Simulate Linear Regression Data with Known Coefficients

Generate a dataset suitable for linear regression with fully specified ground-truth coefficients and predictor standard deviations. Designed so that lm(y ~ ., data = r$data) recovers the true coefficients at large n.

Usage

simulate_regression(coefs, predictor_sds, error_sd, n, seed = NULL)

Arguments

coefs: Named numeric vector. May include "(Intercept)". All other names become predictor column names. Predictors are generated as independent $N(0, \sigma_j)$ variables.
predictor_sds: Named numeric vector. Names must exactly match the non-intercept names in coefs. All values must be positive.
error_sd: Positive numeric. Standard deviation of the residuals.
n: Positive integer. Sample size.
seed: Integer or NULL. Random seed.

Value

A named list with elements:

data: data.frame with column y and one column per predictor.
params: list with coefs, predictor_sds, and error_sd.

Examples

coefs <- c("(Intercept)" = 2, x1 = 3, x2 = -1)
r <- simulate_regression(coefs = coefs,
                          predictor_sds = c(x1 = 1, x2 = 1),
                          error_sd = 0.5, n = 500, seed = 42)
coef(lm(y ~ ., data = r$data))  # should be close to c(2, 3, -1)
#> (Intercept)          x1          x2 
#>   1.9798791   3.0200245  -0.9995026