Suppose x is uniformly distributed between 0 and 100, and y is binary with log[????i∕(1 − ????i)] = −2.0 + 0.04xi. Randomly generate n = 25 independent observations from this model. Fit the model, and find corr(y − ????̂ , ????̂). Do the same for n = 100, n = 1000, and n = 10, 000, and summarize how the correlation seems to depend on n.