Generate a data matrix X with 100 rows, 10 columns, and values sampled from the continuous uniform distribution. Construct β as a vector with all 0’s. Using a simulation with 1000 replications,...

Generate a data matrix X with 100 rows, 10 columns, and values sampled from the continuous uniform distribution. Construct β as a vector with all 0’s. Using a simulation with 1000 replications, produce various response vectors y by adding Gaussian noise with variance 0.5 to the projected data and record the `2-norm error in prediction of β. How does the average error change if the noise variance is doubled? How about if it is multiplied by 4 or 8? What seems to be the general relationship between σ 2 and the error?