Generate X and e to be independent standard normal random vectors of length n. Compute Y = 2 + 3X + σe, where in this problem we take σ = 1. Draw the scatterplot of Y versus X, add the true regression...

Generate X and e to be independent standard normal random vectors of length n. Compute Y = 2 + 3X + σe, where in this problem we take σ = 1. Draw the scatterplot of Y versus X, add the true regression line Y = 2 + 3X, and the ols regression line. Verify that the scatter of points is approximately elliptical, and the regression line is similar to, but not exactly the same as, the major axis of the ellipse.