## The objective of this simulation is to prove the following hypothesis: ## In a regression model, when you have predictors with different standard deviations, the standardized coefficients will be no longer reliable # repeat the simulation N times N = 1000 results = replicate(N, { # create 2 variables x1 and x2, normally distributed with mean 0 with the only difference that x2 has a larger standard deviation x1 = rnorm(n = 30, mean = 0, sd = 1) x2 = rnorm(n = 30, mean = 0, sd = 20) # create the y variable such as the true coefficients of x1 and x2 are equal to 1 # and add a small error term to avoid a perfect model fit y = x1 + x2 + 0.01 * rnorm(30, 0, 20) # standardize the variables x1 = scale(x1) x2 = scale(x2) y = scale(y) # run a linear regression model model = lm(y ~ x1 + x2) # save the difference between the coefficient of x2 and x1 in the variable "results" abs(model\$coefficients[3]) - abs(model\$coefficients[2]) }) # get the mean difference between the standardized coefficients of x2 and x1 mean(results) ## HOW TO INTERPRET THE OUTCOME ## the output is close to 1, which means that ## x2 has a standardized coefficient bigger than that of x1 ## which proves the above hypothesis ## NOTE: ## try re-running this simulation without standardizing the variables ## the output will be very close to 0 ## i.e. the unstandardized coefficients of x1 and x2 will be equal