Randomly generate 100 observations (xi, yi) that are independent uniform random variables over [0, 100]. Fit a sequence of successively more complex polynomial models for using x to predict y, of degree 1, 2, 3, …. In principle, even though the true model is E(y) = 50 with population R2 = 0, you should be able to fit a polynomial of degree 99 to the data and achieve R2 = 1. Note that when you get to p ≈ 15, (XTX) is effectively singular and effects of collinearity appear. As p increases, monitor R2, adjusted R2, and the P-value for testing significance of the intercept term. Summarize your results.