Problem 2 Consider the nonlinear regression model, with n = 100 and data (xi, Yi) provided in "HW10_data.csv" (the same dataset as Problem 1), Yi = m(xi) + ei, 2; (-3,3), i = 1,..., n, and the aim is to split the range of x = (-3,3) into two intervals; the start of a regression tree. That is, we are looking for the estimator m(x) = { m1 x r m2 x > r. (1) (10 pts) Find the optimal choice of r which minimizes the sum of square errors. Show your working and algorithm. (2) (10 pts) What is your result from (1)? State your optimal choice of r and m(x) function. (3) (5 pts) What is the predictive value for the y corresponding to x = : 0.5? (4) (15 pts) Using the non-parametric bootstrap, find an estimator for the variance of m(0.5). Provide all your working. (5) (10 pts) Using the answer to part (4), construct an approximate 95% confidence interval for m(0.5).