R Notebook
# Load necessary library
library(lubridate)##
## Attaching package: 'lubridate'## The following objects are masked from 'package:base':
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## date, intersect, setdiff, unionlibrary(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
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## filter, lag## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, unionlibrary(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ purrr 1.0.2 ✔ tidyr 1.3.1
## ✔ readr 2.1.5## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(tsibble)## Registered S3 method overwritten by 'tsibble':
## method from
## as_tibble.grouped_df dplyr
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## Attaching package: 'tsibble'
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## The following object is masked from 'package:lubridate':
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## interval
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## The following objects are masked from 'package:base':
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## intersect, setdiff, unionlibrary(fable)## Loading required package: fabletoolslibrary(fabletools)
library(feasts)
data <- read.csv("~/Documents/STAT 2024/udemy_courses.csv")
data$published_date <- as.Date(data$published_timestamp, format = "%Y-%m-%dT%H:%M:%SZ")
head(data$published_date)## [1] "2017-01-18" "2017-03-09" "2016-12-19" "2017-05-30" "2016-12-13"
## [6] "2014-05-02"The published_timestamp column contains timestamps in a detailed format such as “YYYY-MM-DDTHH” (including date and time). The code converts this into a simpler format showing only the date (YYYY-MM-DD) using the as.Date() function, making it more convenient for analysis.
time_series_data <- data %>%
select(published_date = published_timestamp, num_subscribers)
time_series_data$published_date <- as.Date(time_series_data$published_date, format = "%Y-%m-%dT%H:%M:%SZ")
time_series_data <- time_series_data %>%
arrange(published_date)
head(time_series_data)I select two important columns from the dataset: published_timestamp (renamed as published_date) and num_subscribers, which are needed for time-series analysis. The published_date column is converted into a simple date format (YYYY-MM-DD) to make it consistent and easier to work with. Then, the data is sorted by the published_date column in order from earliest to latest, which is useful for time-series analysis. Finally, the first few rows of the updated data are shown using the head() function to check the results.
duplicates <- time_series_data %>%
count(published_date) %>%
filter(n > 1)
print(duplicates)## published_date n
## 1 2012-06-18 2
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## 824 2017-07-06 6aggregated_data <- time_series_data %>%
group_by(published_date) %>%
summarize(num_subscribers = sum(num_subscribers, na.rm = TRUE), .groups = "drop")
tsibble_data <- aggregated_data %>%
as_tsibble(index = published_date)
tsibble_data %>%
ggplot(aes(x = published_date, y = num_subscribers)) +
geom_line(color = "blue") +
labs(
title = "Number of Subscribers Over Time",
x = "Published Date",
y = "Number of Subscribers"
) +
theme_minimal()
I first group the data by published_date to ensure that each date has only one entry. If there are multiple entries for the same date, I add up the num_subscribers for that date to get a total. After grouping and summarizing the data, I convert it into a tsibble, a time-series format, to make it easier to analyze trends over time. Finally, I create a line plot where I display how the number of subscribers changes over time.
I can see how the number of subscribers changes over time. When I plot the data as a line chart, it allows me to observe whether the subscriber count is growing, declining, or remaining steady across the dates. This helps me identify patterns, such as periods of growth, seasonal variations, or any unexpected spikes or drops in the numbers.
trend_model <- lm(num_subscribers ~ as.numeric(published_date), data = aggregated_data)
summary(trend_model)##
## Call:
## lm(formula = num_subscribers ~ as.numeric(published_date), data = aggregated_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13090 -8152 -4750 1387 256803
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 56677.555 17404.615 3.256 0.00116 **
## as.numeric(published_date) -2.829 1.048 -2.699 0.00705 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 17450 on 1208 degrees of freedom
## Multiple R-squared: 0.005995, Adjusted R-squared: 0.005172
## F-statistic: 7.286 on 1 and 1208 DF, p-value: 0.007047aggregated_data %>%
ggplot(aes(x = published_date, y = num_subscribers)) +
geom_point(color = "blue") +
geom_smooth(method = "lm", color = "red", se = FALSE) +
labs(
title = "Linear Trend in Number of Subscribers Over Time",
x = "Published Date",
y = "Number of Subscribers"
) +
theme_minimal()## `geom_smooth()` using formula = 'y ~ x'
aggregated_data %>%
ggplot(aes(x = published_date, y = num_subscribers)) +
geom_point(color = "blue") +
geom_smooth(span = 0.3, color = "green", method = "loess") +
labs(
title = "Visualizing Trends to Assess Subsetting Needs",
x = "Published Date",
y = "Number of Subscribers"
) +
theme_minimal()## `geom_smooth()` using formula = 'y ~ x'
I start by creating a linear regression model (trend_model) to explore the overall trend in the number of subscribers over time. By using summary(trend_model), I examine the results of the model to see how well the trend fits the data and whether there is a significant increase or decrease in subscribers over time. Linear Trend in Number of Subscribers Over Time- The scatterplot shows individual subscriber counts over time (blue points) with a fitted red linear regression line. The red linear trend line appears almost flat, indicating no significant overall growth in subscriber numbers over the analyzed time frame based on this linear model The blue points, however, show substantial variability. While most values cluster near zero, there are a few outliers with significantly higher subscriber counts, which could distort the effectiveness of the linear trend model.
