# Reproducible R code  # Load necessary libraries library(ggplot2) library(patchwork)  # Set seed for reproducibility set.seed(123)  # Generate data n <- 10000 x <- sort(runif(n, min = 1, max = 100)) intercept <- 0.000001 slope <- 0.5 y_true_log <- intercept + slope * log10(x) noise <- rnorm(n, mean = 0, sd = .1) y_observed_log <- y_true_log + noise y_observed <- 10^y_observed_log y_true <- 10^y_true_log  # Create data frame df <- data.frame(x = x, y_true = y_true, y_observed = y_observed)  # Load necessary libraries library(dplyr) library(ggplot2) library(zoo)  # Define window size window_size <- 28  # Calculate error metrics over sliding window df <- df %>%   arrange(x) %>%   mutate(MAE = rollapply(abs(y_true - y_observed), width = window_size, FUN = mean, align = "right", fill = NA),          RMSE = sqrt(rollapply((y_true - y_observed)^2, width = window_size, FUN = mean, align = "right", fill = NA)),          MALE = rollapply(abs(log10(y_true) - log10(y_observed)), width = window_size, FUN = mean, align = "right", fill = NA))  # Load necessary library library(tidyr)  # Reshape data to long format df_long <- df %>%   gather(key = "error_type", value = "error_value", MAE, RMSE, MALE)  options(   repr.plot.width  = 12,   # in inches (default = 7)   repr.plot.height = 10   # in inches (default = 7) )  # Plot error metrics ggplot(df_long, aes(x = x, y = error_value, color = error_type)) +   geom_line(alpha = .5) +   geom_smooth() + #   scale_x_log10() + #   scale_y_log10() +    coord_cartesian(ylim = c(0, 2.5)) + # Set the limits of the plot without excluding obs   theme_bw() + theme(text = element_text(size = 25)) +   theme(legend.position="bottom") +    labs(x = 'X', y = 'Error', title = 'Sliding Window Analysis of Error Metrics\nin Loglog Normal Data') 

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