This question is required to be solved this by R.

Question 2 [3 Points] Consider the situation where we may want to explain each response variable Y C R by a p-dimensional variable X - Unif ([0, 1]"). Suppose our data consists of n i.i.d. observations (Y,, X,) i-1....) of the variables Y and X. We could then model them with the classic regression equation Y = f(X))+6, i=1....n with f : [0, 1] - R and 61. .... , are independent and centered random variables. It is typical to assume that the function f is smooth and we can estimate f(x) by some averaging of the Y, associated to the X, in the vicinity of x. The simplest version of this idea is the k-nearest neighbor estimator where f(x) is estimated by the mean of the Y associated with the k points X, that are nearest to x. This works well in a low-dimensional setting as it is easy to make sense of what "nearest points" means. (a) Show that the notion of nearest points vanishes as the dimensionality p increases by plotting the histogram of the distribution of pairwise-distances { X - Xi| :1