Solved – How to simulate regression residuals with serial correlation or autocorrelation

I can easily simulate a data set where the regression residuals are iid with 0 mean and constant variance.

set.seed(123) x = rnorm(100) y = 50 + 25* x + rnorm(100)  df = data.frame(y=y, x=x) 

The data assumes that the population regression equation is $$y = beta_0 + beta_1X_1 + epsilon$$

And $epsilon$ is white noise (0 mean, constant variance).

I want to simulate a data set where the residuals are correlated and assume the following population regression equation
$$
begin{aligned}
y_t &= beta_0 + beta_1X_{1,t} + epsilon_t, \
epsilon_t &= rhoepsilon_{t-1} + v_t, \
end{aligned}
$$
and $v_t$ is white noise (0 mean, constant variance).

How would I create this data frame in R?

set.seed(123)  ar.epsilon <- arima.sim(list(order = c(1,0,0), ar = 0.7), n = 200, sd=20)  plot(ar.epsilon)  x=rnorm(200)  y = 50 + 25*x + ar.epsilon  df2 = data.frame(x=x, y=y)  lm.mod <- lm(y~., data=df2)  summary(lm.mod) 

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