What is Bootstrapping in R?

Bootstrapping is a powerful non-parametric statistical method used to estimate the distribution of a statistic by resampling from the data. It is useful when we want to make inferences but are unsure about the data's underlying distribution.

Basic Steps of Bootstrapping:

Repeatedly resample the dataset with replacement.

Compute a statistic (mean, median, etc.) for each sample.

Analyze the distribution of those computed statistics.

Non-parametric Bootstrapping in R

To perform bootstrapping in R, we commonly use the boot package. It allows us to calculate statistics like the mean, median, or even regression coefficients.

Format of boot() function:

bootobject <- boot(data = , statistic = , R = , ...) 

Parameters:

data: The dataset (vector, matrix, or data frame).

statistic: A custom function that returns the statistic to be bootstrapped.

R: Number of bootstrap resamples.

Bootstrapping Example in R

Let’s perform bootstrapping to compute a 95% confidence interval for R-squared in a linear regression using the mtcars dataset.

# Load library library(boot) # Function to calculate R-squared r_squared <- function(formula, data, indices) {  val <- data[indices, ]   # Bootstrap sample  fit <- lm(formula, data = val)  return(summary(fit)$r.squared) } # Perform bootstrapping with 1500 resamples output <- boot(data = mtcars, statistic = r_squared,               R = 1500, formula = mpg ~ wt + disp) # View result print(output) plot(output) # Calculate 95% Confidence Interval boot.ci(output, type = "bca") 

Parameters in boot() Function

Here are some important arguments:

Types of Bootstrap Confidence Intervals

Using boot.ci(), we can calculate five types of confidence intervals:

Norm (Normal) CI

Basic CI

Stud (Studentized) CI

Perc (Percentile) CI

BCa (Bias-Corrected and Accelerated) CI

Each has its own method of estimating the confidence interval based on the bootstrap distribution.

R Bootstrapping Methods

There are two major ways of applying bootstrap in regression:

Bootstrapping Residuals – Resample residuals and create new response values.

Bootstrapping Pairs – Resample (X, Y) pairs directly. This method is more robust.

When to Use Bootstrapping

Bootstrapping is valuable when:

The statistic’s true sampling distribution is unknown.

You want to estimate confidence intervals or standard errors without complex formulas.

When Bootstrapping Might Fail

Be cautious when:

Sample size is too small (less than 10).

Distributions have infinite variance.

You're estimating extreme quantiles.

The process is highly unstable (e.g., certain time series).

Pros and Cons of Bootstrapping in R

Pros

Great for small datasets when distribution is unknown.

Avoids complex mathematical derivations.

Flexible and widely applicable in various models.

Cons

Less reliable for very small datasets.

Computationally expensive.

May fail with unstable or extreme data scenarios.

R Bootstrap for Web Development? (Clarification)

There was confusion in some tutorials between Bootstrapping in R (statistical resampling) and Bootstrap (HTML/CSS framework).

In this context, we're only referring to statistical bootstrapping in R, not the Bootstrap web development framework.