no significant seasonal component in the data.

Overall, the PACF plot indicates that the “Total Hours in Space” data exhibits some short-term dependence but lacks a strong seasonal component or long-term trends.

I think this maybe due to removal of duplicates from the entry.