File:Visualizing Loglog Normal Data.png
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This is a file from the Wikimedia Commons. The description on its description page there is shown below.
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Summary
| Description |
English: This image presents two plots generated from a dataset of 10,000 points.
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. 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) line. |
| Date | |
| Source | Own work |
| Author | Talgalili |
# 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))
)
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
File history
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| Date/Time | Dimensions | User | Comment | |
|---|---|---|---|---|
| current | 03:25, 15 April 2024 | 2,400 × 1,200 (439 KB) | Talgalili | Uploaded own work with UploadWizard |
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