192:# 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) # For jupyter notebook options( repr.plot.width = 20, # in inches (default = 7) repr.plot.height = 10 # in inches (default = 7) ) # Plot data p1 <- ggplot(df, aes(x = x, y = y_observed)) + geom_point() + geom_line(aes(y = y_true, color = 'Median line'), size = 3) + geom_smooth(aes(color = 'Mean line'), size = 3, se = F) + coord_cartesian(ylim = c(0, 20)) + # Set the limits of the plot without excluding obs scale_color_manual(values = c('Median line' = 'red', 'Mean line' = 'blue')) + theme_bw() + theme(text = element_text(size = 25)) + theme(legend.position="bottom") + labs(x = 'X', y = 'Y', title = 'Concave Line with Log-Normal Noise') p2 <- ggplot(df, aes(x = x, y = y_observed)) + geom_point() + geom_line(aes(y = y_true, color = 'Mean and Median line'), size = 3) + scale_x_log10() + scale_y_log10() + scale_color_manual(values = c('Mean and Median line' = 'red')) + theme_bw() + theme(text = element_text(size = 25)) + theme(legend.position="bottom") + labs(x = 'X (log scale)', y = 'Y (log scale)', title = 'Log-Log Linear Line with Normal Noise') p1 + p2 + plot_annotation( title = 'Visualizing Loglog Normal Data: Scatter-plots in Original and Log10 Scales', theme = theme(plot.title = element_text(hjust = 0.5, size = 40)) )
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The first plot, titled 'Concave Line with Log-Normal Noise', displays a scatter plot of the observed data (y_observed) against the independent variable (x). The red line represents the 'Median line', while the blue line is the 'Mean line'. The y-axis is limited to a range of 0 to 20.
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The second plot, titled 'Log-Log Linear Line with Normal Noise', also displays a scatter plot of the observed data against the independent variable, but both axes are on a logarithmic scale. Here, both the mean and median lines are the same (red)
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I, the copyright holder of this work, hereby publish it under the following license:
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Visualizing Loglog Normal Data: Scatter-plots in
Original and Log10 Scales
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This image presents two plots generated from a dataset of 10,000 points.
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