Suppose the relationship between y = college GPA and x = high school GPA satisfies yi ∼ N(1.80 + 0.40xi, 0.302). Simulate and construct a scatterplot for n = 1000 independent observations taken from this model when xi has a uniform distribution

(a) over (2.0, 4.0),

(b) over (3.5, 4.0). In each case, find R2. How do R2 and corr(x, y) depend on the range sampled for {xi}? Use the formula for R2 to explain why this happens.