How to calculate standardized residuals in R

To calculate standardized residuals in R, you can follow these steps:

  1. Fit a regression model using the lm() function. This function takes the form lm(formula, data), where formula specifies the relationship between the variables and data is the data frame containing the variables.

  2. Use the residuals() function to extract the residuals from the fitted model. This function takes the form residuals(model), where model is the fitted model object obtained from the lm() function.

  3. Calculate the mean and standard deviation of the residuals using the mean() and sd() functions, respectively. These functions take the form mean(residuals) and sd(residuals), where residuals is the vector of residuals obtained from the previous step.

  4. Standardize the residuals by subtracting the mean and dividing by the standard deviation. This can be done using the formula (residuals - mean(residuals)) / sd(residuals).

Here is an example that demonstrates these steps:

# Step 1: Fit a regression model
model <- lm(y ~ x, data = my_data)

# Step 2: Extract residuals
residuals <- residuals(model)

# Step 3: Calculate mean and standard deviation of residuals
residuals_mean <- mean(residuals)
residuals_sd <- sd(residuals)

# Step 4: Calculate standardized residuals
standardized_residuals <- (residuals - residuals_mean) / residuals_sd

The standardized_residuals vector will contain the standardized residuals for each observation in the dataset.