nonlin_data_lin_model.R

# testing effect of correlated predictors on non-linearity when assuming a linear model

rho = 0.9
N = 20
set.seed(1)

# generate correlated x1 and x2 predictors
z = matrix(rnorm(N*2, 0, 1), 2)
L = t(chol(matrix(c(1, rho, rho, 1), 2)))
x = L %*% z

# y depends only on x1, not on x2
y = (1 + x[1,])^2 + rnorm(N, 0, 0.1)

# and yet we have a "significant" effect for both x1 and x2
fit = lm(y ~ x1 + x2, data = data.frame(y = y, x1 = x[1,], x2 = x[,2]))
print(summary(fit))