Simulate data with R

Last semester I was attending a boring class, even though the professor was really clever, he was always bouncing around the main theme and never got straight to the point. While thinking about everything but the class, I had an idea: when you are given a set of data, say X and Y, you can easily compute a linear regression model, e.g. the regression line, and find out information on the data. Now, you will also find information on the error that the linear model made in predicting the data. By finding out the distribution of the error you can somehow simulate data similar to the original, from the regression line, by simply adding a random error (whose distribution is known) to the predicted data.
Furthermore, we know from the regression line that the expected error is 0.

Here is the code to implement this idea in R. You can get the data to work on in the bottom of the page.

	data <- read.csv("data.csv", header = T)
	attach(data)
	plot(Y~X, col = "blue")
	# Generate a linear model and plot it
	model <- lm(Y ~ X)
	abline(model, lwd=2, col="red")
	# Calculate the residuals
	resid <- signif(residuals(model), 5)
	# and the predicted values
	predicted_values <- predict(model)
	# Set the bounds
	bounds <- seq(from = min(resid), to = max(resid), by = 0.2)
	# Check the relative frequencies and error distribution
	error_distribution <- table(cut(resid, bounds))/sum(table(cut(resid,bounds)))
	# Plot error distribution
	plot(error_distribution, main = "Frequencies")
	# From the plot, we can assume, that the error should be approximately iid.
	# Therefore runif() could work as an error simulator
	# We now generate 10 errors
	simulated_errors <- runif(length(predicted_values), min = min(resid), max = max(resid))
	simulated_values <- c()
	# We simulate actual values of Y by adding errors to the predicted values
	for(i in 1:length(X))
	{
	simulated_values[i] <- (predicted_values[i] + simulated_errors[i])
	}
	# Here are our simulated_values
	simulated_values
	# We plot again the data and the model, then we add our simulated values
	plot(Y~X, col = "blue")
	abline(model, lwd=2, col="red")
	points(X, simulated_values, type = "p",col="red")
	detach(data)

view raw simData.R hosted with ❤ by GitHub

The result should look something like this: In blue the actual data and in red the simulated one.

Hope this was useful, if you know the name of this method, please leave a comment and let me know. Click here to get the data I used.