Knowledge

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)) ) 497:"}},"text\/plain":{"en":{"":"inception"}}},"{\"value\":{\"time\":\"+2024-04-15T00:00:00Z\",\"timezone\":0,\"before\":0,\"after\":0,\"precision\":11,\"calendarmodel\":\"http:\\\/\\\/www.wikidata.org\\\/entity\\\/Q1985727\"},\"type\":\"time\"}":{"text\/html":{"en":{"P571":"15 April 2024"}},"text\/plain":{"en":{"P571":"15 April 2024"}}}}": --> 38: 209: 321: 94: 333:"}},"text\/plain":{"en":{"P2093":"Talgalili","P4174":"Talgalili"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":4174,\"id\":\"P4174\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":" 453:"}},"text\/plain":{"en":{"":"copyright license"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":20007257,\"id\":\"Q20007257\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P275":" 409:"}},"text\/plain":{"en":{"":"copyright status"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":50423863,\"id\":\"Q50423863\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P6216":" 573:"}},"text\/plain":{"en":{"":"source of file"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":66458942,\"id\":\"Q66458942\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P7482":" 535:"}},"text\/plain":{"en":{"":"media type"}}},"{\"value\":\"image\\\/png\",\"type\":\"string\"}":{"text\/html":{"en":{"P1163":"image\/png"}},"text\/plain":{"en":{"P1163":"image\/png"}}}}": --> 325:"}},"text\/plain":{"en":{"":"creator"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":2093,\"id\":\"P2093\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":" 569: 329:"}},"text\/plain":{"en":{"":"author name string"}}},"{\"value\":\"Talgalili\",\"type\":\"string\"}":{"text\/html":{"en":{"P2093":"Talgalili","P4174":" 150: 153: 256:– You must give appropriate credit, provide a link to the license, and indicate if changes were made. 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