rollling regression airplane dataset

3 min read 07-12-2024

Rolling Regression on Airplane Dataset: Unveiling Temporal Trends in Flight Delays

Analyzing time-series data, like flight delays, often reveals patterns hidden in static snapshots. Rolling regression is a powerful technique to uncover these trends, providing insights into how delays evolve over time. This article explores how to apply rolling regression to an airplane dataset, focusing on identifying temporal dependencies and forecasting potential delays.

Understanding Rolling Regression

Rolling regression, also known as moving window regression, involves fitting a regression model to a sliding window of data. As the window moves through the dataset, a new model is estimated for each position. This provides a sequence of model parameters, allowing us to observe how relationships between variables change over time. This is especially useful for non-stationary time series where the relationship between variables isn't constant.

For our airplane dataset, we can use rolling regression to analyze how various factors (e.g., time of day, day of week, weather conditions) influence delays over different time periods. This allows us to move beyond simple correlations and understand the dynamic nature of these influences.

The Airplane Dataset: A Closer Look

A typical airplane dataset might include variables such as:

Departure Time: The time the flight departed.
Arrival Time: The time the flight arrived.
Delay: The difference between scheduled and actual arrival times (our target variable).
Day of Week: Categorical variable representing the day of the week.
Month: Categorical variable representing the month.
Weather Conditions: Categorical or numerical variable representing weather at departure and arrival airports.
Aircraft Type: Categorical variable specifying the aircraft used.
Origin Airport: Categorical variable specifying the departure airport.
Destination Airport: Categorical variable specifying the arrival airport.

Data Preprocessing: Before applying rolling regression, the dataset needs careful preprocessing. This includes:

Handling Missing Values: Addressing missing data points using imputation techniques (e.g., mean imputation, k-nearest neighbors) or removal if appropriate.
Feature Engineering: Creating new features from existing ones. For example, we might create features like "hour of day" or "is_weekend" from the departure time and day of week.
Data Transformation: Applying transformations like standardization or normalization to ensure features have similar scales. Log transformations might be useful for skewed delay data.

Applying Rolling Regression

We'll use a rolling window of a specified size (e.g., 30 days). For each window, we fit a linear regression model predicting delay based on the selected features. The choice of features depends on the specific hypotheses and the goal of the analysis. For example, we might start with a simple model including time of day and day of week:

import pandas as pd
from sklearn.linear_model import LinearRegression
import numpy as np

# Assuming 'df' is your preprocessed pandas DataFrame with a 'delay' column and features

window_size = 30
rolling_coeffs = []
for i in range(window_size, len(df)):
    window = df[i-window_size:i]
    X = window[['hour_of_day', 'is_weekend']]  # Select features
    y = window['delay']
    model = LinearRegression().fit(X, y)
    rolling_coeffs.append(model.coef_)

rolling_coeffs = np.array(rolling_coeffs)

This code iterates through the data, fitting a linear regression model for each window. The resulting rolling_coeffs array contains the coefficients for each model, showing how the effect of hour of day and weekend status on delays changes over time.

Interpreting Results

Plotting the coefficients over time reveals interesting patterns. For example, we might observe:

Seasonal Trends: Changes in the coefficients related to time of day or day of week, reflecting seasonal variations in delays.
Impact of Events: Sudden shifts in the coefficients potentially indicating the effect of major events (e.g., weather disruptions, airport closures).
Long-term Trends: Gradual changes in coefficients reflecting long-term shifts in operational efficiency or infrastructure.

Forecasting

Rolling regression can also be used for forecasting. The model fitted on the most recent window can be used to predict delays in the near future. However, it's crucial to acknowledge the limitations of such forecasts, as they assume that the relationships observed in the past will continue in the future.

Conclusion

Rolling regression provides a powerful tool to analyze temporal dependencies in flight delay data. By revealing dynamic relationships between delays and various factors, it can help airlines improve operational efficiency, better manage resources, and potentially improve forecasting accuracy. Remember to carefully consider feature selection, model selection, and interpretation of results to draw meaningful conclusions. Further analysis might involve exploring non-linear relationships or incorporating more sophisticated time series models.