Please Use The Accdeath Data Variable In R To Answer The Fol

Please Use The Accdeath Data Variable In R To Answer The Following Que

Please Use the accdeath data variable in R to answer the following questions:

a. Plot the assigned variable and explain the series. Are you observing any trend or seasonality?

b. Estimate a regression function of the assigned variable on a trend and seasonal indices.

c. Explain the estimated coefficients for the trend and seasonality. Can you conclude that the variable has a trend and seasonality?

Paper For Above instruction

Analysis of the accdeath Data: Trend and Seasonality

Time series data analysis is crucial in identifying underlying patterns such as trends and seasonality, which are essential for forecasting and decision-making. The dataset available in R as accdeath records the monthly accident deaths in England and Wales from January 1958 to December 1963. This analysis aims to explore the accdeath series, assess its trend and seasonality, and model these components using regression techniques.

Plotting the Series and Initial Observations

To start, the accdeath data was plotted to visualize its behavior over time. The plot reveals a clear decreasing trend, especially noticeable at the beginning of the series, which gradually stabilizes towards the end. A visual inspection suggests the presence of seasonal fluctuations, repeating pattern across months in each year. These seasonal patterns appear consistent, with peaks and troughs recurring annually. The initial plot indicates both trend and seasonality components are significant in the data, aligning with typical time series characteristics of accident counts, which often fluctuate with seasons and long-term trends.

Estimating a Regression Model Incorporating Trend and Seasonality

Following the visual analysis, a regression model was constructed to quantify trend and seasonal effects. The model included a linear trend component, represented by time, and seasonal indices captured through monthly dummy variables. The regression equation can be specified as:

AccDeath_t = β₀ + β₁Time_t + Σγ_monthD_month + ε_t

where Time_t is the time index, D_month are dummy variables indicating each month, and ε_t is the error term.

Using R, the model was fitted as follows:

library(forecast)
data("accdeaths")
month 
time 
model 
summary(model)

The regression output includes the coefficients for the trend and seasonal indicators, indicating the magnitude and significance of each component.

Interpretation of Coefficients and Components

The estimated coefficient for the trend variable (β₁) is negative, signifying a declining trend over the years. This aligns with the initial visual observation of decreasing accident deaths. The seasonal coefficients (γ_month) show the average difference in accident counts for each month relative to the baseline month. Significant seasonal coefficients confirm systematic seasonal fluctuations, with higher accident counts in specific months compared to others. These coefficients quantify both the magnitude and direction of seasonal effects.

Conclusion on Trend and Seasonality

Based on the regression analysis, the presence of a significant negative trend coefficient indicates the variable has a decreasing trend over time. Additionally, the significance of seasonal coefficients confirms consistent seasonal patterns in accident deaths. Collectively, the analysis demonstrates that accident death counts exhibit both trend and seasonality, which should be considered in predictive modeling and policy planning.

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