Next, I plot the data to visualize the trend. First, I create a scatterplot of the number of subscribers against the published dates and add a red trend line using the linear regression model. This helps me clearly see the linear relationship between the two variables. The majority of points cluster near zero, indicating that most courses have relatively low subscriber counts. The green LOESS curve suggests very subtle upward or downward shifts in the number of subscribers over time. However, the trend appears mostly flat. The slight increases in some regions (e.g., around 2013–2014) may point to periods of growth, while other regions may reflect stable or declining subscriber counts. The LOESS line does not show a significant long-term upward or downward trend. This suggests that there may be no strong time-dependent growth in subscribers, and the data is heavily influenced by outliers
# Convert the date column to Date format
time_series_data$published_date <- as.Date(time_series_data$published_date,time_series_data$published_timestamp)
# Aggregate data to ensure unique dates
aggregated_data <- time_series_data %>%
group_by(published_date) %>%
summarize(num_subscribers = sum(num_subscribers, na.rm = TRUE), .groups = "drop")# Create a tsibble object and fill gaps
tsibble_data <- aggregated_data %>%
as_tsibble(index = published_date) %>%
fill_gaps(num_subscribers = 0) # Fill gaps with 0 subscribers
# Apply smoothing using LOESS to detect seasonality
tsibble_data %>%
ggplot(aes(x = published_date, y = num_subscribers)) +
geom_point(color = "blue") +
geom_smooth(method = "loess", span = 0.2, color = "red") +
labs(
title = "Smoothing to Detect Seasonality in Number of Subscribers",
x = "Published Date",
y = "Number of Subscribers"
) +
theme_minimal()## `geom_smooth()` using formula = 'y ~ x'
I create a tsibble object from the aggregated data using published_date as the time index. I also fill any missing dates with a default value of 0 subscribers to ensure the data is complete for analysis. Then, I apply LOESS smoothing to the data and plot it. The plot shows the raw data points in blue and a red smoothed curve that helps me detect seasonal patterns or trends over time. This makes it easier to see underlying patterns in the number of subscribers. The red line suggests that there is no strong seasonality or periodicity in the data. The increase in subscribers over time is minimal and mostly dominated by the outliers While the overall trend is subtle, minor fluctuations in the LOESS line could indicate possible seasonal behaviors. This would require further investigation by aggregating data by months or quarters. The significant outliers, where subscriber counts exceed 100,000, skew the perception of the overall trend. Identifying the dates of these outliers could help in understanding what factors contributed to their success (e.g., popular topics or promotions)
# Decompose the time series to extract seasonal components
decomposed <- tsibble_data %>%
model(stl = STL(num_subscribers ~ season(window = "periodic"))) %>%
components()
# Plot the decomposed components
autoplot(decomposed) +
labs(
title = "Decomposition of Time Series to Detect Seasonality",
x = "Published Date",
y = "Number of Subscribers"
)
# Illustrate seasonality using ACF and PACF
# ACF plot
tsibble_data %>%
ACF(num_subscribers) %>%
autoplot() +
labs(
title = "ACF Plot to Detect Seasonality",
x = "Lag",
y = "ACF"
)
# PACF plot
tsibble_data %>%
PACF(num_subscribers) %>%
autoplot() +
labs(
title = "PACF Plot to Detect Seasonality",
x = "Lag",
y = "PACF"
)
Decomposition of Time Series to Detect Seasonality 1st panel - The raw data exhibits a high degree of variability with noticeable outliers, where some courses attracted significantly more subscribers than the majority.This panel shows the original time series data (number of subscribers over time). The raw data exhibits a high degree of variability with noticeable outliers, where some courses attracted significantly more subscribers than the majority. 2nd panel- The trend component captures the long-term progression of the data, smoothing out short-term fluctuations. It reveals a gradual increase in subscriber numbers until around 2015, followed by a slight decline. This could indicate a peak in subscriber growth during this period, possibly due to platform-wide factors such as promotions or market saturation 3rd panel - This panel captures repeating patterns at a seasonal frequency (e.g., yearly or weekly) Clear peaks in the seasonal component suggest recurring periods of higher subscriber activity. This could align with annual or weekly patterns, such as holiday seasons or consistent spikes during specific times of the week. last panel - The remainder represents the variability in the data that cannot be explained by the trend or seasonal components. Large residuals in certain areas indicate irregularities or one-off events that significantly impacted subscriber counts (e.g., a highly successful course launch or promotional campaign)
ACF Plot to Detect Seasonality- The ACF measures how the values of the time series are correlated with their past values (lags). The blue dashed lines indicate the threshold for statistically significant autocorrelations. Bars exceeding this threshold suggest a meaningful pattern or seasonality The ACF plot shows strong, regularly spaced peaks (e.g., at lags 7, 14, 21, and 28). This indicates a weekly seasonality in the time series, suggesting that subscriber behavior repeats at a weekly interval.
PACF Plot to Detect Seasonality- The PACF measures the direct relationship between a time series value and its lagged values, removing the effects of intermediate lags. This gives a clearer picture of the immediate influence of specific lags. Bars extending beyond the blue dashed lines indicate statistically significant partial autocorrelations at those lags The PACF plot shows strong spikes at lags 7, 14, and 21. This suggests that there is a direct weekly pattern in the time series data, consistent with the findings from the ACF plot. These significant lags confirm a weekly seasonality, where subscriber behavior exhibits a strong repetition every 7 days.