Generate a 5-by-1000 dimensional data matrix X with independent standard random normal variables and set β = (1, 1, 1, 0, 0). For 1000 replications each, construct a response vector y with each of the...

Generate a 5-by-1000 dimensional data matrix X with independent standard random normal variables and set β = (1, 1, 1, 0, 0). For 1000 replications each, construct a response vector y with each of the following random variables: • runif(1000, min = -sqrt(3), max = sqrt(3)) • rnorm(1000, mean = 0, sd = 1) • rcauchy(1000, scale = 1 / 1.4826) The parameters have been chosen so that each has a mean (or median, in the case of the Cauchy) of zero and similar scales. Using these replications, estimate the mean squared error in estimated β with ordinary least squares. The classic theory gives no convergence results regarding Cauchy errors. How well does it perform in practice?