Suppose that you run linear regression on some dataset and obtain the coefficients β^OLS. Recall that if X is the data and σ2 is the variance of the IID normal errors, then Var(β^OLS)=σ2(XTX)−1. If you were to run linear regression again on the dataset where you double the values of each point in your original dataset and obtain new coefficients β^OLS′, find the constant c such that Var(β^OLS′)=cVar(β^OLS). If no such constant exists, enter −1.
