CODEWITHSUNDEEP
rstatisticslinear-regression
Ryan
Ryan

Reputation: 15

generating errors with heteroscedasticity

I have a question regarding generating errors with heteroscedasticity

This is how my friend told me to do it: 

n <- 30  
x1 <- rnorm(n,0,1) # 1st predictor 
x2 <- rnorm(n,0,1)  # 2nd predictor   
e <- rnorm(n,0,x1^2)  # errors with heteroscedaticity     
b1 <- 0.5; b2 <- 0.5     
y <- x1*b1+x2*b2+e

For me, e <-rnorm(n,0,x1^2) -- this is autocorrelation rather than heteroscedastic error distribution. But my friend said this is the correct way to generate errors with heteroscedasticity.

Am I missing something here?

I thought heteroscedasticity occurs when the variance of the error terms differ across observations.

Does e<-rnorm(n,0,x1^2) this syntax generate errors with heteroscedasticity correctly?

If not, could anyone tell me how to generate errors with heteroscedasticity?

Upvotes: 0

Views: 276

Answers (1)

Ben Bolker
Ben Bolker

Reputation: 226532

This specification does generate a particular (slightly odd) kind of heteroscedasticity. You define heteroscedasticity as "the variance of the error term differ[ing] across observations". Since the value of x1 is different for different observations, and you have chosen your error values with a standard deviation of x1^2, the variances will be different for different observations.

note that

  • rnorm() specifies variability in terms of the standard deviation rather than the variance
  • autocorrelation refers to non-independence between (successive) observations. rnorm() chooses independent deviates, so this specification doesn't constitute an autocorrelated sample.

Upvotes: 1

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